This document discusses measures of dispersion, which indicate how spread out or variable observed data values are around a central measure like the mean. It describes two main types of dispersion measures: range measures, which consider the distance between extreme values, and deviation measures, which consider the average distance of values from the mean. Specific measures discussed include the total range, interdecile and interquartile ranges, mean deviation, variance, and standard deviation. The standard deviation is typically the preferred measure because it is expressed in the original units of the data and is easier to interpret than the variance.
The document discusses measures of dispersion, which indicate how spread out or far apart observed values are from the average or central value. There are two main types of measures: range measures, which look at the distance between extreme values, and deviation measures, which calculate the average distance of values from the mean. The most common deviation measure is the standard deviation, which finds the average squared distance from the mean. The standard deviation provides a measure of dispersion in the original units of measurement.
The document discusses various concepts related to variability and measures of dispersion in statistics:
- Variability refers to the spread or deviation of scores from the mean in a data set. Measures of variability quantify how concentrated or dispersed the data is.
- Common measures of variability include range, quartile deviation, mean deviation, variance, standard deviation, and coefficient of variation. Range simply measures the highest and lowest scores while other measures account for dispersion across all scores.
- The standard deviation is the most widely used measure of variability as it expresses dispersion in the same units as the original data. It quantifies how far scores deviate from the mean on average.
- Understanding variability is important for determining if averages
This document discusses various statistical measures of dispersion. It defines dispersion as how spread out or varied a set of numerical data is from the average value. There are two types of measures - absolute, which have the same units as the data, and relative, which are unit-less and used to compare datasets. Examples of measures discussed include range, mean deviation, standard deviation, variance, and coefficient of variation. The document also covers frequency distributions, binomial distributions, chi-square tests, and data analysis processes.
This document is highly important for the learners of research methodology. A number of statistical terminologies are defined with examples for the simplicity of learners.
The document discusses measures of dispersion, which describe how varied or spread out a data set is around the average value. It defines several measures of dispersion, including range, interquartile range, mean deviation, and standard deviation. The standard deviation is described as the most important measure, as it takes into account all values in the data set and is not overly influenced by outliers. The document provides a detailed example of calculating the standard deviation, which involves finding the differences from the mean, squaring those values, summing them, and taking the square root.
A teacher calculated the standard deviation of test scores to see how close students scored to the mean grade of 65%. She found the standard deviation was high, indicating outliers pulled the mean down. An employer also calculated standard deviation to analyze salary fairness, finding it slightly high due to long-time employees making more. Standard deviation measures dispersion from the mean, with low values showing close grouping and high values showing a wider spread. It is calculated using the variance formula of summing the squared differences from the mean divided by the number of values.
Biostatistics is the science of collecting, summarizing, analyzing, and interpreting data in the fields of medicine, biology, and public health. It involves both descriptive and inferential statistics. Descriptive statistics summarize data through measures of central tendency like mean, median, and mode, and measures of dispersion like range and standard deviation. Inferential statistics allow generalization from samples to populations through techniques like hypothesis testing, confidence intervals, and estimation. Sample size determination and random sampling help ensure validity and minimize errors in statistical analyses.
The document discusses measures of dispersion, which indicate how spread out or far apart observed values are from the average or central value. There are two main types of measures: range measures, which look at the distance between extreme values, and deviation measures, which calculate the average distance of values from the mean. The most common deviation measure is the standard deviation, which finds the average squared distance from the mean. The standard deviation provides a measure of dispersion in the original units of measurement.
The document discusses various concepts related to variability and measures of dispersion in statistics:
- Variability refers to the spread or deviation of scores from the mean in a data set. Measures of variability quantify how concentrated or dispersed the data is.
- Common measures of variability include range, quartile deviation, mean deviation, variance, standard deviation, and coefficient of variation. Range simply measures the highest and lowest scores while other measures account for dispersion across all scores.
- The standard deviation is the most widely used measure of variability as it expresses dispersion in the same units as the original data. It quantifies how far scores deviate from the mean on average.
- Understanding variability is important for determining if averages
This document discusses various statistical measures of dispersion. It defines dispersion as how spread out or varied a set of numerical data is from the average value. There are two types of measures - absolute, which have the same units as the data, and relative, which are unit-less and used to compare datasets. Examples of measures discussed include range, mean deviation, standard deviation, variance, and coefficient of variation. The document also covers frequency distributions, binomial distributions, chi-square tests, and data analysis processes.
This document is highly important for the learners of research methodology. A number of statistical terminologies are defined with examples for the simplicity of learners.
The document discusses measures of dispersion, which describe how varied or spread out a data set is around the average value. It defines several measures of dispersion, including range, interquartile range, mean deviation, and standard deviation. The standard deviation is described as the most important measure, as it takes into account all values in the data set and is not overly influenced by outliers. The document provides a detailed example of calculating the standard deviation, which involves finding the differences from the mean, squaring those values, summing them, and taking the square root.
A teacher calculated the standard deviation of test scores to see how close students scored to the mean grade of 65%. She found the standard deviation was high, indicating outliers pulled the mean down. An employer also calculated standard deviation to analyze salary fairness, finding it slightly high due to long-time employees making more. Standard deviation measures dispersion from the mean, with low values showing close grouping and high values showing a wider spread. It is calculated using the variance formula of summing the squared differences from the mean divided by the number of values.
Biostatistics is the science of collecting, summarizing, analyzing, and interpreting data in the fields of medicine, biology, and public health. It involves both descriptive and inferential statistics. Descriptive statistics summarize data through measures of central tendency like mean, median, and mode, and measures of dispersion like range and standard deviation. Inferential statistics allow generalization from samples to populations through techniques like hypothesis testing, confidence intervals, and estimation. Sample size determination and random sampling help ensure validity and minimize errors in statistical analyses.
Lecture. Introduction to Statistics (Measures of Dispersion).pptxNabeelAli89
1) The document discusses various measures of dispersion used to quantify how spread out or varied a set of data values are from the average.
2) There are two types of dispersion - absolute dispersion measures how varied data values are in the original units, while relative dispersion compares variability between datasets with different units.
3) Common measures of absolute dispersion include range, variance, and standard deviation. Range is the difference between highest and lowest values, while variance and standard deviation take into account how far all values are from the mean.
This document discusses measures of dispersion, which indicate how spread out or variable a set of data is. There are three main measures: the range, which is the difference between the highest and lowest values; the semi-interquartile range (SIR), which is the difference between the first and third quartiles divided by two; and variance/standard deviation. Variance is the average of the squared deviations from the mean, while standard deviation is the square root of the variance. These measures provide summaries of how concentrated or dispersed the observed values are from the average or expected value.
This document provides an overview of key concepts in statistics including measures of central tendency, measures of dispersion, probability, correlation, time series analysis, and network planning methods like CPM and PERT. It defines terms like mean, median, mode, standard deviation, variance, probability, random experiment, correlation, time series, network, critical path, slack time, and differences between CPM and PERT. It also lists advantages and limitations of using PERT/CPM for project management.
The document discusses various measures of variability that can be used to describe the spread or dispersion of data, including the range, interquartile range, mean absolute deviation, variance, standard deviation, and coefficient of variation. It also covers how to calculate and interpret these measures of variability for both ungrouped and grouped data. Various other concepts are introduced such as the empirical rule, z-scores, skewness, the 5-number summary, and how to construct and interpret a box-and-whisker plot.
BRM_Data Analysis, Interpretation and Reporting Part II.pptAbdifatahAhmedHurre
This document provides an overview of data analysis, interpretation, and reporting. It discusses descriptive and inferential analysis, and univariate, bivariate, and multivariate analysis. Specific quantitative analysis techniques covered include measures of central tendency, dispersion, frequency distributions, histograms, and tests of normality. Hypothesis testing procedures like t-tests, ANOVA, and non-parametric alternatives are also summarized. Steps in hypothesis testing include stating the null hypothesis, choosing a statistical test, specifying the significance level, and deciding whether to reject or fail to reject the null hypothesis based on findings.
Measure of dispersion and it’s need.pptx by waseem javidwaseemjavid2004
Measure of dispersion are statistics that describe how similar or different values in a data set are. They are needed to determine the reliability of averages, compare variability between data sets, and facilitate the use of other statistics. Common measures of dispersion include range, interquartile range, mean deviation, standard deviation, coefficient of variation, and Lorenz curves. Standard deviation is the most widely used as it measures how far values are from the mean.
Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
This document discusses measures of dispersion in statistics. It defines dispersion as the extent of variation in a data set from the average value. There are two main types of dispersion - absolute and relative. Absolute measures express variation in units of the data and include range, variance, standard deviation, and quartile deviation. Relative measures allow comparison between data sets by being unit-free, such as the coefficient of variation. Key absolute measures are then explained in more detail, along with their merits and demerits.
PART 1 DISCUSSION MEASURES OF CENTAL TENDENCY.pptDavidJenil
This document discusses measures of central tendency (averages) including the mode, median, and mean. It defines each measure and describes how to calculate them from raw data, frequency tables, and histograms. The mode is the most frequently occurring value. The median is the middle value when values are ranked from lowest to highest. The mean is the sum of all values divided by the number of cases and represents the "center of gravity" of the data. The document compares the different measures and notes situations where one may be higher or lower than the others.
This document discusses various measures of central tendency and dispersion that are commonly used in epidemiology to summarize data distributions. It describes the mean, median and mode as measures of central tendency that convey the average or typical value, and how the appropriate measure depends on the data's measurement level, shape and research purpose. Measures of dispersion like range, interquartile range, variance and standard deviation describe how spread out the data is from the central value. The document provides formulas and explanations for calculating and interpreting each measure.
- Univariate normal distribution describes the distribution of a single random variable and is characterized by its bell-shaped curve. The mean, median, and mode are equal and located at the center. Approximately 68% of the data falls within one standard deviation of the mean.
- Multivariate normal distribution describes the joint distribution of multiple random variables. It generalizes the univariate normal distribution to multiple dimensions. The variables have a consistent relationship that can be modeled as a covariance matrix.
- Examples of data that may follow a normal distribution include heights, test scores, measurement errors, and stock price changes over time. Normal distributions are widely used in statistics
This document provides an overview of descriptive statistics. It discusses key topics including measures of central tendency (mean, median, mode), measures of variability (range, IQR, variance, standard deviation, skewness, kurtosis), probability and probability distributions (binomial distribution), and how descriptive statistics is used to understand and describe data. Descriptive statistics involves numerically summarizing and presenting data through methods such as graphs, tables, and calculations without inferring conclusions about a population.
1. Measures of dispersion quantify the variability or spread of data around a central value. Absolute measures express dispersion in the same units as the data, while relative measures allow comparison between data sets.
2. Common measures of dispersion include range, quartile deviation, mean deviation, variance, and standard deviation. A good measure of dispersion should be simple, easy to compute, based on all observations, and unaffected by outliers.
3. Variance and standard deviation are widely used as they satisfy these properties and allow algebraic manipulation. Variance is the average of the squared deviations from the mean, while standard deviation is the positive square root of variance.
Frequencies provides statistics and graphical displays to describe variables. It can order values by ascending/descending order or frequency. Key outputs include mean, median, mode, quartiles, standard deviation, variance, skewness, and kurtosis. Quartiles divide data into four equal groups. Skewness measures asymmetry while kurtosis measures clustering around the mean. Charts like pie charts, bar charts, and histograms can visualize the data distribution. Crosstabs forms two-way and multi-way tables to analyze relationships between variables.
This document provides an overview of basic statistical concepts for bio science students. It defines measures of central tendency including mean, median, and mode. It also discusses measures of dispersion like range and standard deviation. Common probability distributions such as binomial, Poisson, and normal distributions are explained. Hypothesis testing concepts like p-values and types of statistical tests for different types of data like t-tests for continuous variables and chi-square tests for categorical data are summarized along with examples.
Measure of dispersion refers to statistical measures that quantify how data values are spread out or vary from the average value. There are various measures of dispersion including standard deviation, mean deviation, variance, range, and quartile deviation. These measures capture how concentrated or scattered the data is and help analyze the characteristics of data sets. Common measures include range, which is the difference between highest and lowest values; variance and standard deviation, which measure average deviation from the mean; and mean deviation, which averages the absolute deviations from the mean or median. Measures can be absolute, using the same units as the data, or relative by standardizing against the mean. Skewness and kurtosis further characterize the shape and outliers of a distribution.
This document discusses measures of central tendency and dispersion in statistics. It defines central tendency as a single value that describes the center of a data distribution. Common measures include the mean, median, and mode. The mean is the average value calculated by adding all values and dividing by the total number. The median is the middle value when data is ordered from lowest to highest. The mode is the most frequent value. Dispersion measures the spread of data and includes the range, mean deviation, standard deviation, and variance. Standard deviation summarizes how far data points are from the mean. Variance is the square of the standard deviation. The document provides examples of calculating these measures and their characteristics and uses.
This document discusses various statistical parameters used in pharmaceutical research and development. It describes parameters like measures of central tendency (mean, median, mode), dispersion (variance, standard deviation), coefficient of dispersion, residuals, factor analysis, absolute error, mean absolute error, and percentage error of estimate. Measures of central tendency provide a summary of the central or typical values in a data set. Dispersion measures provide a way to quantify how spread out the data is from the central value. Other parameters like residuals, errors, and factor analysis are used to analyze relationships in complex data.
This document covers dividing polynomials using long division and synthetic division. It includes examples of using both long division and synthetic division to divide polynomials. It also discusses using synthetic division, called synthetic substitution, to evaluate polynomials for given values. The examples walk through the step-by-step processes of long division, synthetic division, and synthetic substitution. Additional examples apply these skills to geometry problems involving the volume, area, height, and length of shapes.
The document compares simple and compound interest over 25 years on an initial $100,000 investment. Simple interest results in $300,000 while compound interest results in $684,848, a difference of $384,848. Compound interest grows exponentially each year as interest is earned on previous interest, resulting in much higher returns over long periods compared to simple interest which grows linearly.
Lecture. Introduction to Statistics (Measures of Dispersion).pptxNabeelAli89
1) The document discusses various measures of dispersion used to quantify how spread out or varied a set of data values are from the average.
2) There are two types of dispersion - absolute dispersion measures how varied data values are in the original units, while relative dispersion compares variability between datasets with different units.
3) Common measures of absolute dispersion include range, variance, and standard deviation. Range is the difference between highest and lowest values, while variance and standard deviation take into account how far all values are from the mean.
This document discusses measures of dispersion, which indicate how spread out or variable a set of data is. There are three main measures: the range, which is the difference between the highest and lowest values; the semi-interquartile range (SIR), which is the difference between the first and third quartiles divided by two; and variance/standard deviation. Variance is the average of the squared deviations from the mean, while standard deviation is the square root of the variance. These measures provide summaries of how concentrated or dispersed the observed values are from the average or expected value.
This document provides an overview of key concepts in statistics including measures of central tendency, measures of dispersion, probability, correlation, time series analysis, and network planning methods like CPM and PERT. It defines terms like mean, median, mode, standard deviation, variance, probability, random experiment, correlation, time series, network, critical path, slack time, and differences between CPM and PERT. It also lists advantages and limitations of using PERT/CPM for project management.
The document discusses various measures of variability that can be used to describe the spread or dispersion of data, including the range, interquartile range, mean absolute deviation, variance, standard deviation, and coefficient of variation. It also covers how to calculate and interpret these measures of variability for both ungrouped and grouped data. Various other concepts are introduced such as the empirical rule, z-scores, skewness, the 5-number summary, and how to construct and interpret a box-and-whisker plot.
BRM_Data Analysis, Interpretation and Reporting Part II.pptAbdifatahAhmedHurre
This document provides an overview of data analysis, interpretation, and reporting. It discusses descriptive and inferential analysis, and univariate, bivariate, and multivariate analysis. Specific quantitative analysis techniques covered include measures of central tendency, dispersion, frequency distributions, histograms, and tests of normality. Hypothesis testing procedures like t-tests, ANOVA, and non-parametric alternatives are also summarized. Steps in hypothesis testing include stating the null hypothesis, choosing a statistical test, specifying the significance level, and deciding whether to reject or fail to reject the null hypothesis based on findings.
Measure of dispersion and it’s need.pptx by waseem javidwaseemjavid2004
Measure of dispersion are statistics that describe how similar or different values in a data set are. They are needed to determine the reliability of averages, compare variability between data sets, and facilitate the use of other statistics. Common measures of dispersion include range, interquartile range, mean deviation, standard deviation, coefficient of variation, and Lorenz curves. Standard deviation is the most widely used as it measures how far values are from the mean.
Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
This document discusses measures of dispersion in statistics. It defines dispersion as the extent of variation in a data set from the average value. There are two main types of dispersion - absolute and relative. Absolute measures express variation in units of the data and include range, variance, standard deviation, and quartile deviation. Relative measures allow comparison between data sets by being unit-free, such as the coefficient of variation. Key absolute measures are then explained in more detail, along with their merits and demerits.
PART 1 DISCUSSION MEASURES OF CENTAL TENDENCY.pptDavidJenil
This document discusses measures of central tendency (averages) including the mode, median, and mean. It defines each measure and describes how to calculate them from raw data, frequency tables, and histograms. The mode is the most frequently occurring value. The median is the middle value when values are ranked from lowest to highest. The mean is the sum of all values divided by the number of cases and represents the "center of gravity" of the data. The document compares the different measures and notes situations where one may be higher or lower than the others.
This document discusses various measures of central tendency and dispersion that are commonly used in epidemiology to summarize data distributions. It describes the mean, median and mode as measures of central tendency that convey the average or typical value, and how the appropriate measure depends on the data's measurement level, shape and research purpose. Measures of dispersion like range, interquartile range, variance and standard deviation describe how spread out the data is from the central value. The document provides formulas and explanations for calculating and interpreting each measure.
- Univariate normal distribution describes the distribution of a single random variable and is characterized by its bell-shaped curve. The mean, median, and mode are equal and located at the center. Approximately 68% of the data falls within one standard deviation of the mean.
- Multivariate normal distribution describes the joint distribution of multiple random variables. It generalizes the univariate normal distribution to multiple dimensions. The variables have a consistent relationship that can be modeled as a covariance matrix.
- Examples of data that may follow a normal distribution include heights, test scores, measurement errors, and stock price changes over time. Normal distributions are widely used in statistics
This document provides an overview of descriptive statistics. It discusses key topics including measures of central tendency (mean, median, mode), measures of variability (range, IQR, variance, standard deviation, skewness, kurtosis), probability and probability distributions (binomial distribution), and how descriptive statistics is used to understand and describe data. Descriptive statistics involves numerically summarizing and presenting data through methods such as graphs, tables, and calculations without inferring conclusions about a population.
1. Measures of dispersion quantify the variability or spread of data around a central value. Absolute measures express dispersion in the same units as the data, while relative measures allow comparison between data sets.
2. Common measures of dispersion include range, quartile deviation, mean deviation, variance, and standard deviation. A good measure of dispersion should be simple, easy to compute, based on all observations, and unaffected by outliers.
3. Variance and standard deviation are widely used as they satisfy these properties and allow algebraic manipulation. Variance is the average of the squared deviations from the mean, while standard deviation is the positive square root of variance.
Frequencies provides statistics and graphical displays to describe variables. It can order values by ascending/descending order or frequency. Key outputs include mean, median, mode, quartiles, standard deviation, variance, skewness, and kurtosis. Quartiles divide data into four equal groups. Skewness measures asymmetry while kurtosis measures clustering around the mean. Charts like pie charts, bar charts, and histograms can visualize the data distribution. Crosstabs forms two-way and multi-way tables to analyze relationships between variables.
This document provides an overview of basic statistical concepts for bio science students. It defines measures of central tendency including mean, median, and mode. It also discusses measures of dispersion like range and standard deviation. Common probability distributions such as binomial, Poisson, and normal distributions are explained. Hypothesis testing concepts like p-values and types of statistical tests for different types of data like t-tests for continuous variables and chi-square tests for categorical data are summarized along with examples.
Measure of dispersion refers to statistical measures that quantify how data values are spread out or vary from the average value. There are various measures of dispersion including standard deviation, mean deviation, variance, range, and quartile deviation. These measures capture how concentrated or scattered the data is and help analyze the characteristics of data sets. Common measures include range, which is the difference between highest and lowest values; variance and standard deviation, which measure average deviation from the mean; and mean deviation, which averages the absolute deviations from the mean or median. Measures can be absolute, using the same units as the data, or relative by standardizing against the mean. Skewness and kurtosis further characterize the shape and outliers of a distribution.
This document discusses measures of central tendency and dispersion in statistics. It defines central tendency as a single value that describes the center of a data distribution. Common measures include the mean, median, and mode. The mean is the average value calculated by adding all values and dividing by the total number. The median is the middle value when data is ordered from lowest to highest. The mode is the most frequent value. Dispersion measures the spread of data and includes the range, mean deviation, standard deviation, and variance. Standard deviation summarizes how far data points are from the mean. Variance is the square of the standard deviation. The document provides examples of calculating these measures and their characteristics and uses.
This document discusses various statistical parameters used in pharmaceutical research and development. It describes parameters like measures of central tendency (mean, median, mode), dispersion (variance, standard deviation), coefficient of dispersion, residuals, factor analysis, absolute error, mean absolute error, and percentage error of estimate. Measures of central tendency provide a summary of the central or typical values in a data set. Dispersion measures provide a way to quantify how spread out the data is from the central value. Other parameters like residuals, errors, and factor analysis are used to analyze relationships in complex data.
This document covers dividing polynomials using long division and synthetic division. It includes examples of using both long division and synthetic division to divide polynomials. It also discusses using synthetic division, called synthetic substitution, to evaluate polynomials for given values. The examples walk through the step-by-step processes of long division, synthetic division, and synthetic substitution. Additional examples apply these skills to geometry problems involving the volume, area, height, and length of shapes.
The document compares simple and compound interest over 25 years on an initial $100,000 investment. Simple interest results in $300,000 while compound interest results in $684,848, a difference of $384,848. Compound interest grows exponentially each year as interest is earned on previous interest, resulting in much higher returns over long periods compared to simple interest which grows linearly.
The document discusses trade discounts and cash discounts. It defines key terms like list price, trade discount, net price, and cash discount. It provides examples of calculating trade discounts when given a list price and discount rate. It also explains how to find the net price using the trade discount amount or discount rate complement. Additionally, it covers calculating cash discounts and net amounts using terms like 2/10 n/30, and discusses exceptions for end-of-month invoice dates.
This document discusses trade discounts and how to calculate net prices. It provides examples of how to calculate:
- Trade discounts using a single discount rate
- Net prices using the complement of a single discount rate
- Net prices when given a trade discount series by taking the net decimal equivalent
- Trade discounts when given a trade discount series by taking the single discount equivalent
Key terms discussed include list price, trade discount, net price, discount rate, and complement. Step-by-step processes are provided for various discount calculation scenarios.
Mindfulness is the practice of paying attention to the present moment in a non-judgemental way. It involves focusing attention on bodily sensations, thoughts, and emotions while accepting them non-reactively. Research shows mindfulness meditation can help reduce stress, anxiety, and depression by breaking harmful thinking patterns and increasing activity in the left prefrontal cortex associated with positive emotions. Formal mindfulness practices include mindful breathing, walking, eating, and yoga, while informal practices bring mindfulness to everyday activities. Mindfulness benefits mental health by helping regulate emotions and develop self-compassion.
The document provides information on arithmetic and geometric sequences. It gives the formulas for finding the nth term and sum of terms for both arithmetic and geometric sequences. Examples are provided of identifying sequences as arithmetic or geometric and calculating sequence terms and sums. Steps are shown to find missing terms, the first term given later terms, and common ratios of geometric sequences.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
2. Measures of Dispersion
• While measures of central tendency indicate what value
of a variable is (in one sense or other) “average” or
“central” or “typical” in a set of data, measures of
dispersion (or variability or spread) indicate (in one
sense or other) the extent to which the observed values
are “spread out” around that center — how “far apart”
observed values typically are from each other and
therefore from some average value (in particular, the
mean). Thus:
– if all cases have identical observed values (and thereby are also
identical to [any] average value), dispersion is zero;
– if most cases have observed values that are quite “close
together” (and thereby are also quite “close” to the average
value), dispersion is low (but greater than zero); and
– if many cases have observed values that are quite “far away”
from many others (or from the average value), dispersion is high.
• A measure of dispersion provides a summary statistic
that indicates the magnitude of such dispersion and, like
a measure of central tendency, is a univariate statistic.
3. Importance of the Magnitude
Dispersion Around the Average
• Dispersion around the mean test score.
• Baltimore and Seattle have about the same mean daily
temperature (about 65 degrees) but very different
dispersions around that mean.
• Dispersion (Inequality) around average household
income.
7. Measures of Dispersion
• Because dispersion is concerned with how “close
together” or “far apart” observed values are (i.e., with the
magnitude of the intervals between them), measures of
dispersion are defined only for interval (or ratio)
variables,
– or, in any case, variables we are willing to treat as interval (like
IDEOLOGY in the preceding charts).
– There is one exception: a very crude measure of dispersion
called the variation ratio, which is defined for ordinal and even
nominal variables. It will be discussed briefly in the Answers &
Discussion to PS #7.)
• There are two principal types of measures of dispersion:
range measures and deviation measures.
8. Range Measures of Dispersion
• Range measures are based on the distance between
pairs of (relatively) “extreme” values observed in the
data.
– They are conceptually connected with the median as a measure
of central tendency.
• The (“total” or “simple”) range is the maximum (highest)
value observed in the data [the value of the case at the
100th percentile] minus the minimum (lowest) value
observed in the data [the value of the case at the 0th
percentile]
– That is, it is the “distance” or “interval” between the values of the
two most extreme cases,
– e.g., range of test scores
9. TABLE 1 – PERCENT OF POPULATION AGED 65 OR HIGHER
IN THE 50 STATES
(UNIVARIATE DATA)
Alabama 12.4 Montana 12.5
Alaska 3.6 Nebraska 13.8
Arizona 12.7 Nevada 10.6
Arkansas 14.6 New Hampshire 11.5
California 10.6 New Jersey 13.0
Colorado 9.2 New Mexico 10.0
Connecticut 13.4 New York 13.0
Delaware 11.6 North Carolina 11.8
Florida 17.8 North Dakota 13.3
Georgia 10.0 Ohio 12.5
Hawaii 10.1 Oklahoma 12.8
Idaho 11.5 Oregon 13.7
Illinois 12.1 Pennsylvania 14.8
Indiana 12.1 Rhode Island 14.7
Iowa 14.8 South Carolina 10.7
Kansas 13.6 South Dakota 14.0
Kentucky 12.3 Tennessee 12.4
Louisiana 10.8 Texas 9.7
Maine 13.4 Utah 8.2
Maryland 10.7 Vermont 11.9
Massachusetts 13.7 Virginia 10.6
Michigan 11.5 Washington 11.8
Minnesota 12.6 West Virginia 13.9
Mississippi 12.1 Wisconsin 13.2
Missouri 13.8 Wyoming 8.9
12. Problems with the [Total] Range
• The problem with the [total] range as a measure of
dispersion is that it depends on the values of just two
cases, which by definition have (possibly extraordinarily)
atypical values.
– In particular, the range makes no distinction between a polarized
distribution in which almost all observed values are close to
either the minimum or maximum values and a distribution in
which almost all observed values are bunched together but there
are a few extreme outliers.
• Recall Ideological Dispersion bar graphs =>
– Also the range is undefined for theoretical distributions that are
“open-ended,” like the normal distribution (that we will take up in
the next topic) or the upper end of an income distribution type of
curve (as in previous slides).
14. The Interdecile Range
• Therefore other variants of the range measure that do
not reach entirely out to the extremes of the frequency
distribution are often used instead of the total range.
• The interdecile range is the value of the case that stands
at the 90th percentile of the distribution minus the value
of the case that stands at the 10th percentile.
– That is, it is the “distance” or “interval” between the
values of these two rather less extreme cases.
15. The Interquartile Range
• The interquartile range is the value of the case that
stands at the 75th percentile of the distribution minus the
value of the case that stands at the 25th percentile.
– The first quartile is the median observed value among
all cases that lie below the overall median and the
third quartile is the median observed value among all
cases that lie above the overall median.
– In these terms, the interquartile range is third quartile
minus the first quartile.
16.
17. The Standard Margin of Error Is a Range Measure
• Suppose the Gallup Poll takes a random sample of n respondents
and reports that the President's current approval rating is 62% and
that this sample statistic has a margin of error of ±3%. Here is what
this means: if (hypothetically) Gallup were to take a great many
random samples of the same size n from the same population (e.g.,
the American VAP on a given day), the different samples would give
different statistics (approval ratings), but 95% of these samples
would give approval ratings within 3 percentage points of the true
population parameter.
• Thus, if our data is the list of sample statistics produced
by the (hypothetical) “great many” random samples, the
margin of error specifies the range between the value of
the sample statistic that stands at the 97.5th percentile
minus the sample statistic that stands at the 2.5th
percentile (so that 95% of the sample statistics lie within
this range). Specifically (and letting P be the value of
the population parameter) this “95% range” is
(P + 3%) - (P -3%) = 6%, i.e., twice the margin error.
18. Deviation Measures of Dispersion
• Deviation measures are based on average deviations
from some average value.
– Since dispersion measures pertain to with interval variables, we
can calculate means, and deviation measures are typically
based on the mean deviation from the mean value.
– Thus the (mean and) standard deviation measures are
conceptually connected with the mean as a measure of central
tendency.
• Review: Suppose we have a variable X and a set of
cases numbered 1,2, . . . , n. Let the observed value of
the variable in each case be designated x1, x2, etc.
Thus:
20. Deviation Measures of Dispersion (cont.)
• The deviation from the mean for a representative case i is xi - mean
of x.
– If almost all of these deviations are close to zero, dispersion is
small.
– If many of these deviations much different from zero, dispersion
is large.
• This suggests we could construct a measure D of dispersion that
would simply be the average (mean) of all the deviations.
But this does not work because, as we saw earlier, it is a property
of the mean that all deviations from it add up to zero (regardless of
how much dispersion there is).
22. The Mean Deviation
• A practical way around this problem is simply to ignore
the fact that some deviations are negative while others
are positive by averaging the absolute values of the
deviations.
• This measure (called the mean deviation) tells us the
average (mean) amount that the values for all cases
deviate (regardless of whether they are higher or lower)
from the average (mean) value.
• Indeed, the Mean Deviation is an intuitive, understand-
able, and perfectly reasonable measure of dispersion,
and it is occasionally used in research.
24. The Variance
• Statisticians dislike this measure because the formula is
mathematically messy by virtue of being “non-algebraic”
(in that it ignores negative signs).
• Therefore statisticians, and most researchers, use
another slightly different deviation measure of dispersion
that is “algebraic.”
– This measure makes use of the fact that the square of any real
(positive or negative) number other than zero is itself always
positive.
• This measure --- the average of the squared deviations
from the mean (as opposed the average of the absolute
deviations) --- is called the variance.
26. The Variance (cont.)
• The variance is the average squared deviation from the
mean.
– The total (and average) average squared deviation from the mean
value of X is smaller than the average squared deviation from any
other value of X.
• The variance is the usual measure of dispersion in
statistical theory, but it has a drawback when researchers
want to describe the dispersion in data in a practical way.
– Whatever units the original data (and its average values and its
mean dispersion) are expressed in, the variance is expressed in
the square of those units, which may not make much (or any)
intuitive or practical sense.
– This can be remedied by finding the (positive) square root of the
variance (which takes us back to the original units).
• The square root of the variance is called the standard
deviation.
28. The Standard Deviation (cont.)
• In order to interpret a standard deviation, or to make a
plausible estimate of the SD of some data, it is useful to
think of the mean deviation because
– it is easier to estimate (or guess) the magnitude of the MD than
the SD; and
– the standard deviation has approximately the same numerical
magnitude as the mean deviation, though it is almost always
somewhat larger.
• The SD is never less than the MD;
• the SD is equal to the mean deviation if the data is distributed in a
maximally “polarized” fashion;
• Otherwise the SD is somewhat larger than the MD — typically about
20-50% larger.
29. Standard Deviation Worksheet
1. Set up a worksheet like the one shown in the previous slides.
2. In the first column, list the values of the variable X for each of the n cases.
[This is the raw data.]
3. Find the mean value of the variable in the data, by adding up the values in
each case and dividing by the number of cases.
4. In the second column, subtract the mean from each value to get, for each
case, the deviation from the mean. Some deviations are positive, others
negative, and (apart from rounding error) they must add up to zero; add
them up as an arithmetic check.
5. In the third column, square each deviation from the mean, i.e., multiply the
deviation by itself. Since the product of two negative numbers is positive,
every squared deviation is non-negative, i.e., either positive or (in the event
a case has a value that coincides with the mean value).
6. Add up the squared deviations over all cases.
7. Divide the sum of the squared deviations by the number of cases; this gives
the average squared deviation from the mean, commonly called the
variance.
8. The standard deviation is the (positive) square root of the variance. (The
square root of x is that number which when multiplied by itself gives x.)
30. The Mean, Deviations, Variance, and SD
• What is the effect of adding a constant amount to (or
subtracting from) each observed value?
• What is the effect of multiplying each observed value (or
dividing it by) a constant amount?
31. Adding (subtracting) the same amount to (from) every
observed value changes the mean by the same amount
but does not change the dispersion (for either range or
deviation measures)
32. Multiplying (or dividing) every observed value by the same
factor changes the mean and the SD [or MD] by that same
factor and changes the variance by that factor squared.
33. Sample Estimates of Population
Dispersion
• Random sample statistics that are percentages or averages
provide unbiased estimates of the corresponding population
parameters.
• However, sample statistics that are dispersion measures
provide estimates of population dispersion that are biased
(at least slightly) downward.
– This is most obvious in the case of the range; it should
be evident that a sample range is almost always smaller
than, and can never be larger than, than the
corresponding population range.
34. Sample Estimates of Population Dispersion (cont.)
• The sample standard deviation (or variance) is also biased
downward, but only slightly if the sample at all large.
– While the SD of a particular sample can be larger than the population
SD, sample SDs are on average slightly smaller than the corresponding
population SDs).
• The sample SD can be adjusted to provide an unbiased estimate of
the population SD
– This simple adjustment consists of dividing the sum of the squared
deviations by n - 1, rather than by n.
– Clearly this adjustment makes no practical difference unless the sample
is quite small.
• Notice that if you apply the SD [or MD or any Range] formula in the
event that you have just a single observation in your sample, sample
dispersion = 0 regardless of what the observed value is.
– More intuitively, you can get no sense of how much dispersion there is
in a population with respect to some variable until you observe at least
two cases and can see how “far apart” they are.
• This is why you will often see the formula for the variance and SD
with an n - 1 divisor (and scientific calculators often build in this
formula).
– However, for POLI 300 problem sets and tests, you should use the
formula given in the previous section of this handout.
35. Dispersion in Ratio Variables
• Given a ratio variable (e.g. income), the interesting
“dispersion question” may pertain not to the interval
between two observed values or between an observed
value and the mean value but to the ratio between the
two values.
– For example, fifty years ago, the income of the household at the
25th percentile was about $5,000 and the income of the
household at the 75th percentile was about $10,000, while today
the figures are about $40,000 and $80,000 respectively.
• While the interval between the two income levels (the interquartile
range) has increased from $5,000 to $40,000, the ratio between the
two income levels has remained a constant 2 to 1.
• Other examples pertain to income:
– One household “poverty level” is defined as half of median
household income.
– Households with more than twice the median income are
sometimes characterized as “well off.”
– The average compensation of CEOs today is about 250 times
that of the average worker, whereas 50 years it was only about
40 times that of the average worker.)
36. Dispersion in Ratio Variables (cont.)
• The degree of dispersion in ratio variables can naturally
be referred to as the degree inequality.
– For example the two sets of income levels ($5K vs.
$10K and $40K vs. $80K) at the 25th and 75th
percentiles respectively seem to be “equally unequal”
because they are in the same ratio.
• Thus the SD does not work well as a measure of
inequality (of income, etc.), because it takes no account
of the ratio property of [ratio] variables.
37. The Coefficient of Variation
• One ratio measure of dispersion/inequality is called the
coefficient of variation, which is simply the standard
deviation divided by the mean.
– It answers the question: how big is the SD of the distribution
relative to the mean of the distribution?
• Recall PS#6, Question #7, comparing the distributions of
height and weight among American adults.
– We naturally to want to say that in some sense that American
adults exhibit more dispersion in weight than height.
– But if by dispersion we mean [any kind of] range, mean
deviation, or variance/SD, the claim is strictly meaningless
because the two variables are measured in in different units
(pounds, kilograms, etc. vs. inches, feet, centimeters, etc.), so
the numerical comparison is not valid.
38. Coefficient of Variation (cont.)
Summary statistics for WEIGHT and HEIGHT (both ratio variables) of American adults in
different units:
Weight Height
Mean 160 pounds 66 inches
72.6 kilograms 5.5 feet
.08 tons 168 centimeters
SD 30 pounds 4 inches
13.6 kilograms .33 feet
.015 tons 10.2 centimeters
Which variable [WEIGHT or HEIGHT] has greater dispersion? [No meaningful answer can
be given]
Which variable has greater dispersion relative to its average, e.g., greater Coefficient of
Dispersion (SD relative to mean)?
30 = 13.6 = .015 = .18 4 = .33 = 10.2 = .06
160 72.6 .08 66 5.5 168
Note that the Coefficient of Variation is a pure number, not expressed in any units and is
the same whatever units the variable is measured in.
39. Coefficient of Variation
• The old and new SDs are the same.
• The old Coefficient of Variation was
SD/Mean = 2/14 = 1/7 = 0.143
• while the new Coefficient of variation is
SD/Mean = 2/4 = 0.5
40. Coefficient of Variation (cont)
• The old and new SDs are the same.
• The old Coefficient of Variation was
– SD/mean = 2/14 = 1/7 = 0.143
• The new Coefficient of Variation is
– SD/mean = 2/114 = 0.0175
41. Coefficient of Variation (cont)
• The new SD is 10 times the old SD.
• But the old and new Coefficients of Variation are the
same:
SD/mean = 2/14 = 20/140 = 1/7 = 0.143
42. The Gini Index
• Another measure of dispersion in ratio variables is the
Gini Index of Inequality.
– The Gini Index is based on a comparison between the
actual cumulative distribution when cases are ranked
ordered from lowest to highest value (e.g., from
poorest to richest) and the cumulative distribution that
would exist if all cases had the same value.
• Both the Coefficient of Variation and the Gini Index are
pure numbers, not expressed in any units ($, pounds,
inches, etc.) and unaffected by changing units.
– However, the Gini Index is also standardized, with
values that range from a minimum of 0 (perfect
equality) to a maximum of 1 (perfect inequality).