This document provides an overview of various statistical measures and methods of analysis. It discusses measures of central tendency including mean, median, and mode. It also covers measures of variability such as range, standard deviation, and correlation. Statistical analysis helps teachers summarize and compare student performance. The steps involved are collecting and organizing data, selecting an appropriate statistical technique, applying the method of analysis, and interpreting the results. Various graphical representations of data are also presented such as histograms, frequency polygons, and ogives.
The document outlines chapters from a statistics textbook, covering topics such as describing and exploring data through frequency tables, histograms, measures of central tendency, dispersion, correlation, and time series analysis. It also discusses deseasonalizing time series data to study trends and uses an example of predicting quarterly sales figures after removing seasonal fluctuations. The later chapters focus on time series forecasting through techniques like determining a seasonal index and forming a least squares regression line to predict future values.
This document provides information about a Business Statistics course including objectives, policies, assessment details, topics, assignments, and formulas. The course aims to teach students how and when to apply statistical techniques to decision making. It will have 57 lectures, 2 class tests, 2 hourly tests, and 3 assignments. Students will be graded based on a mid-semester exam, presentation, tests, assignments collected throughout the course. Topics include data collection, frequency distributions, measures of central tendency, and measures of dispersion. Formulas covered include arithmetic mean, median, mode, standard deviation, and correlation.
This document provides information about a Business Statistics course including objectives, policies, assessment details, topics, assignments, and formulas. The course aims to teach students how and when to apply statistical techniques to decision making. It will have 57 lectures, 2 class tests, 2 hourly tests, and 3 assignments. Internal assessment will be based on a mid-semester exam, presentation, tests, assignments. Topics will cover data collection, distributions, central tendency measures, dispersion measures, and correlation. Students will complete activities collecting and analyzing preference data, and presenting organizational sales and production data. Formulas taught will include measures of central tendency, dispersion, correlation, and error.
This document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, and standard deviation. It provides definitions and formulas for calculating each measure, as well as examples of calculating the measures for both ungrouped and grouped quantitative data. The key measures discussed are the range, which is the difference between the maximum and minimum values; quartile deviation, which is the difference between the third and first quartiles; mean deviation, which is the mean of the absolute deviations from the mean; and standard deviation, which is the square root of the mean of the squared deviations from the arithmetic mean.
This document discusses various statistical measures of dispersion and variation in data, including range, interquartile range, mean deviation, and standard deviation. It provides formulas and examples for calculating each measure. The range is defined as the difference between the highest and lowest values. The interquartile range is the difference between the first and third quartiles. Mean deviation measures the average distance from the mean. Standard deviation uses the differences from the mean to calculate the average deviation and is the most common measure of variation.
This document provides an overview of various statistical measures and methods of analysis. It discusses measures of central tendency including mean, median, and mode. It also covers measures of variability such as range, standard deviation, and correlation. Statistical analysis helps teachers summarize and compare student performance. The steps involved are collecting and organizing data, selecting an appropriate statistical technique, applying the method of analysis, and interpreting the results. Various graphical representations of data are also presented such as histograms, frequency polygons, and ogives.
The document outlines chapters from a statistics textbook, covering topics such as describing and exploring data through frequency tables, histograms, measures of central tendency, dispersion, correlation, and time series analysis. It also discusses deseasonalizing time series data to study trends and uses an example of predicting quarterly sales figures after removing seasonal fluctuations. The later chapters focus on time series forecasting through techniques like determining a seasonal index and forming a least squares regression line to predict future values.
This document provides information about a Business Statistics course including objectives, policies, assessment details, topics, assignments, and formulas. The course aims to teach students how and when to apply statistical techniques to decision making. It will have 57 lectures, 2 class tests, 2 hourly tests, and 3 assignments. Students will be graded based on a mid-semester exam, presentation, tests, assignments collected throughout the course. Topics include data collection, frequency distributions, measures of central tendency, and measures of dispersion. Formulas covered include arithmetic mean, median, mode, standard deviation, and correlation.
This document provides information about a Business Statistics course including objectives, policies, assessment details, topics, assignments, and formulas. The course aims to teach students how and when to apply statistical techniques to decision making. It will have 57 lectures, 2 class tests, 2 hourly tests, and 3 assignments. Internal assessment will be based on a mid-semester exam, presentation, tests, assignments. Topics will cover data collection, distributions, central tendency measures, dispersion measures, and correlation. Students will complete activities collecting and analyzing preference data, and presenting organizational sales and production data. Formulas taught will include measures of central tendency, dispersion, correlation, and error.
This document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, and standard deviation. It provides definitions and formulas for calculating each measure, as well as examples of calculating the measures for both ungrouped and grouped quantitative data. The key measures discussed are the range, which is the difference between the maximum and minimum values; quartile deviation, which is the difference between the third and first quartiles; mean deviation, which is the mean of the absolute deviations from the mean; and standard deviation, which is the square root of the mean of the squared deviations from the arithmetic mean.
This document discusses various statistical measures of dispersion and variation in data, including range, interquartile range, mean deviation, and standard deviation. It provides formulas and examples for calculating each measure. The range is defined as the difference between the highest and lowest values. The interquartile range is the difference between the first and third quartiles. Mean deviation measures the average distance from the mean. Standard deviation uses the differences from the mean to calculate the average deviation and is the most common measure of variation.
ch-4-measures-of-variability-11 2.ppt for nursingwindri3
This document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.
This document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.
This document discusses dimensionality reduction techniques for machine learning. It introduces Fisher Linear Discriminant analysis, which seeks projection directions that maximize separation between classes while minimizing within-class variance. It describes using the means and scatter measures of each class to define a cost function that is maximized to find the optimal projection direction. Principal Component Analysis is also briefly mentioned as another technique for dimensionality reduction.
This document discusses measures of dispersion, specifically standard deviation and quartile deviation. It defines standard deviation as a measure of how closely values are clustered around the mean. Standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. Quartile deviation is defined as half the difference between the third quartile (Q3) and first quartile (Q1), which divide a data set into four equal parts. The document provides examples of calculating standard deviation and quartile deviation for both individual and grouped data sets. It also discusses the merits, demerits, and uses of these statistical measures.
1. The document discusses various measures of dispersion used to quantify how spread out or variable a data set is. It describes measures such as range, mean deviation, variance, and standard deviation.
2. It also discusses relative measures of dispersion like the coefficient of variation, which allows comparison of variability between data sets with different units or averages. The coefficient of variation expresses variability as a percentage of the mean.
3. Additional concepts covered include skewness, which refers to the asymmetry of a distribution, and kurtosis, which measures the peakedness of a distribution compared to a normal distribution. Positive or negative skewness and leptokurtic, mesokurtic, or platykurtic k
3Measurements of health and disease_MCTD.pdfAmanuelDina
The document discusses measures of central tendency and dispersion (MCTD) that are used to summarize data. It defines and provides examples of calculating the mean, median, mode, range, variance, standard deviation, interquartile range, and coefficient of variation. Examples are provided to illustrate how to compute these MCTD and interpret them to understand the concentration and variability of data from a sample population. Guidance is given on choosing the appropriate measure of central tendency or dispersion depending on the characteristics of the data set.
The document presents information on statistical methods and quality budgeting procedures. It discusses the five steps of quality - say what you do, do what you say, record what you do, review what you do, and restart the process. The budget is divided according to these steps, first describing measures of central tendency like mean, median and mode. It then covers measuring dispersion through tools like range, variance and standard deviation. The document reviews the processes and asks if quality is achieved or not.
The document defines common statistical terms used to describe data distributions, including measures of central tendency (mean, median, mode), measures of variability (range, average deviation, variance, standard deviation), and how to construct a frequency distribution table from raw data by grouping values into classes and calculating frequencies. Key steps covered are determining the number of classes, class boundaries, frequencies, and how to find the mean, median, mode from the frequency distribution table.
The document defines common statistical terms used to describe data distributions, including measures of central tendency (mean, median, mode), measures of variability (range, average deviation, variance, standard deviation), and how to construct a frequency distribution table from raw data by grouping values into classes and calculating frequencies. Key steps covered are determining the number of classes, class boundaries, frequencies, and how to find the mean, median, mode from the frequency distribution table.
This chapter discusses measures of central tendency, dispersion, and position. It defines statistics, parameters, population and sample means, medians, modes, and weighted means. It discusses estimating means and medians for grouped data using class midpoints and boundaries. Examples are provided to demonstrate calculating measures for raw data and frequency distributions. Measures of variability like range, mean deviation, variance, and standard deviation are also introduced.
Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari
This document discusses measures of dispersion used in statistics. It defines measures such as range, quartile deviation, mean deviation, variance, and standard deviation. It provides formulas to calculate these measures and examples showing how to apply the formulas. The key points are:
- Measures of dispersion quantify how spread out or varied the values in a data set are. They help identify variation, compare data sets, and enable other statistical techniques.
- Common absolute measures include range, quartile deviation, and mean deviation. Common relative measures include coefficient of range, coefficient of quartile deviation, and coefficient of variation.
- Variance and standard deviation are calculated using all data points. Variance is the average of squared deviations
The document discusses various measures used to describe the dispersion or variability in a data set. It defines dispersion as the extent to which values in a distribution differ from the average. Several measures of dispersion are described, including range, interquartile range, mean deviation, and standard deviation. The document also discusses measures of relative standing like percentiles and quartiles, and how they can locate the position of observations within a data set. The learning objectives are to understand how to describe variability, compare distributions, describe relative standing, and understand the shape of distributions using these measures.
The document discusses statistical concepts including Gaussian distributions, standard deviation, confidence intervals, t-tests, and calibration curves. It provides examples of how to calculate the mean, standard deviation, confidence intervals using t-tables, and how to perform t-tests to compare two data sets. It also describes constructing a calibration curve using the method of least squares to determine the best-fit line and using that line to find the concentration of an unknown sample.
1. The document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, standard deviation, coefficient of variation, and coefficient of quartile deviation.
2. It provides definitions and formulas for calculating each measure. For example, it states that range is defined as the difference between the maximum and minimum values, while standard deviation is the square root of the average of the squared deviations from the mean.
3. The document also compares absolute and relative measures of dispersion. Absolute measures use numerical variations to determine error, while relative measures express dispersion as a proportion of the mean or other measure of central tendency.
Clustering algorithms are used to group similar data points together. K-means clustering aims to partition data into k clusters by minimizing distances between data points and cluster centers. Hierarchical clustering builds nested clusters by merging or splitting clusters based on distance metrics. Density-based clustering identifies clusters as areas of high density separated by areas of low density, like DBScan which uses parameters of minimum points and epsilon distance.
Different analytical techniques in managementSohel Rana
This document discusses different analytical techniques used in management, including frequency distribution, measures of central tendency, measures of dispersion, and correlation and regression analysis. It provides an example using real data from an English course given to employees. The data is analyzed to calculate the mean, median, mode, range, mean deviation, variance, standard deviation, and a correlation coefficient and regression equation are determined from a separate age and salary data set. The analysis demonstrates various statistical techniques for summarizing and analyzing data sets.
The document discusses variability and measures of variability. It defines variability as a quantitative measure of how spread out or clustered scores are in a distribution. The standard deviation is introduced as the most commonly used measure of variability, as it takes into account all scores in the distribution and provides the average distance of scores from the mean. Properties of the standard deviation are examined, such as how it does not change when a constant is added to all scores but does change when all scores are multiplied by a constant.
This document summarizes chapter 3 section 2 of an elementary statistics textbook. It discusses measures of variation, including range, variance, and standard deviation. The standard deviation describes how spread out data values are from the mean and is used to determine consistency and predictability within a specified interval. Several examples demonstrate calculating range, variance, and standard deviation for data sets. Chebyshev's theorem and the empirical rule relate standard deviations to the percentage of values that fall within certain intervals of the mean.
The document discusses various measures of central tendency and variability used in descriptive statistics. It defines the mean as the sum of all values divided by the number of values. The median is the middle value when values are sorted in ascending order. The mode is the most frequently occurring value. Variability measures the dispersion of scores around the mean and includes the range, interquartile range, standard deviation, and variance. The interquartile range is the difference between the third and first quartiles. Covariance measures how two variables vary together and is used to calculate the correlation coefficient. Factors like extreme scores, sample size, stability under sampling, and open-ended distributions can affect measures of variability.
The document provides an overview of topics to be covered in Chapter 16 on time series and forecasting, including using trend equations to forecast future periods and develop seasonally adjusted forecasts, determining and interpreting seasonal indexes, and deseasonalizing data using a seasonal index. It also includes examples of calculating seasonal indices and adjusting sales data to remove seasonal variation. The document is a lecture outline and review for a class on international business taught by Dr. Ning Ding at Hanze University of Applied Sciences Groningen.
ch-4-measures-of-variability-11 2.ppt for nursingwindri3
This document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.
This document discusses measures of variability used in statistics. It defines variability as the spread or dispersion of scores. The key measures of variability discussed are the range, variance, and standard deviation. The range is the difference between the highest and lowest scores. The variance is the average of the squared deviations from the mean and represents how far the scores deviate from the mean. The standard deviation is the square root of the variance and represents how much scores typically deviate from the mean. Larger standard deviations indicate greater variability in the scores.
This document discusses dimensionality reduction techniques for machine learning. It introduces Fisher Linear Discriminant analysis, which seeks projection directions that maximize separation between classes while minimizing within-class variance. It describes using the means and scatter measures of each class to define a cost function that is maximized to find the optimal projection direction. Principal Component Analysis is also briefly mentioned as another technique for dimensionality reduction.
This document discusses measures of dispersion, specifically standard deviation and quartile deviation. It defines standard deviation as a measure of how closely values are clustered around the mean. Standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. Quartile deviation is defined as half the difference between the third quartile (Q3) and first quartile (Q1), which divide a data set into four equal parts. The document provides examples of calculating standard deviation and quartile deviation for both individual and grouped data sets. It also discusses the merits, demerits, and uses of these statistical measures.
1. The document discusses various measures of dispersion used to quantify how spread out or variable a data set is. It describes measures such as range, mean deviation, variance, and standard deviation.
2. It also discusses relative measures of dispersion like the coefficient of variation, which allows comparison of variability between data sets with different units or averages. The coefficient of variation expresses variability as a percentage of the mean.
3. Additional concepts covered include skewness, which refers to the asymmetry of a distribution, and kurtosis, which measures the peakedness of a distribution compared to a normal distribution. Positive or negative skewness and leptokurtic, mesokurtic, or platykurtic k
3Measurements of health and disease_MCTD.pdfAmanuelDina
The document discusses measures of central tendency and dispersion (MCTD) that are used to summarize data. It defines and provides examples of calculating the mean, median, mode, range, variance, standard deviation, interquartile range, and coefficient of variation. Examples are provided to illustrate how to compute these MCTD and interpret them to understand the concentration and variability of data from a sample population. Guidance is given on choosing the appropriate measure of central tendency or dispersion depending on the characteristics of the data set.
The document presents information on statistical methods and quality budgeting procedures. It discusses the five steps of quality - say what you do, do what you say, record what you do, review what you do, and restart the process. The budget is divided according to these steps, first describing measures of central tendency like mean, median and mode. It then covers measuring dispersion through tools like range, variance and standard deviation. The document reviews the processes and asks if quality is achieved or not.
The document defines common statistical terms used to describe data distributions, including measures of central tendency (mean, median, mode), measures of variability (range, average deviation, variance, standard deviation), and how to construct a frequency distribution table from raw data by grouping values into classes and calculating frequencies. Key steps covered are determining the number of classes, class boundaries, frequencies, and how to find the mean, median, mode from the frequency distribution table.
The document defines common statistical terms used to describe data distributions, including measures of central tendency (mean, median, mode), measures of variability (range, average deviation, variance, standard deviation), and how to construct a frequency distribution table from raw data by grouping values into classes and calculating frequencies. Key steps covered are determining the number of classes, class boundaries, frequencies, and how to find the mean, median, mode from the frequency distribution table.
This chapter discusses measures of central tendency, dispersion, and position. It defines statistics, parameters, population and sample means, medians, modes, and weighted means. It discusses estimating means and medians for grouped data using class midpoints and boundaries. Examples are provided to demonstrate calculating measures for raw data and frequency distributions. Measures of variability like range, mean deviation, variance, and standard deviation are also introduced.
Measure of dispersion by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari
This document discusses measures of dispersion used in statistics. It defines measures such as range, quartile deviation, mean deviation, variance, and standard deviation. It provides formulas to calculate these measures and examples showing how to apply the formulas. The key points are:
- Measures of dispersion quantify how spread out or varied the values in a data set are. They help identify variation, compare data sets, and enable other statistical techniques.
- Common absolute measures include range, quartile deviation, and mean deviation. Common relative measures include coefficient of range, coefficient of quartile deviation, and coefficient of variation.
- Variance and standard deviation are calculated using all data points. Variance is the average of squared deviations
The document discusses various measures used to describe the dispersion or variability in a data set. It defines dispersion as the extent to which values in a distribution differ from the average. Several measures of dispersion are described, including range, interquartile range, mean deviation, and standard deviation. The document also discusses measures of relative standing like percentiles and quartiles, and how they can locate the position of observations within a data set. The learning objectives are to understand how to describe variability, compare distributions, describe relative standing, and understand the shape of distributions using these measures.
The document discusses statistical concepts including Gaussian distributions, standard deviation, confidence intervals, t-tests, and calibration curves. It provides examples of how to calculate the mean, standard deviation, confidence intervals using t-tables, and how to perform t-tests to compare two data sets. It also describes constructing a calibration curve using the method of least squares to determine the best-fit line and using that line to find the concentration of an unknown sample.
1. The document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, standard deviation, coefficient of variation, and coefficient of quartile deviation.
2. It provides definitions and formulas for calculating each measure. For example, it states that range is defined as the difference between the maximum and minimum values, while standard deviation is the square root of the average of the squared deviations from the mean.
3. The document also compares absolute and relative measures of dispersion. Absolute measures use numerical variations to determine error, while relative measures express dispersion as a proportion of the mean or other measure of central tendency.
Clustering algorithms are used to group similar data points together. K-means clustering aims to partition data into k clusters by minimizing distances between data points and cluster centers. Hierarchical clustering builds nested clusters by merging or splitting clusters based on distance metrics. Density-based clustering identifies clusters as areas of high density separated by areas of low density, like DBScan which uses parameters of minimum points and epsilon distance.
Different analytical techniques in managementSohel Rana
This document discusses different analytical techniques used in management, including frequency distribution, measures of central tendency, measures of dispersion, and correlation and regression analysis. It provides an example using real data from an English course given to employees. The data is analyzed to calculate the mean, median, mode, range, mean deviation, variance, standard deviation, and a correlation coefficient and regression equation are determined from a separate age and salary data set. The analysis demonstrates various statistical techniques for summarizing and analyzing data sets.
The document discusses variability and measures of variability. It defines variability as a quantitative measure of how spread out or clustered scores are in a distribution. The standard deviation is introduced as the most commonly used measure of variability, as it takes into account all scores in the distribution and provides the average distance of scores from the mean. Properties of the standard deviation are examined, such as how it does not change when a constant is added to all scores but does change when all scores are multiplied by a constant.
This document summarizes chapter 3 section 2 of an elementary statistics textbook. It discusses measures of variation, including range, variance, and standard deviation. The standard deviation describes how spread out data values are from the mean and is used to determine consistency and predictability within a specified interval. Several examples demonstrate calculating range, variance, and standard deviation for data sets. Chebyshev's theorem and the empirical rule relate standard deviations to the percentage of values that fall within certain intervals of the mean.
The document discusses various measures of central tendency and variability used in descriptive statistics. It defines the mean as the sum of all values divided by the number of values. The median is the middle value when values are sorted in ascending order. The mode is the most frequently occurring value. Variability measures the dispersion of scores around the mean and includes the range, interquartile range, standard deviation, and variance. The interquartile range is the difference between the third and first quartiles. Covariance measures how two variables vary together and is used to calculate the correlation coefficient. Factors like extreme scores, sample size, stability under sampling, and open-ended distributions can affect measures of variability.
The document provides an overview of topics to be covered in Chapter 16 on time series and forecasting, including using trend equations to forecast future periods and develop seasonally adjusted forecasts, determining and interpreting seasonal indexes, and deseasonalizing data using a seasonal index. It also includes examples of calculating seasonal indices and adjusting sales data to remove seasonal variation. The document is a lecture outline and review for a class on international business taught by Dr. Ning Ding at Hanze University of Applied Sciences Groningen.
Here are the steps to solve this problem:
1) Code the year as t = 1 for 1999, t = 2 for 2000, etc.
2) Calculate the sums: Σt = 15, ΣY = 211.9, Σt2 = 30, ΣtY = 332.5
3) b = (ΣtY - ΣtΣY/n) / (Σt2 - Σt2/n) = 6.55
4) a = Y - bX = 29.4 - 6.55(1) = 22.85
5) Ŷ = 22.85 + 6.55t
To estimate vending sales
This document provides an overview of simple linear regression and correlation. It discusses key concepts such as dependent and independent variables, scatter diagrams, regression analysis, the least-squares estimating equation, and the coefficients of determination and correlation. Scatter diagrams are used to determine the nature and strength of relationships between variables. Regression analysis finds relationships of association but not necessarily of cause and effect. The least-squares estimating equation models the dependent variable as a function of the independent variable.
This document provides an overview of central tendency measures that will be covered in Chapter 3-A, including the mean, mode, and median for both ungrouped and grouped data. It also includes examples of calculating the mean, weighted mean, and mode. The document reviews key concepts such as the difference between parameters and statistics. Overall, the document previews and reviews important concepts related to measures of central tendency that will be covered in the upcoming chapter.
Lesson 06 chapter 9 two samples test and Chapter 11 chi square testNing Ding
This document is a PowerPoint presentation about hypothesis testing for two samples and chi-square tests. It covers topics like independent and dependent sample tests, testing differences between proportions, one-tailed and two-tailed tests. Examples are provided to demonstrate how to perform two-sample t-tests, tests of proportions, and chi-square tests using contingency tables with 2 rows and 3 rows. Step-by-step instructions and formulas are given. Key chapters from the textbook are reviewed.
This document provides an outline and overview of topics covered in a course on inductive statistics, including probability distributions, sampling distributions, estimation, and hypothesis testing. Key topics discussed include interval estimation for means and proportions, using t-distributions when sample sizes are small and variances are unknown, and the basics of hypothesis testing such as null and alternative hypotheses. Examples are provided to illustrate concepts like confidence intervals for means, proportions, and hypothesis testing.
This document contains a PowerPoint presentation on inductive statistics covering topics like probability distributions, sampling distributions, estimation, hypothesis testing for means and proportions, and two-sample hypothesis tests. It provides an overview of the chapters that will be covered, examples of hypothesis tests for means and proportions when the population standard deviation is known and unknown, and examples of independent and dependent two-sample hypothesis tests for differences in means and proportions with both large and small sample sizes. Step-by-step explanations are given for conducting hypothesis tests.
The document summarizes key concepts from chapters 6 and 7 of a statistics textbook. Chapter 6 discusses sampling and calculating standard error for infinite and finite populations. Chapter 7 introduces estimation, including interval estimates and point estimates. It provides examples of calculating standard error and confidence intervals. The document also lists SPSS tips for t-tests.
This document provides an overview and summary of topics covered in a research methods course. It discusses reviewing concepts from prior lectures, including different types of research and variables. Today's lecture will cover instrumentation, validity and reliability, and threats to internal validity. Instrumentation discusses how to collect and measure data. Validity and reliability refer to the accuracy and consistency of measurements. Threats to internal validity could interfere with determining the true effect of independent variables on dependent variables.
This document provides an overview of content covered in Statistics 2, including a review of chapter 5 on sampling distributions. It includes examples of questions from quizzes on topics like the normal distribution and binomial approximation. The document also provides tips on using SPSS for descriptive statistics, such as inputting and defining variable data, and analyzing frequencies.
This document summarizes a course on research methods and techniques. It outlines the structure and requirements of the course, including reading a textbook and attending lectures. It discusses different types of research and variables. The document covers defining research problems, formulating hypotheses, research ethics, and instrumentation. Self-check exercises are provided to help students understand key concepts.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
Lesson 3
1. Hanze University of
Applied Science
Groningen
Ning Ding, PhD
Lecturer of International Business
School (IBS)
n.ding@pl.hanze.nl
2. What we are going to learn?
• Review
• Chapter 3: Dispersion
• Range
• Variance (SD2)
• Standard Deviation (SD)
• Coefficient of variation (CV)
• Chapter 4: Displaying and exploring data
• Dotplot
• Stem-leaf
• Boxplot
• Skewness
3. Review
a b
Review
Chapter 3:
Discrete counting Continuous measuring
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and 1.Age 5. Salary
exploring data
–Dotplot
–Stem-leaf
2.Sales volume 6. Class size
–Boxplot
–Skewness 3. Temperature 7. Height
4. Weight 8. Shoe size (NL)
4. Review
Constructing Frequency Distribution: Quantitative Data
a. 4 b.5 c.6 d.70
25 = 32, 26 = 64, suggests 6 classes
Use interval of 100
a. 80 b.100 c.120 d.150
i> 571- 41 = 88.33
6
P46. N.30 Ch.2
6. Central Tendency : Mean, Mode, Median
Mean: Average
SCCoast, an Internet provider in the Southeast, developed the
following frequency distribution on the age of Internet users.
Describe the central tendency:
X = 2410 / 60 = 40.17 (years)
P87 N.60 Ch.3
7. Review
Central Tendency : Mean, Mode, Median
Mean: Average Mode: Most Frequency
SCCoast, an Internet provider in the Southeast, developed the
following frequency distribution on the age of Internet users.
Describe the central tendency:
Mode = 45 (years)
P87 N.60 Ch.3
8. Review
Central Tendency : Mean, Mode, Median
Mean: Average Mode: Most Frequency Median: Midpoint
SCCoast, an Internet provider in the Southeast, developed the
following frequency distribution on the age of Internet users.
Describe the central tendency:
a.40.25
b.41.25
c.30.50
d.37.50
Median = ? (years)
P87 N.60 Ch.3
9. Review
Step 1: Define the location of the median Step 2: Calculate the median
M
Lm=(60+1)/2=30.5 Value:40 50
Location: 28 48
30.5
30.5-28 M-40
=
48-28 50-40
Median= 41.25
P87 N.60 Ch.3
10. Dispersion
Review
Range
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
Variance (SD2) and Standard Deviation (SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
Interquartile Range
exploring data
–Dotplot
–Stem-leaf
–Boxplot Coefficient of variation (CV)
–Skewness
11. Dispersion
Review
– tells us about the spread of the data.
Chapter 3:
– Help us to compare the spread in two or more
Dispersion distributions.
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
12. Dispersion: Range
Review Range:
Chapter 3: is the difference between the largest and
Dispersion
–Range the smallest value in a data set.
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Example:
Chapter 4:
Displaying and To find the range in 3,5,7,3,11
exploring data
–Dotplot
–Stem-leaf Range = 11-3 = 8
–Boxplot
–Skewness
13. Dispersion: Variance
Review
Population Variance:
• is the mean of the squared difference between each
Chapter 3:
Dispersion value and the mean.
–Range • overcomes the weakness of the range by using all the
–Variance (SD2)
–Standard Deviation values in the population.
(SD)
–Coefficient of
variation (CV) Σ(X - μ) 2
σ2 =
Chapter 4: N
Displaying and
exploring data
–Dotplot
–Stem-leaf
Sample Variance:
–Boxplot
Σ(X - X) 2
–Skewness
s2 =
n -1
14. EXAMPLE – Variance Variance
Dispersion: and Standard
Deviation
Population Variance: Σ(X - μ) 2
σ2 =
Review N
The number of traffic citations issued during the last five months in
Chapter 3:
Dispersion
Beaufort County, South Carolina, is 38, 26, 13, 41, and 22. What
–Range is the population variance?
–Variance (SD2)
–Standard Deviation Step 2: Find the difference between each observation and the mean
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and Step 1: Get the mean
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Step 3: Square the difference and sum up Step 4: Divided by N
27
15. Dispersion: Standard Deviation
Review
Chapter 3:
Dispersion
Population Standard Deviation:
–Range
–Variance (SD2)
is the square root of the population variance.
–Standard Deviation
σ= σ2
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot Sample Standard Deviation:
–Stem-leaf
–Boxplot is the square root of the sample variance.
–Skewness
s = s2
16. Dispersion: Standard Deviation
Example:
Review The hourly wages earned by a sample of five students are:
€7, €5, €11, €8, €6.
Chapter 3:
Dispersion Find the variance and standard deviation.
–Range
Step 1: Get the mean ΣX 37
–Variance (SD2) X= = = 7.40
–Standard Deviation
(SD)
n 5
2
Σ(X - X )
2 2
–Coefficient of
Step 2: Sum up the (7 - 7.4) + ... + (6 - 7.4)
variation (CV)
squared differences s2 = =
n -1 5 -1
Chapter 4:
21.2
Displaying and
= = 5.30
exploring data
–Dotplot
Step 3: Divided by N-1 5 -1
–Stem-leaf
–Boxplot
–Skewness Step 4: Square root it s = €2.30
The variance is €5.30; the standard deviation is €2.30.
17. Dispersion: Standard Deviation
Review
Chapter 3:
Dispersion
Compare
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of 20 40 50 60 80 20 49 50 51 80
variation (CV)
Chapter 4:
Displaying and
Step 1: Get the mean
exploring data
–Dotplot
–Stem-leaf Step 2: Sum up the
–Boxplot
squared differences
–Skewness
Step 3: Divided by N-1
Step 4: Square root it
18. Dispersion: Standard Deviation
Review
Chapter 3:
Dispersion
Compare
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of 20 40 50 60 80 20 49 50 51 80
variation (CV)
Chapter 4:
Displaying and
exploring data •The sales of
–Dotplot
–Stem-leaf MANGO is more
–Boxplot
–Skewness closely clustered
around the mean
of 50 than the
sales of ZARA.
19. Dispersion: Standard Deviation
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
The standard deviation decreases because the new value 20 is very close to
the mean 20.36.
22. Dispersion: Coefficient of Variation
Review
Coefficient of Variation:
Chapter 3: describes the magnitude sample values and the variation within
Dispersion them.
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
The following times were recorded by the quarter-mile and mile runners of a
Chapter 4: university track team (times are in minutes).
Displaying and
exploring data Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99
–Dotplot
–Stem-leaf Mile Times: 4.52 4.35 4.60 4.70 4.50
–Boxplot After viewing this sample of running times, one of the coaches commented that
–Skewness
the quarter milers turned in the more consistent times. Calculate the appropriate
measure to check this and comment on the coach’s statement.
We can compare the dispersion with the coefficient of variation because they
have different “magnitudes”.
24. Dispersion: Coefficient of Variation
The following times were recorded by the quarter-mile and mile runners of a
Review university track team (times are in minutes).
Chapter 3:
Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99
Dispersion
Mile Times: 4.52 4.35 4.60 4.70 4.50
–Range
–Variance (SD2) After viewing this sample of running times, one of the coaches commented that
–Standard Deviation the quarter milers turned in the more consistent times. Calculate the appropriate
(SD) measure to check this and comment on the coach’s statement.
–Coefficient of
variation (CV) We can compare the dispersion with the coefficient of variation because they
have different “magnitudes”.
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
No, the mile-time team showed more consistent times.
25. Displaying and Exploring Data
Review Dot plots:
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
26. Displaying and Exploring Data
Review Stem-and-Leaf Displays:
Chapter 3: Each numerical value is divided into two parts. The leading
Dispersion
–Range
digit(s) becomes the stem and the trailing digit the leaf. The
–Variance (SD2) stems are located along the vertical axis, and the leaf values are
–Standard Deviation
(SD) stacked against each other along the horizontal axis.
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Stem
27. Displaying and Exploring Data
Stem-and-Leaf Displays:
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
28. Displaying and Exploring Data
Review Quartiles, Deciles, and Percentiles
Chapter 3:
Alternative ways of describing spread of data include determining
Dispersion the location of values that divide a set of observations into equal
–Range parts.
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
29. Displaying and Exploring Data
Review
Quartiles, Deciles, and Percentiles
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
30. Displaying and Exploring Data
Review
Quartiles, Deciles, and Percentiles
Chapter 3:
Dispersion Raw Percentile
–Range
Score Frequency Frequency Rank
–Variance (SD2)
–Standard Deviation
(SD) 95 1 25 100
–Coefficient of 93 1 24 96
variation (CV)
88 2 23 92
Chapter 4: 85 3 21 84
Displaying and
exploring data 79 1 18 72
–Dotplot 75 4 17 68
–Stem-leaf
–Boxplot 70 6 13 52
–Skewness 65 2 7 28
62 1 5 20
58 1 4 16
54 2 3 12
50 1 1 4
N = 25
31. Displaying and Exploring Data
Review
Quartiles, Deciles, and Percentiles
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV) Example:
Chapter 4:
Displaying and 101 43 75 61 91 104
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
The first quartile is ?
32. Displaying and Exploring Data
Review
Chapter 3: Step 1: Organize the data from lowest to largest value
Dispersion
–Range 101 43 75 61 91 104
–Variance (SD2)
–Standard Deviation
P1 P2 P3 P4 P5 P6
(SD)
–Coefficient of
variation (CV) Step 2: P1.75
Chapter 4:
Displaying and
exploring data
Step 3: Draw two lines
–Dotplot
–Stem-leaf
–Boxplot
–Skewness 43 61-43 = 18 61
P1 0.75 P2
33. Displaying and Exploring Data
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
Step 3: Draw two lines
(SD)
–Coefficient of
variation (CV) 43+13.5 = 56.5
Chapter 4:
Displaying and 43 61-43 = 18 61
exploring data
–Dotplot
–Stem-leaf
–Boxplot
P1 0.75 * 18 = 13.5 P2
–Skewness
The first quartile is 56.5.
34. Displaying and Exploring Data
Listed below, ordered from smallest to largest, are the number
of visits last week.
a. Determine the median number of calls.
a. 57median is 58.
The b.58 c.59 d.56
b. Determine the first and third quartiles.
Q1 = 51.25 Q3 = 66.00
a. 50.25 b.51.25 c.60.00 d.62.25 e.63.00 f. 66.00
P110. N.14 Ch.4
35. Displaying and Exploring Data
Listed below, ordered from smallest to largest, are the number of
visits last week.
c. Determine the first decile and the ninth decile.
D1 = 45.30 D9 = 76.40
d. Determine the 33rd percentile.
P33 = 53.53
P110. N.14 Ch.4
36. Displaying and Exploring Data
Review
Box Plots
A graphical display, based on quartiles to visualize a set of data.
Chapter 3:
Dispersion
–Range
minimum Q1 Median Q3 maximum
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
37. Displaying and Exploring Data
Review
Box Plots
A graphical display, based on quartiles to visualize a set of data.
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation minimum Q1 Median Q3 maximum
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
38. Displaying and Exploring Data
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and Zero skewness positive skewness negative skewness
exploring data
–Dotplot mode=median=mean Mode < Median < Mean Mode > Median > Mean
–Stem-leaf
–Boxplot
–Skewness
39. Displaying and Exploring Data
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
40. Displaying and Exploring Data
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
minimum Q1 Median Q3 maximum
41. Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness •The graph is called a cumulative frequency distribution.
•The interquartile range is 45-35=10 years and the median is 40 years
a. 10 b.35 c.40 d.45 e.15 f.20
•50% of the employees are between 35 years and 45 years old.
42. What we have learnt?
1. Why Failed in
Statistics?
• Review
2. Chapter 1:
What is • Chapter 3: Dispersion
Statistics?
A.Why? What? • Range
B.Types of
statistics, • Variance (SD2)
variables
C.Levels of • Standard Deviation (SD)
measurement
• Coefficient of variation (CV)
3. Chapter 2:
Describing Data • Chapter 4: Displaying and exploring data
A.Frequency
tables
• Dotplot
B.Frequency • Stem-leaf
distributions
C.Graphic • Boxplot
presentation
• Skewness