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the mean,median, mode, their uses and how reliable they can be. the upgrade from variance to standard deviation

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3 descritive statistics measure of central tendency variatio

This document provides an overview of descriptive statistics and properties of numerical data, including measures of central tendency (mean, median, mode), variation (range, variance, standard deviation), and shape (skewness, kurtosis). It explains how to calculate the mean, median, and mode. The mean is the average and is calculated by summing all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the most frequent value. Extreme values affect the mean more than the median.

Lesson 6 measures of central tendency

This document discusses measures of central tendency including the mean, median, and mode. It defines each measure and explains their properties and appropriate uses. The mean is the average value obtained by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequently occurring value. Each measure can be affected differently by outliers, with the median being least affected. The appropriate measure depends on the scale of measurement and distribution of the data.

Measures of central tendency and dispersion

This document discusses various measures of central tendency and dispersion. It defines the mean, median, and mode as measures of central tendency, and describes how to calculate the arithmetic mean, geometric mean, harmonic mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation, and classifies them as either measures of absolute dispersion or relative dispersion.

MEASURESOF CENTRAL TENDENCY

This document discusses measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by summing all values and dividing by the total number of items. The median is the middle value when items are arranged from lowest to highest. The mode is the value that occurs most frequently in a data set. Examples are given to demonstrate calculating each measure using raw data.

Statistical measures

This document defines and provides examples of statistical measures used to describe data, including measures of central tendency (mean, median, mode) and measures of variation (range, variance, standard deviation). It explains that the mean is the average value, the median is the middle number, and the mode is the most frequent value. The best measure of central tendency to use depends on whether the data is spread out or clustered around certain values. Measures of variation describe how spread out the data is, with the range being the difference between highest and lowest values, and the variance and standard deviation measuring differences from the mean. Step-by-step processes are provided for calculating these statistical measures.

3.1 Measures of center

This document provides an overview of measures of central tendency including the mean, median, and mode. It discusses how to calculate and interpret each measure using examples with data sets. The mean is calculated by adding all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently. Other measures discussed include the midrange and calculating the mean from a frequency distribution. Proper rounding of measures is also covered.

Measure of Dispersion

Measures of dispersion describe how spread out or clustered the data is. The range is the difference between the highest and lowest values. Standard deviation measures how far each value deviates from the mean by finding the deviations, squaring them, summing them, dividing by n-1, and taking the square root. It accounts for all data points unlike the range. To calculate standard deviation, first find the mean, then deviations from it, square those values, sum them, and divide the sum by n-1 before taking the square root.

Lect w2 measures_of_location_and_spread

This document discusses measures of central tendency (mean, median, mode) and measures of spread (range, variance, standard deviation). It provides formulas and examples to calculate each measure. It also presents two problems, asking to calculate and compare various descriptive statistics for different data sets, such as milk yields from two cow herds and weaning weights of lambs from two breeds. A third problem asks to analyze and compare price data for rice from two markets.

3 descritive statistics measure of central tendency variatio

This document provides an overview of descriptive statistics and properties of numerical data, including measures of central tendency (mean, median, mode), variation (range, variance, standard deviation), and shape (skewness, kurtosis). It explains how to calculate the mean, median, and mode. The mean is the average and is calculated by summing all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the most frequent value. Extreme values affect the mean more than the median.

Lesson 6 measures of central tendency

This document discusses measures of central tendency including the mean, median, and mode. It defines each measure and explains their properties and appropriate uses. The mean is the average value obtained by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequently occurring value. Each measure can be affected differently by outliers, with the median being least affected. The appropriate measure depends on the scale of measurement and distribution of the data.

Measures of central tendency and dispersion

This document discusses various measures of central tendency and dispersion. It defines the mean, median, and mode as measures of central tendency, and describes how to calculate the arithmetic mean, geometric mean, harmonic mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation, and classifies them as either measures of absolute dispersion or relative dispersion.

MEASURESOF CENTRAL TENDENCY

This document discusses measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by summing all values and dividing by the total number of items. The median is the middle value when items are arranged from lowest to highest. The mode is the value that occurs most frequently in a data set. Examples are given to demonstrate calculating each measure using raw data.

Statistical measures

This document defines and provides examples of statistical measures used to describe data, including measures of central tendency (mean, median, mode) and measures of variation (range, variance, standard deviation). It explains that the mean is the average value, the median is the middle number, and the mode is the most frequent value. The best measure of central tendency to use depends on whether the data is spread out or clustered around certain values. Measures of variation describe how spread out the data is, with the range being the difference between highest and lowest values, and the variance and standard deviation measuring differences from the mean. Step-by-step processes are provided for calculating these statistical measures.

3.1 Measures of center

This document provides an overview of measures of central tendency including the mean, median, and mode. It discusses how to calculate and interpret each measure using examples with data sets. The mean is calculated by adding all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently. Other measures discussed include the midrange and calculating the mean from a frequency distribution. Proper rounding of measures is also covered.

Measure of Dispersion

Measures of dispersion describe how spread out or clustered the data is. The range is the difference between the highest and lowest values. Standard deviation measures how far each value deviates from the mean by finding the deviations, squaring them, summing them, dividing by n-1, and taking the square root. It accounts for all data points unlike the range. To calculate standard deviation, first find the mean, then deviations from it, square those values, sum them, and divide the sum by n-1 before taking the square root.

Lect w2 measures_of_location_and_spread

This document discusses measures of central tendency (mean, median, mode) and measures of spread (range, variance, standard deviation). It provides formulas and examples to calculate each measure. It also presents two problems, asking to calculate and compare various descriptive statistics for different data sets, such as milk yields from two cow herds and weaning weights of lambs from two breeds. A third problem asks to analyze and compare price data for rice from two markets.

Measure of central tendency (Mean, Median and Mode)

This tutorial explain the measure of central tendency (Mean, Median and Mode in detail with suitable working examples pictures. The tutorial also teach the excel commands for calculation of Mean, Median and Mode.

CABT Math 8 measures of central tendency and dispersion

This document provides an introduction to statistics. It discusses what statistics is, the two main branches of statistics (descriptive and inferential), and the different types of data. It then describes several key measures used in statistics, including measures of central tendency (mean, median, mode) and measures of dispersion (range, mean deviation, standard deviation). The mean is the average value, the median is the middle value, and the mode is the most frequent value. The range is the difference between highest and lowest values, the mean deviation is the average distance from the mean, and the standard deviation measures how spread out values are from the mean. Examples are provided to demonstrate how to calculate each measure.

Lesson03_new

This document summarizes various statistical measures used to describe and analyze numerical data, including measures of central tendency (mean, median, mode), measures of variation (range, interquartile range, variance, standard deviation, coefficient of variation), and ways to describe the shape of distributions (symmetric vs. skewed using box-and-whisker plots). It provides definitions and formulas for calculating these common statistical concepts.

Mba i qt unit-2.1_measures of variations

This document discusses various measures of variability or variation used in statistics. It defines variability as the extent to which observations vary from each other or from the average. The key measures discussed are range, interquartile range, average deviation, and standard deviation. Range is the simplest but ignores the distribution within its limits. Interquartile range excludes outliers but also ignores half the data. Average deviation measures average distance from the mean/median and indicates how compact 50% of data is. Examples are provided to demonstrate calculating and comparing these measures.

Statistics

The class consists of 8 classes taught by two instructors. There are 3 take-home assignments due in classes 3, 5, and 7. A final take-home exam is assigned in class 8. The default dataset contains data from 60 subjects across 3-4 groups with different variable types. Students can also bring their own de-identified datasets. Special topics may include microarray analysis, pattern recognition, machine learning, and time series analysis.

Stat3 central tendency & dispersion

This document discusses measures used to describe the central tendency and dispersion of a frequency distribution. It describes the arithmetic mean, median, and mode as measures of central tendency and their advantages and disadvantages. Measures of dispersion discussed include range, variance, standard deviation, coefficient of variation, and standard error. The choice of central tendency measure depends on the distribution shape, and the mean is most useful for statistical tests while the median is unaffected by outliers.

S1 pn

This document discusses measures of central tendency and different methods for calculating averages. It begins by defining central tendency as a single value that represents the characteristics of an entire data set. Three common measures of central tendency are introduced: the mean, median, and mode. The document then focuses on explaining how to calculate the arithmetic mean, or average, including the direct method, shortcut method, and how it applies to discrete and continuous data series. Weighted averages are also covered. In summary, the document provides an overview of key concepts in measures of central tendency and how to calculate various types of averages.

Measure OF Central Tendency

The document discusses various measures of central tendency used in statistics. The three most common measures are the mean, median, and mode. The mean is the sum of all values divided by the number of values and is affected by outliers. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value in a data set. Each measure has advantages and disadvantages depending on the type of data distribution. The mean is the most reliable while the mode can be undefined. In symmetrical distributions, the mean, median and mode are equal, but the mean is higher than the median for positively skewed data and lower for negatively skewed data.

Moments in statistics

This document presents information about moment systems in statistics. It defines moments as a method to summarize descriptive statistical measures, analogous to moments in physics. It discusses different types of moments including moments about the mean, moments about arbitrary points, central moments, and moments about zero. The document provides notation used in moments and formulas to calculate first, second, third, and fourth moments. It includes an example problem calculating moments about an arbitrary point of 120 for a data set on employee earnings.

Measures of Central Tendency

This document discusses various measures of central tendency including arithmetic mean, median, mode, geometric mean, and harmonic mean. It provides definitions and formulas for calculating each measure, along with examples to illustrate how to calculate the median, mode, geometric mean, and harmonic mean. The document is intended as a guide for understanding and calculating different types of averages and measures of central tendency.

Measure of central tendency

This document discusses various measures of central tendency including arithmetic mean, median, mode, and quartiles. It provides definitions and formulas for calculating each measure, and describes how to calculate the mean and median for different types of data distributions including raw data, continuous series, and less than/more than/inclusive series. It also covers weighted mean, combined mean, and properties and limitations of the arithmetic mean.

Measures of Variation or Dispersion

Dr Athar Khan
Associate Professor
Liaquat College of Medicine & Dentistry
Karachi, Pakistan 2019
matharm@yahoo.com

Lesson 7 measures of dispersion part 2

This document provides an introduction and overview of key concepts related to measures of variability and dispersion in statistics. It discusses average absolute deviation, which is the mean of the absolute values of deviations from the data's mean or median. It then covers standard deviation, which is the positive square root of the average of squared deviations from the mean, and is the most widely used measure of dispersion. Formulas and steps for calculating average absolute deviation and standard deviation are provided. An example of calculating standard deviation using a data set of ages is worked through.

Statistics

This document discusses measures of dispersion and the normal distribution. It defines measures of dispersion as ways to quantify the variability in a data set beyond measures of central tendency like mean, median, and mode. The key measures discussed are range, quartile deviation, mean deviation, and standard deviation. It provides formulas and examples for calculating each measure. The document then explains the normal distribution as a theoretical probability distribution important in statistics. It outlines the characteristics of the normal curve and provides examples of using the normal distribution and calculating z-scores.

Measure of dispersion

Mean deviation is a measure of dispersion that calculates the average distance of data points from the central value (usually the mean). It is calculated by taking the absolute value of differences between each data point and the mean, then finding the average of those absolute differences. For a sample of data, the formula is the sum of the absolute values of (x - x-bar) divided by n. Mean deviation indicates how far data points typically are from the central value. It is useful for business applications but can be affected by outliers and does not retain positive and negative signs.

Presentation on "Measure of central tendency"

This presentation introduces measures of central tendency including mean, median, and mode. It provides definitions and formulas for calculating each measure using both ungrouped and grouped data. The mean is the average and is used for less scattered data. It is calculated by summing all values and dividing by the number of values. The median is the middle value when values are arranged in order. For even numbers of values, the median is the average of the two middle values. The mode is the most frequently occurring value in a data set and there can be single or multiple modes. Formulas are provided for calculating the median and mode using grouped frequency data.

Measure of central tendency

Statistics is the study of collecting, analyzing, and interpreting data. It involves determining measures of central tendency like the mean, median, and mode to describe patterns in data. Forensic statistics applies these statistical techniques to scientific evidence used in legal cases. It aims to evaluate likelihoods in an unbiased way using likelihood ratios. Professor Aitken developed Bayesian methods for interpreting forensic evidence and determining optimal sample sizes, helping forensic scientists evaluate uncertainties and provide statistically sound evidence for trials.

3.2 measures of variation

This document discusses measures of variation used to assess how far data points are from the average or mean. It defines key terms like range, variance, and standard deviation. Variance measures the mathematical dispersion of data relative to the mean, while standard deviation gives a value in the original units of measurement, making it easier to interpret. Formulas are provided for calculating sample variance and standard deviation versus population variance and standard deviation. Chebyshev's Theorem is introduced, stating that a certain minimum percentage of data must fall within a specified number of standard deviations of the mean. An example applies these concepts.

G7-quantitative

This document provides an outline and summary of key concepts related to data analysis, including measures of central tendency (mean, median, mode), spread of distribution (range, variance, standard deviation), and experimental designs (paired t-test, ANOVA). It explains how to calculate and interpret the mean, median, mode, range, variance, and standard deviation. It also provides brief definitions and examples of paired t-tests and ANOVA.

Central tendency _dispersion

This document discusses descriptive statistics and summarizing distributions. It covers measures of central tendency including the mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation. These measures are used to describe the characteristics of frequency distributions and determine where the center is located and how spread out the data is. The choice between measures depends on whether the distribution is normal or skewed.

Paul Partlow Highlighted Portfolio

This document contains a portfolio and contact information for Paul Partlow. It includes summaries of over 30 of his illustration and graphic design projects from 2012 to 2014 for schools including Rhode Island School of Design and Suffolk County Community College. The projects cover a wide range of mediums from graphite, ink and digital to found objects. They include personal works as well as assignments covering topics like visual storytelling, conveying personality, and combining cityscapes.

Cold drawn guide rail, Elevator guide Rail India

elevator machined guide rail, Cold drawn guide rail, elevator guide rail manufacturer, Elevator guide Rail India, Elevator guide Rail.

Measure of central tendency (Mean, Median and Mode)

This tutorial explain the measure of central tendency (Mean, Median and Mode in detail with suitable working examples pictures. The tutorial also teach the excel commands for calculation of Mean, Median and Mode.

CABT Math 8 measures of central tendency and dispersion

This document provides an introduction to statistics. It discusses what statistics is, the two main branches of statistics (descriptive and inferential), and the different types of data. It then describes several key measures used in statistics, including measures of central tendency (mean, median, mode) and measures of dispersion (range, mean deviation, standard deviation). The mean is the average value, the median is the middle value, and the mode is the most frequent value. The range is the difference between highest and lowest values, the mean deviation is the average distance from the mean, and the standard deviation measures how spread out values are from the mean. Examples are provided to demonstrate how to calculate each measure.

Lesson03_new

This document summarizes various statistical measures used to describe and analyze numerical data, including measures of central tendency (mean, median, mode), measures of variation (range, interquartile range, variance, standard deviation, coefficient of variation), and ways to describe the shape of distributions (symmetric vs. skewed using box-and-whisker plots). It provides definitions and formulas for calculating these common statistical concepts.

Mba i qt unit-2.1_measures of variations

This document discusses various measures of variability or variation used in statistics. It defines variability as the extent to which observations vary from each other or from the average. The key measures discussed are range, interquartile range, average deviation, and standard deviation. Range is the simplest but ignores the distribution within its limits. Interquartile range excludes outliers but also ignores half the data. Average deviation measures average distance from the mean/median and indicates how compact 50% of data is. Examples are provided to demonstrate calculating and comparing these measures.

Statistics

The class consists of 8 classes taught by two instructors. There are 3 take-home assignments due in classes 3, 5, and 7. A final take-home exam is assigned in class 8. The default dataset contains data from 60 subjects across 3-4 groups with different variable types. Students can also bring their own de-identified datasets. Special topics may include microarray analysis, pattern recognition, machine learning, and time series analysis.

Stat3 central tendency & dispersion

This document discusses measures used to describe the central tendency and dispersion of a frequency distribution. It describes the arithmetic mean, median, and mode as measures of central tendency and their advantages and disadvantages. Measures of dispersion discussed include range, variance, standard deviation, coefficient of variation, and standard error. The choice of central tendency measure depends on the distribution shape, and the mean is most useful for statistical tests while the median is unaffected by outliers.

S1 pn

This document discusses measures of central tendency and different methods for calculating averages. It begins by defining central tendency as a single value that represents the characteristics of an entire data set. Three common measures of central tendency are introduced: the mean, median, and mode. The document then focuses on explaining how to calculate the arithmetic mean, or average, including the direct method, shortcut method, and how it applies to discrete and continuous data series. Weighted averages are also covered. In summary, the document provides an overview of key concepts in measures of central tendency and how to calculate various types of averages.

Measure OF Central Tendency

The document discusses various measures of central tendency used in statistics. The three most common measures are the mean, median, and mode. The mean is the sum of all values divided by the number of values and is affected by outliers. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value in a data set. Each measure has advantages and disadvantages depending on the type of data distribution. The mean is the most reliable while the mode can be undefined. In symmetrical distributions, the mean, median and mode are equal, but the mean is higher than the median for positively skewed data and lower for negatively skewed data.

Moments in statistics

This document presents information about moment systems in statistics. It defines moments as a method to summarize descriptive statistical measures, analogous to moments in physics. It discusses different types of moments including moments about the mean, moments about arbitrary points, central moments, and moments about zero. The document provides notation used in moments and formulas to calculate first, second, third, and fourth moments. It includes an example problem calculating moments about an arbitrary point of 120 for a data set on employee earnings.

Measures of Central Tendency

This document discusses various measures of central tendency including arithmetic mean, median, mode, geometric mean, and harmonic mean. It provides definitions and formulas for calculating each measure, along with examples to illustrate how to calculate the median, mode, geometric mean, and harmonic mean. The document is intended as a guide for understanding and calculating different types of averages and measures of central tendency.

Measure of central tendency

This document discusses various measures of central tendency including arithmetic mean, median, mode, and quartiles. It provides definitions and formulas for calculating each measure, and describes how to calculate the mean and median for different types of data distributions including raw data, continuous series, and less than/more than/inclusive series. It also covers weighted mean, combined mean, and properties and limitations of the arithmetic mean.

Measures of Variation or Dispersion

Dr Athar Khan
Associate Professor
Liaquat College of Medicine & Dentistry
Karachi, Pakistan 2019
matharm@yahoo.com

Lesson 7 measures of dispersion part 2

This document provides an introduction and overview of key concepts related to measures of variability and dispersion in statistics. It discusses average absolute deviation, which is the mean of the absolute values of deviations from the data's mean or median. It then covers standard deviation, which is the positive square root of the average of squared deviations from the mean, and is the most widely used measure of dispersion. Formulas and steps for calculating average absolute deviation and standard deviation are provided. An example of calculating standard deviation using a data set of ages is worked through.

Statistics

This document discusses measures of dispersion and the normal distribution. It defines measures of dispersion as ways to quantify the variability in a data set beyond measures of central tendency like mean, median, and mode. The key measures discussed are range, quartile deviation, mean deviation, and standard deviation. It provides formulas and examples for calculating each measure. The document then explains the normal distribution as a theoretical probability distribution important in statistics. It outlines the characteristics of the normal curve and provides examples of using the normal distribution and calculating z-scores.

Measure of dispersion

Mean deviation is a measure of dispersion that calculates the average distance of data points from the central value (usually the mean). It is calculated by taking the absolute value of differences between each data point and the mean, then finding the average of those absolute differences. For a sample of data, the formula is the sum of the absolute values of (x - x-bar) divided by n. Mean deviation indicates how far data points typically are from the central value. It is useful for business applications but can be affected by outliers and does not retain positive and negative signs.

Presentation on "Measure of central tendency"

This presentation introduces measures of central tendency including mean, median, and mode. It provides definitions and formulas for calculating each measure using both ungrouped and grouped data. The mean is the average and is used for less scattered data. It is calculated by summing all values and dividing by the number of values. The median is the middle value when values are arranged in order. For even numbers of values, the median is the average of the two middle values. The mode is the most frequently occurring value in a data set and there can be single or multiple modes. Formulas are provided for calculating the median and mode using grouped frequency data.

Measure of central tendency

Statistics is the study of collecting, analyzing, and interpreting data. It involves determining measures of central tendency like the mean, median, and mode to describe patterns in data. Forensic statistics applies these statistical techniques to scientific evidence used in legal cases. It aims to evaluate likelihoods in an unbiased way using likelihood ratios. Professor Aitken developed Bayesian methods for interpreting forensic evidence and determining optimal sample sizes, helping forensic scientists evaluate uncertainties and provide statistically sound evidence for trials.

3.2 measures of variation

This document discusses measures of variation used to assess how far data points are from the average or mean. It defines key terms like range, variance, and standard deviation. Variance measures the mathematical dispersion of data relative to the mean, while standard deviation gives a value in the original units of measurement, making it easier to interpret. Formulas are provided for calculating sample variance and standard deviation versus population variance and standard deviation. Chebyshev's Theorem is introduced, stating that a certain minimum percentage of data must fall within a specified number of standard deviations of the mean. An example applies these concepts.

G7-quantitative

This document provides an outline and summary of key concepts related to data analysis, including measures of central tendency (mean, median, mode), spread of distribution (range, variance, standard deviation), and experimental designs (paired t-test, ANOVA). It explains how to calculate and interpret the mean, median, mode, range, variance, and standard deviation. It also provides brief definitions and examples of paired t-tests and ANOVA.

Central tendency _dispersion

This document discusses descriptive statistics and summarizing distributions. It covers measures of central tendency including the mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation. These measures are used to describe the characteristics of frequency distributions and determine where the center is located and how spread out the data is. The choice between measures depends on whether the distribution is normal or skewed.

Measure of central tendency (Mean, Median and Mode)

Measure of central tendency (Mean, Median and Mode)

CABT Math 8 measures of central tendency and dispersion

CABT Math 8 measures of central tendency and dispersion

Lesson03_new

Lesson03_new

Mba i qt unit-2.1_measures of variations

Mba i qt unit-2.1_measures of variations

Statistics

Statistics

Stat3 central tendency & dispersion

Stat3 central tendency & dispersion

S1 pn

S1 pn

Measure OF Central Tendency

Measure OF Central Tendency

Moments in statistics

Moments in statistics

Measures of Central Tendency

Measures of Central Tendency

Measure of central tendency

Measure of central tendency

Measures of Variation or Dispersion

Measures of Variation or Dispersion

Lesson 7 measures of dispersion part 2

Lesson 7 measures of dispersion part 2

Statistics

Statistics

Measure of dispersion

Measure of dispersion

Presentation on "Measure of central tendency"

Presentation on "Measure of central tendency"

Measure of central tendency

Measure of central tendency

3.2 measures of variation

3.2 measures of variation

G7-quantitative

G7-quantitative

Central tendency _dispersion

Central tendency _dispersion

Paul Partlow Highlighted Portfolio

This document contains a portfolio and contact information for Paul Partlow. It includes summaries of over 30 of his illustration and graphic design projects from 2012 to 2014 for schools including Rhode Island School of Design and Suffolk County Community College. The projects cover a wide range of mediums from graphite, ink and digital to found objects. They include personal works as well as assignments covering topics like visual storytelling, conveying personality, and combining cityscapes.

Cold drawn guide rail, Elevator guide Rail India

elevator machined guide rail, Cold drawn guide rail, elevator guide rail manufacturer, Elevator guide Rail India, Elevator guide Rail.

Pattern Matching in Scala

Senior Software Developer and Lead Trainer Alejandro Lujan explains pattern matching, a very powerful and elegant feature of Scala, using a series of examples.
Learn more about this topic and find more presentation on Scala at:

What Are For Expressions in Scala?

In his latest Typesafe tutorial video, Alejandro Lujan explains for expressions in Scala, and provides an example of them in action.
For expressions are a very useful construct that can simplify manipulation of collections and several other data structures. They can be used in place of nested for loops, or to replace calls to map and flatMap in non-collection structures.
Learn more

Partial Functions in Scala

A function can be either total or partial. In this presentation, we explain how we can create and use partial functions from Scala code.

Taste of korea

This document provides a summary of Korean cuisine and traditional Korean dishes. It discusses how Korean food often involves fermentation, which adds beneficial bacteria and nutrients. It also notes that Korean diet may help prevent obesity due to its emphasis on vegetables, soups and stews. Some key Korean dishes summarized are bibimbap (mixed rice bowl), doenjang jjigae (soybean paste stew), yukgaejang (spicy beef soup), and maeuntang (hot spicy fish soup). The document promotes Korean food as a healthy and balanced way of eating.

Value Classes in Scala | BoldRadius

This presentation provides an overview on Value Classes in Scala, which is explained in the video on the last slide by Alejandro Lujan. He explains why you would want to use them, outlines the restrictions that are associated with them, and shows examples of how you would use them. Value classes are a mechanism that Scala provides to create a certain type of wrapper classes that provide memory and performance optimizations. In this video, we show a use case for Tiny Types with Value classes.

String Interpolation in Scala | BoldRadius

Alejandro Lujan introduces us to String Interpolation, a feature of Scala that allows us to have placeholders inside of string definitions, and explains why you would want to use them. Video included!

Functional Programming - Worth the Effort

This presentation explores the benefits of functional programming, especially with respect to reliability. It presents a sample of types that allow many program invariants to be enforced by compilers. We also discuss the industrial adoption of functional programming, and conclude with a live coding demo in Scala.

Curriculum

The curriculum document discusses social studies and focuses on the environment both before and after children wash a car. It examines the environment of the car wash location initially and then analyzes changes to the environment after the children complete the car washing activity. The document appears to use a hands-on car washing project to teach social studies lessons about environments and environmental changes.

Scala: Collections API

Senior Software Developer Alejandro Lujan discusses the collections API in Scala, and provides some insight into what it can do with with some examples.

Test

This very short document contains only two words: "TEST" and "Test". It provides minimal information to summarize in only a sentence or two.

Code Brevity in Scala

In this video, senior software developer Alejandro Lujan explores the elements of Scala's language that allow you to write clean and powerful code in a more brief manner.

Earth moon 1

This document provides information about the sun, earth, and moon through a presentation by Dr. Marjorie Anne Wallace. It asks and answers several questions about these celestial bodies, including what causes day and night, their relative sizes, what percentage of the atmosphere is various gases, tidal patterns, and other details. It explains concepts such as rotation, revolution, phases of the moon, and seasons in 3-5 sentences per topic.

Scala Days Highlights | BoldRadius

Did you miss Scala Days 2015 in San Francisco? Have no fear! BoldRadius was there and we've compiled the best of the best! Here are the highlights of a great conference.

Why Not Make the Transition from Java to Scala?

As a full-time Scala developer, I often find myself talking about Scala and functional programming in different kinds of situations, ranging from meeting a friend working in J2EE, Ruby or C++, to dedicated Scala Meetups aiming to promote deeper understanding of the language. However, something occurred to me lately. By hanging out with people who have some Scala knowledge or experience, I am somewhat holding on to a safe place. By presenting only to people who are curious about Scala, I'm preaching to the converted.
To make a long story short, I recently made an attempt at getting out of my comfort zone by presenting about how making the transition from Java to Scala makes total sense (from Java developer point of view). The presentation went through proof-hearing of approximately 60 experienced Java programmers (with almost no prior Scala knowledge) gathered in one room for a Lunch & Learn. Here are my slides.

Punishment Driven Development #agileinthecity

What is the first thing we do when a major issue occurs in a live system? Sort it out of course. Then we start the hunt for the person to blame so that they can suffer the appropriate punishment. What do we do if a person is being awkward in the team and won’t agree to our ways of doing things? Ostracise them of course, and see how long it is until they hand in their notice – problem solved.
This highly interactive talk delves into why humans have this tendency to blame and punish. It looks at real examples of punishment within the software world and the results which were achieved. These stories not only cover managers punishing team members but also punishment within teams and self-punishment. We are all guilty of some of the behaviours discussed.
This is aimed at everyone involved in software development. It covers:
• Why we tend to blame and punish others.
• The impact of self-blame.
• The unintended (but predictable) results from punishment.
• The alternatives to punishment, which get real results.

Immutability in Scala

This document discusses immutability in Scala. It recommends immutability to avoid unexpected values, concurrent state issues, and most container types are immutable by default. It provides examples of using vals for immutable variables, creating new instances instead of modifying existing ones, using the copy method for case classes, and hiding vars to prevent external modification of mutable state. It cautions being mindful of modifying immutable nested structures, fields initialized each instance, and closing over mutable state.

Paul Partlow Highlighted Portfolio

Paul Partlow Highlighted Portfolio

Cold drawn guide rail, Elevator guide Rail India

Cold drawn guide rail, Elevator guide Rail India

Pattern Matching in Scala

Pattern Matching in Scala

Presentation1

Presentation1

What Are For Expressions in Scala?

What Are For Expressions in Scala?

Partial Functions in Scala

Partial Functions in Scala

Taste of korea

Taste of korea

Pow séminaire "Divine Protection"

Pow séminaire "Divine Protection"

Value Classes in Scala | BoldRadius

Value Classes in Scala | BoldRadius

String Interpolation in Scala | BoldRadius

String Interpolation in Scala | BoldRadius

Functional Programming - Worth the Effort

Functional Programming - Worth the Effort

Curriculum

Curriculum

Scala: Collections API

Scala: Collections API

Test

Test

Code Brevity in Scala

Code Brevity in Scala

Earth moon 1

Earth moon 1

Scala Days Highlights | BoldRadius

Scala Days Highlights | BoldRadius

Why Not Make the Transition from Java to Scala?

Why Not Make the Transition from Java to Scala?

Punishment Driven Development #agileinthecity

Punishment Driven Development #agileinthecity

Immutability in Scala

Immutability in Scala

LESSON-8-ANALYSIS-INTERPRETATION-AND-USE-OF-TEST-DATA.pptx

This document discusses analyzing and interpreting test data using various statistical measures. It describes desired learning outcomes around measures of central tendency, variability, position, and covariability. Key measures are defined, including:
- Mean, median, and mode as measures of central tendency
- Standard deviation as a measure of variability
- Measures of position like percentiles and z-scores
- Covariability measures the relationship between two variables
Examples are provided to demonstrate calculating and interpreting these different statistical measures from test data distributions. The appropriate use of measures depends on the level of measurement (nominal, ordinal, interval, ratio). Measures reveal properties like skewness and help evaluate teaching and learning.

SAMPLING MEANDEFINITIONThe term sampling mean is a stati.docx

The document defines key statistical terms and concepts including:
- Sampling mean is an estimate of the population mean based on a sample. It is calculated by adding all values and dividing by the sample size.
- Sample variance measures the variation or spread of values in a sample. It is calculated by finding the mean of squared differences from the sample mean.
- Standard deviation is the square root of the variance, providing a measure of dispersion from the mean.
- Hypothesis testing uses sample data to determine the validity of claims about a population. The null hypothesis is tested against an alternative using statistical significance.
- Decision trees visually represent decision problems by showing possible choices, outcomes, and probabilities to

SAMPLING MEANDEFINITIONThe term sampling mean is a stati.docx

SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6
So the Mean is 6
SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number of items taken from a population. For example, if you are measuring American people’s weights, it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the weights of every person in the population. The solution is to take a sample of the population, say 1000 people, and use that sample size to estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in the data you have collected or are going to analyze. In statistical terminology, it can be defined as the average of the squared differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
· Determine the mean
· Then for each number: subtract the Mean and square the result
· Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we want.
· Next we need to divide by the number of data points, which is simply done by multiplying by "1/N":
Statistically it can be stated by the following:
·
· This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each bush is
9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
Work out the sample variance
Step 1. Work out the mean
In the formula above, μ (the Greek letter "mu") is the mean of all our values.
For this example, the data points are: 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
The mean is:
(9+2+5+4+12+7+8+11+9+3+7+4+12+5+4+10+9+6+9+4) / 20 = 140/20 = 7
So:
μ = 7
Step 2. Then for each number: subtract the Mean and square the result
This is t.

SAMPLING MEAN DEFINITION The term sampling mean is.docx

The document provides definitions and explanations of statistical concepts including:
- Sampling mean, which is an estimate of the population mean based on a sample.
- Sample variance, which measures the spread or variation of values in a sample from the sample mean.
- Standard deviation, which is the square root of the sample variance and measures how dispersed the values are from the mean.
- Hypothesis testing, which determines the validity of claims about a population by distinguishing rare events that occur by chance from those unlikely to occur by chance.
- Decision trees, which use a tree structure to systematically layout and analyze decisions and their potential consequences.

Measure of Central Tendency

What is mean?
Different types of mean, & their relation.
What is median?
What is mode?
Relation between mean, median, mode.
Usage in Business.

Statistics " Measurements of central location chapter 2"

This is the power point presentation on measurement of central location chapter 2 in Statics field.

Measurement of central tendency

Measurement of central tendencyResearch Scholar - HNB Garhwal Central University, Srinagar, Uttarakhand.

The document discusses measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. For the mean, formulas are given for both raw data and frequency data. The relationships between the mean, median, and mode are explored, including an empirical relationship that can be used to find one value if the other two are known for symmetrical data. The importance of each measure is discussed for different business applications depending on the characteristics of the data.Describing quantitative data with numbers

1. Quantitative data can be summarized using measures of center (mean, median), spread (range, IQR, standard deviation), and position (quartiles, percentiles, z-scores).
2. The mean is more affected by outliers than the median. The median is more resistant to outliers and a better measure of center for skewed data.
3. Additional summaries like the five-number summary and boxplots provide a graphical view of the distribution and identify potential outliers.

Describing Distributions with Numbers

The document discusses various methods for describing data distributions numerically, including measures of center (mean, median), measures of spread (standard deviation, interquartile range), and graphical representations (boxplots). It explains how to calculate and interpret the mean, median, quartiles, five-number summary, standard deviation, and identifies outliers. Choosing an appropriate measure of center and spread depends on the symmetry of the distribution and presence of outliers. Changing the measurement units affects the calculated values but not the underlying shape of the distribution.

5.DATA SUMMERISATION.ppt

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Central Tendency.pptx

Central tendency refers to measures that describe the center or typical value of a dataset. The three main measures of central tendency are the mean, median, and mode.
The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when data is arranged in order. For even datasets, the median is the average of the two middle values. The mode is the value that occurs most frequently in the dataset.

central tendency.pptx

The document discusses different measures of central tendency including the mean, median, and mode. It provides formulas and examples for calculating each measure. The mean is the average value and is calculated by summing all values and dividing by the total number. The median is the middle value when values are arranged in order. The mode is the value that appears most frequently in a data set.

SAMPLING MEAN DEFINITION The term sampling mean .docx

SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical
distributions. In statistical terms, the sample mean from a group of observations is an
estimate of the population mean . Given a sample of size n, consider n independent random
variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these
variables has the distribution of the population, with mean and standard deviation . The
sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that
it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6
So the Mean is 6
SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number
of items taken from a population. For example, if you are measuring American people’s weights,
it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the
weights of every person in the population. The solution is to take a sample of the population, say
1000 people, and use that sample size to estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in the data you have collected or are
going to analyze. In statistical terminology, it can be defined as the average of the squared
differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
• Determine the mean
• Then for each number: subtract the Mean and square the result
• Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we want.
• Next we need to divide by the number of data points, which is simply done by
multiplying by "1/N":
Statistically it can be stated by the following:
•
http://www.statisticshowto.com/find-sample-size-statistics/
http://www.mathsisfun.com/algebra/sigma-notation.html
• This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each bush is
9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4
Work out the sample variance
Step 1. Work out the mean
In the formula above, μ (the Greek letter "mu") is the mean of all our values.
For this example, the data points are: 9, 2, 5, 4, 12, 7, 8,.

Mean

This document discusses the concept and calculation of the mean as a measure of central tendency. It defines the mean as the sum of all values divided by the total number of items. It provides the formula for calculating the mean from both ungrouped and grouped data, using frequency tables. It gives an example of calculating the mean from an ungrouped data set and from a grouped frequency table using midpoints. It also describes a shortcut formula that can be used to calculate the mean from grouped data. Finally, it discusses when the mean is most appropriate to use, noting that it is the most reliable measure when accuracy is needed and when further statistical analysis will be done.

Education Assessment in Learnings 1.pptx

This document discusses analyzing and interpreting test data using measures of central tendency, variability, position, and co-variability. It defines these statistical measures and how to calculate and apply them. Key points covered include calculating the mean, median, and mode of a data set; measures of variability like standard deviation; and how these measures can be used to analyze test scores and interpret results to improve teaching. Formulas and examples are provided to demonstrate calculating and applying these statistical concepts to educational test data.

Measures of Central Tendency, Variability and Shapes

The PPT describes the Measures of Central Tendency in detail such as Mean, Median, Mode, Percentile, Quartile, Arthemetic mean. Measures of Variability: Range, Mean Absolute deviation, Standard Deviation, Z-Score, Variance, Coefficient of Variance as well as Measures of Shape such as kurtosis and skewness in the grouped and normal data.

Topic 2 Measures of Central Tendency.pptx

This document discusses various measures of central tendency used in statistics including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average value found by summing all values and dividing by the total count. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequently occurring value. The document also discusses weighted mean, geometric mean, harmonic mean, and compares the properties of each central tendency measure.

descriptive statistics- 1.pptx

This document discusses descriptive statistics techniques for quantitative data analysis. It defines two main approaches in statistics - descriptive statistics which are used to summarize and organize data, and inferential statistics which are used to make inferences about populations from samples. Descriptive statistics techniques discussed include visual displays, measures of central tendency (mean, median, mode), and measures of variability or dispersion (range, variance, standard deviation). Formulas for calculating various measures are provided along with explanations of their advantages and disadvantages.

Ders 1 mean mod media st dev.pptx

This document discusses computing statistics for single-variable data. It describes six common statistics: three measures of central tendency (mean, median, mode), two measures of spread (variance and standard deviation), and one measure of symmetry (skewness). Formulas are provided for calculating each statistic. Examples are given for computing statistics for both discrete and continuous data sets.

Descriptive statistics

This document discusses measures of central tendency and dispersion used in descriptive statistics. It defines the mode, median, and mean as measures of central tendency and how to calculate each for both raw and grouped data. It also discusses properties of each measure. For measures of dispersion, it defines the range, interquartile range, variance and standard deviation, providing formulas and examples of calculating each for a set of test score data. It concludes with notes on rounding rules and homework questions.

LESSON-8-ANALYSIS-INTERPRETATION-AND-USE-OF-TEST-DATA.pptx

LESSON-8-ANALYSIS-INTERPRETATION-AND-USE-OF-TEST-DATA.pptx

SAMPLING MEANDEFINITIONThe term sampling mean is a stati.docx

SAMPLING MEANDEFINITIONThe term sampling mean is a stati.docx

SAMPLING MEANDEFINITIONThe term sampling mean is a stati.docx

SAMPLING MEANDEFINITIONThe term sampling mean is a stati.docx

SAMPLING MEAN DEFINITION The term sampling mean is.docx

SAMPLING MEAN DEFINITION The term sampling mean is.docx

Measure of Central Tendency

Measure of Central Tendency

Statistics " Measurements of central location chapter 2"

Statistics " Measurements of central location chapter 2"

Measurement of central tendency

Measurement of central tendency

Describing quantitative data with numbers

Describing quantitative data with numbers

Describing Distributions with Numbers

Describing Distributions with Numbers

5.DATA SUMMERISATION.ppt

5.DATA SUMMERISATION.ppt

Central Tendency.pptx

Central Tendency.pptx

central tendency.pptx

central tendency.pptx

SAMPLING MEAN DEFINITION The term sampling mean .docx

SAMPLING MEAN DEFINITION The term sampling mean .docx

Mean

Mean

Education Assessment in Learnings 1.pptx

Education Assessment in Learnings 1.pptx

Measures of Central Tendency, Variability and Shapes

Measures of Central Tendency, Variability and Shapes

Topic 2 Measures of Central Tendency.pptx

Topic 2 Measures of Central Tendency.pptx

descriptive statistics- 1.pptx

descriptive statistics- 1.pptx

Ders 1 mean mod media st dev.pptx

Ders 1 mean mod media st dev.pptx

Descriptive statistics

Descriptive statistics

一比一原版(heriotwatt学位证书)英国赫瑞瓦特大学毕业证如何办理

原版一模一样【微信：741003700 】【(heriotwatt学位证书)英国赫瑞瓦特大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(heriotwatt学位证书)英国赫瑞瓦特大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(heriotwatt学位证书)英国赫瑞瓦特大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(heriotwatt学位证书)英国赫瑞瓦特大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(heriotwatt学位证书)英国赫瑞瓦特大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。

一比一原版(曼大毕业证书)曼尼托巴大学毕业证如何办理

原版一模一样【微信：741003700 】【(曼大毕业证书)曼尼托巴大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(曼大毕业证书)曼尼托巴大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(曼大毕业证书)曼尼托巴大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(曼大毕业证书)曼尼托巴大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(曼大毕业证书)曼尼托巴大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。

Do People Really Know Their Fertility Intentions? Correspondence between Sel...

Fertility intention data from surveys often serve as a crucial component in modeling fertility behaviors. Yet, the persistent gap between stated intentions and actual fertility decisions, coupled with the prevalence of uncertain responses, has cast doubt on the overall utility of intentions and sparked controversies about their nature. In this study, we use survey data from a representative sample of Dutch women. With the help of open-ended questions (OEQs) on fertility and Natural Language Processing (NLP) methods, we are able to conduct an in-depth analysis of fertility narratives. Specifically, we annotate the (expert) perceived fertility intentions of respondents and compare them to their self-reported intentions from the survey. Through this analysis, we aim to reveal the disparities between self-reported intentions and the narratives. Furthermore, by applying neural topic modeling methods, we could uncover which topics and characteristics are more prevalent among respondents who exhibit a significant discrepancy between their stated intentions and their probable future behavior, as reflected in their narratives.

Interview Methods - Marital and Family Therapy and Counselling - Psychology S...

A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!

How To Control IO Usage using Resource Manager

How To Control IO Usage using Resource Manager
In Multitenant and Exadata architecture

[VCOSA] Monthly Report - Cotton & Yarn Statistics May 2024

We are pleased to share with you the latest VCOSA statistical report on the cotton and yarn industry for the month of May 2024.
Starting from January 2024, the full weekly and monthly reports will only be available for free to VCOSA members. To access the complete weekly report with figures, charts, and detailed analysis of the cotton fiber market in the past week, interested parties are kindly requested to contact VCOSA to subscribe to the newsletter.

一比一原版澳洲西澳大学毕业证（uwa毕业证书）如何办理

原版一模一样【微信：741003700 】【澳洲西澳大学毕业证（uwa毕业证书）成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理澳洲西澳大学毕业证（uwa毕业证书）【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理澳洲西澳大学毕业证（uwa毕业证书）【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理澳洲西澳大学毕业证（uwa毕业证书）【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理澳洲西澳大学毕业证（uwa毕业证书）【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。

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06-20-2024-AI Camp Meetup-Unstructured Data and Vector Databases

Tech Talk: Unstructured Data and Vector Databases
Speaker: Tim Spann (Zilliz)
Abstract: In this session, I will discuss the unstructured data and the world of vector databases, we will see how they different from traditional databases. In which cases you need one and in which you probably don’t. I will also go over Similarity Search, where do you get vectors from and an example of a Vector Database Architecture. Wrapping up with an overview of Milvus.
Introduction
Unstructured data, vector databases, traditional databases, similarity search
Vectors
Where, What, How, Why Vectors? We’ll cover a Vector Database Architecture
Introducing Milvus
What drives Milvus' Emergence as the most widely adopted vector database
Hi Unstructured Data Friends!
I hope this video had all the unstructured data processing, AI and Vector Database demo you needed for now. If not, there’s a ton more linked below.
My source code is available here
https://github.com/tspannhw/
Let me know in the comments if you liked what you saw, how I can improve and what should I show next? Thanks, hope to see you soon at a Meetup in Princeton, Philadelphia, New York City or here in the Youtube Matrix.
Get Milvused!
https://milvus.io/
Read my Newsletter every week!
https://github.com/tspannhw/FLiPStackWeekly/blob/main/141-10June2024.md
For more cool Unstructured Data, AI and Vector Database videos check out the Milvus vector database videos here
https://www.youtube.com/@MilvusVectorDatabase/videos
Unstructured Data Meetups -
https://www.meetup.com/unstructured-data-meetup-new-york/
https://lu.ma/calendar/manage/cal-VNT79trvj0jS8S7
https://www.meetup.com/pro/unstructureddata/
https://zilliz.com/community/unstructured-data-meetup
https://zilliz.com/event
Twitter/X: https://x.com/milvusio https://x.com/paasdev
LinkedIn: https://www.linkedin.com/company/zilliz/ https://www.linkedin.com/in/timothyspann/
GitHub: https://github.com/milvus-io/milvus https://github.com/tspannhw
Invitation to join Discord: https://discord.com/invite/FjCMmaJng6
Blogs: https://milvusio.medium.com/ https://www.opensourcevectordb.cloud/ https://medium.com/@tspann
https://www.meetup.com/unstructured-data-meetup-new-york/events/301383476/?slug=unstructured-data-meetup-new-york&eventId=301383476
https://www.aicamp.ai/event/eventdetails/W2024062014

一比一原版斯威本理工大学毕业证（swinburne毕业证）如何办理

原版一模一样【微信：741003700 】【斯威本理工大学毕业证（swinburne毕业证）成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理斯威本理工大学毕业证（swinburne毕业证）【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理斯威本理工大学毕业证（swinburne毕业证）【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理斯威本理工大学毕业证（swinburne毕业证）【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理斯威本理工大学毕业证（swinburne毕业证）【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。

Drownings spike from May to August in children

Did you know that drowning is a leading cause of unintentional death among young children? According to recent data, children aged 1-4 years are at the highest risk. Let's raise awareness and take steps to prevent these tragic incidents. Supervision, barriers around pools, and learning CPR can make a difference. Stay safe this summer!

一比一原版南昆士兰大学毕业证如何办理

原版一模一样【微信：741003700 】【南昆士兰大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理南昆士兰大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理南昆士兰大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理南昆士兰大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理南昆士兰大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。

Sid Sigma educational and problem solving power point- Six Sigma.ppt

Sid Sigma educational and problem solving power point

Discovering Digital Process Twins for What-if Analysis: a Process Mining Appr...

This webinar discusses the limitations of traditional approaches for business process simulation based on had-crafted model with restrictive assumptions. It shows how process mining techniques can be assembled together to discover high-fidelity digital twins of end-to-end processes from event data.

reading_sample_sap_press_operational_data_provisioning_with_sap_bw4hana (1).pdf

Gran libro. Lo recomiendo

PyData London 2024: Mistakes were made (Dr. Rebecca Bilbro)

To honor ten years of PyData London, join Dr. Rebecca Bilbro as she takes us back in time to reflect on a little over ten years working as a data scientist. One of the many renegade PhDs who joined the fledgling field of data science of the 2010's, Rebecca will share lessons learned the hard way, often from watching data science projects go sideways and learning to fix broken things. Through the lens of these canon events, she'll identify some of the anti-patterns and red flags she's learned to steer around.

一比一原版爱尔兰都柏林大学毕业证(本硕）ucd学位证书如何办理

原版一模一样【微信：741003700 】【爱尔兰都柏林大学毕业证(本硕）ucd成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
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◇面对父母的压力，希望尽快拿到；
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◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
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2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理爱尔兰都柏林大学毕业证(本硕）ucd学位证书【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理爱尔兰都柏林大学毕业证(本硕）ucd学位证书【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理爱尔兰都柏林大学毕业证(本硕）ucd学位证书【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理爱尔兰都柏林大学毕业证(本硕）ucd学位证书【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。

Telemetry Solution for Gaming (AWS Summit'24)

Discover the cutting-edge telemetry solution implemented for Alan Wake 2 by Remedy Entertainment in collaboration with AWS. This comprehensive presentation dives into our objectives, detailing how we utilized advanced analytics to drive gameplay improvements and player engagement.
Key highlights include:
Primary Goals: Implementing gameplay and technical telemetry to capture detailed player behavior and game performance data, fostering data-driven decision-making.
Tech Stack: Leveraging AWS services such as EKS for hosting, WAF for security, Karpenter for instance optimization, S3 for data storage, and OpenTelemetry Collector for data collection. EventBridge and Lambda were used for data compression, while Glue ETL and Athena facilitated data transformation and preparation.
Data Utilization: Transforming raw data into actionable insights with technologies like Glue ETL (PySpark scripts), Glue Crawler, and Athena, culminating in detailed visualizations with Tableau.
Achievements: Successfully managing 700 million to 1 billion events per month at a cost-effective rate, with significant savings compared to commercial solutions. This approach has enabled simplified scaling and substantial improvements in game design, reducing player churn through targeted adjustments.
Community Engagement: Enhanced ability to engage with player communities by leveraging precise data insights, despite having a small community management team.
This presentation is an invaluable resource for professionals in game development, data analytics, and cloud computing, offering insights into how telemetry and analytics can revolutionize player experience and game performance optimization.

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- 1. Empirics of Standard Deviation In research, there are the different methods of measuring data to be analyzed. The reason for these is to measure the level of dispersion (Eboh, 2009). Dispersion is the tendency of values of a variable to scatter away from the mean or midpoint. The data are measured majorly with basic statistical tools such as mean, median and mode. To arrive at accurate measurement, the use of standard deviation is employed. Standard deviation is a measurement that is designed to find the disparity between the calculated mean.it is one of the tools for measuring dispersion. To have a good understanding of these, it is of general interest to give a better light to the following terms (mean, median, mode) and variance) also their uses. MEAN Panneerslvam (2008) defined mean as the ratio between the sum of the observations and the number of the observation.in his study, he termed it as arithmetic mean. .Eboh (2009) said it is sum of observations divided by the number of observations. Mathematically, the mean is the arithmetic average of a number of scores. To obtain the mean, add your scores and divide by the number of scores that you have. Simply put that the mean is the addition of all the collated data that are to be analyzed, which is then divided by the number of the data to the analyzed.it is generally stated as /x = ∑ 𝑥𝑖𝑛 𝑖=1 /n Where /x is the arithmetic mean; xi, the ith observation; and n, the total number of observations Example 1.1 determine the arithmetic mean of salaries of the employees s shown in the table 1.1 below Employees no. 1 2 3 4 5 6 7 8 9 Monthly salary N ,000 20 27 34 56 34 45 20 29 41 Solution-----------The number of observations, n =9 Using the above formula, /x = ∑ 𝑥𝑖𝑛 𝑖=1 /n 20000+27000+34000+56000+34000+45000+20000+29000+41000 = N34000 9 It should be noted that before summing them up, they must be in the same units and also in the same scale. This means that there can’t different values that ought to be summated, such as having naira and dollars values that are to be summated, it will be impossible to do so. The summation of these two different scales of measurement won’t be possible. Consider the following data, which represents the time needed to complete a reading task, as an example.
- 2. Example 1.2 Times in miuntes 6 3 5 5 2 7 6 4 3 Total = 43 The mean is the sum of scores divided by the number of scores, mathematically: Mean = ΣX/N = 43/10 = 4.3 PROPERTIES of THE MEAN The mean has certain properties that are attributed to it (Eboh, 2009). They include 1. It has algebraic property that the sum of the deviations of each observation from the mean will always be zero.it means that when the mean observation is subtracted from the mean and summed together (which will comprise of both the positive and negative values), it must result to zero. This is expressed mathematically as thus: ∑ (𝑥𝑖 − 𝑥 )𝑁 𝑖=1 = 0 2. The sum of the squared deviations of each observation from the mean is less than the sum of the squared deviations about any other number ∑ (𝑥𝑖 − 𝑥 )𝑁 𝑖=1 2= minimum This means that the when the various values that were computed together to form the mean are being subtracted, originally when summed up, they will give a zero value. But when squared together after the subtraction from the mean, the result arrived it the minimum value. 3. When mean is commuted from a grouped data which is a special case, midpoints of each assumed that each of the interval classes is being assumed. This is illustrated mathematically as this 𝑋− = ∑ 𝒌 𝒊=𝟏 fi mi = N Where fi = number of cases in the ith category, with f, =N M1 = midpoint of the ith category K = number of categories This is further expressed as finding the idle point of a grouped data that is expected to be analyzed.an example of a grouped data is 1950-2950. Such a grouped data has its midpoint has 2,450.the 2,450 is what will be used for mean analysis. MEDIAN According to R.panneerslvam (2008), the median is the score found at the exact middle of the set of values. It refers to the midpoint in a series of numbers. To find the median the values are arranged in order from smallest to largest. If there is an odd number of values, the middle value is the median. If there is an even number of values, the average of the two middle values is the median.
- 3. Example 1.3: Find the median of 19, 29, 36, 15, and 20 In order: 15, 19, 20, 29, 36 since there are 5 values (odd number), 20 is the median (middle number) Example 1.4: Find the median of 67, 28, 92, 37, 81, 75 In order: 28, 37, 67, 75, 81, 92 since there are 6 values (even number), we must average those two middle numbers to get the median value. Average: 67 + 75 = 142 = 71 is the median value 2 2 MODE The mode of a set of values is the value that occurs most often. A set of values may have more than one mode or no mode. Example 1.5: Find the mode of 15, 21, 26, 25, 21, 23, 28, 21 The mode is 21 since it occurs three times and the other values occur only once. Example 1.6: Find the mode of 12, 15, 18, 26, 15, 9, 12, 27 The modes are 12 and 15 since both occur twice. Example 1.7: Find the mode of 4, 8, 15, 21, 23 There is no mode since all the values occur the same number of times. Since there are 3 different measures of centers, it seems reasonable to ask which is best to use. There are advantages and disadvantages to each of them, depending on the nature of the data set. These are listed below. Measure Advantages Disadvantages Mean Easy to Compute Sample Means tend to Vary Less Good properties as sample size increases (more to come on that later) Sensitive to extreme values (outliers) Median Resistant to outlying values Good for skewed data (see below) Harder to calculate Less useful than the mean for inference (more to come on that later) Mode Easy to compute Good for qualitative (categorical) data Not very useful for quantitative data Skewness Using the mean, median, and mode together can help to describe the skewness of a data set. A data set is considered skewed if the values extend more to one side of the distribution than the other. (Schuetter, 2007)
- 4. VARIANCE The variance ( S2 ) is the average squared deviation from the mean. It is also known as the square of the standard deviation. Both measures are interchangeable. These means that the standard deviation is the square root of the variance. The defining formula is S2 = ∑(x−m)2 N−1 Where: x is each individual score making up the distribution M is the mean of the distribution N is the number of scores. This is illustrated below Example 1.8 calculation of variance Calculation of a variance x x2 x-m, (x-m)2 3 9 -2 4 5 25 0 0 2 4 -3 9 7 49 2 4 9 81 4 16 4 16 -1 1 ∑ 30 184 34 M = 30/6 = 5.0 S2 = 34/5 = 6.8 (Keronanton, 2004) Standard Deviation Though the variance is frequently used as a measure of spread in certain statistical calculations, it does have the disadvantage of being expressed in units different from those of those of the summarized data. Which means the expressed units is going to be far smaller than the data. However the variance can be easily converted into a measure of spread expressed in the same unit of measurement as the original scores: the standard deviation(s). It should be noted that Standard deviation indicate the fluctuation of the variables around their mean. To convert from variance to the standard deviation simply find the square root of the variance. It is the most popular measure of spread. The formula for the standard deviation is given below. 1)-(N N )x( -x =S 2 2
- 5. Example 1.8 calculation of standard deviation Find the standard deviation of example 1.7 √6.8 = 2.61 Example 1.9 Find the standard deviation of the following distributed values Times score 6 3 5 5 2 7 6 4 3 2 Mean score 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 4.3 To get the standard deviation, subtract the mean from each of the scores, square the deviation, and then add up the squared deviations. This process is outlined below. Time Scores Mean Score - mean (Score - mean) 6 4.3 1.7 2.89 3 4.3 -1.3 1.69 5 4.3 0.7 0.49 5 4.3 0.7 0.49 2 4.3 -2.3 5.29 7 4.3 2.7 7.29 6 4.3 1.7 2.89 4 4.3 -0.3 0.09 3 4.3 -1.3 1.69 2 4.3 -2.3 5.29 Total = 28.10 Therefore, the standard deviation becomes: 1.77=3.12= 9 28.10 =S Grouped Data: Often, data will be reported in terms of grouped observation and the calculation of the standard is obtained by a slightly different formula, which is easier to apply in this situation. An example is presented below: Example 1.10 Ages f 51 - 60 3 41 - 50 10 31 - 40 15
- 6. 21 - 30 11 11 - 20 5 To calculate the mean and standard deviation of a grouped data, you must determine the midpoint for each of the groups of observations. (Panneerselvam, 2008) Adding the upper and lower scores for each interval and dividing by two can obtain the midpoints. For example, for the first group of data the midpoint would be (51 + 60)/2 = 111/2 = 55.5. I have redrawn the data below with the midpoints inserted. Also, I have included in the redrawn data a column headed by the term fxMidpoint, which is simply the midpoint multiplied by the frequency Ages f Midpoints fxMidpoint 51 - 60 3 55.5 166.5 41 - 50 10 45.5 455.0 31 - 40 15 35.5 532.5 21 - 30 11 25.5 280.5 11 - 20 5 15.5 77.5 Total = 1512.0 The mean becomes the sum of the scores in the fxMidpoint column divided by the sample size. The sample size can be determined by adding the f column (N = 44). Therefore, the mean = 1512.0/44 = 34.36 (rounded to 34.4).To determine the standard deviation there is a need to add one additional column to the table of calculations above. This additional column is fxmidpoint2 and I have redrawn our table below with the added column. Ages f Midpoints fxMidpoint fxMidpoint2 51 - 60 3 55.5 166.5 9240.75 41 - 50 10 45.5 455.0 20702.50 31 - 40 15 35.5 532.5 18903.75 21 - 30 11 25.5 280.5 7152.75 11.04=121.93= 43 51957.82-57201 = 43 44 01512. -57201.0 =S 2
- 7. Chapter Exercises 1. A magazine is interested in expanding its readership to "yuppies," defined as people between the ages of 30 to 40. Following are the ages of a random selection of the magazine's readership, is there any reason to be concerned? Draw the theoretical distribution and contrast the actual score distribution with the theoretical distribution. Is the sample adequate? 23, 31, 29, 21, 25, 27, 25, 21, 29, 30, 35, 41, 23, 35, 19, 20, 26, 24, 26, 25, 28, 27, 51, 15, 28, 21, 23, 25 2. A more extensive examination of the readership was undertaken after the initiation of a one-year advertising program, designed to increase the readership age range. Following are the data collected from this more extensive study. Draw the theoretical distribution of the ages of the readers. What do you conclude? Is the sample adequate? Ages Frequency 20 - 24 26 25 - 29 45 30 - 34 87 35 - 39 30 40 - 44 8 45 - 49 4 References Eboh, E. (2009). Social and economic Research Principles and Method. Enugu: African institute for applied method. Keronanton, A. (2004). Statistics: Median, Mode and Frequency Distribution. In A. Keronanton. Dublin: Dublin Institution of Technology. Obadan, M. I. (2012). research porcess,report writing and referencing. Ugbowo,Benin City,Nigeria: Goldmark Press Limited. Panneerselvam, R. (2008). Research Method. New delhi: Prentice hall of india limited. Schuetter, J. (2007). Chapter 1. In J. Schuetter, measures of dispersation (pp. 45-54). Walonick, D. S. (1993). The Reseach Process. minneapolis.