Standard deviation was first introduced by Karl Pearson in 1893 as a more scientific way to measure dispersion than existing methods. It is calculated by taking the deviations of individual observations from the mean, squaring them, summing them, and dividing by the total observations. The square root of the result is the standard deviation. It is the most useful and popular measure of dispersion as it is always calculated from the arithmetic mean rather than the median or mode.
This document discusses measures of central tendency, including the mean, median, and mode. It defines each measure and describes their characteristics and how to calculate them. The mean is the average value and is affected by outliers. The median is the middle value and is not affected by outliers. The mode is the most frequently occurring value. The document provides examples of calculating each measure from data sets and discusses their advantages and disadvantages.
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
1. The document discusses the concept of mode in statistics, including definitions, methods of computing mode in individual, discrete, and grouped series, merits and demerits, and uses.
2. Key methods discussed include computing mode by inspection when values are small, making discrete or grouped series when values are large, and using the formula Mode = 3Median - 2Mean.
3. The mode is the value that occurs most frequently in a data set and indicates the central tendency. It is useful when wanting a representative typical value.
The document provides objectives and instructions for calculating standard deviation, variance, and student's t-test. It defines standard deviation as the positive square root of the arithmetic mean of the squared deviations from the mean. Standard deviation is considered the most reliable measure of variability. Variance is defined as the square of the standard deviation. Student's t-test is used to compare means of two samples and determine if they are statistically different. The document provides examples of calculating standard deviation, variance, and performing matched pairs and independent samples t-tests on sets of data.
The mode is defined as the score that occurs most frequently in a data set. It is a measure of central tendency that indicates the most common value. For an ungrouped data set, the mode is simply the value that repeats most. For a grouped data set, the mode is calculated using a formula that finds the midpoint of the interval with the highest frequency while accounting for the differences in frequencies on either side of that interval. The mode is useful when wanting a quick approximation of central tendency or when trying to find the most typical value in a data set. Data sets can have one, two, or more modes depending on the number of most frequent values.
This document defines and provides the formula for calculating mean deviation, which is a measure of variation that uses all the scores in a distribution. It is more reliable than range. Mean deviation is calculated by finding the absolute difference between each score and the mean, summing the absolute differences, and dividing by the number of observations. Two examples of calculating mean deviation for sets of data are provided, along with exercises asking students to find the mean deviation of additional data sets and define standard deviation.
Measure of Central Tendency (Mean, Median, Mode and Quantiles)Salman Khan
A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most values in a distribution fall and are also referred to as the central location of a distribution. You can think of it as the tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method.
This document discusses various measures of dispersion in statistics including range, mean deviation, variance, and standard deviation. It provides definitions and formulas for calculating each measure along with examples using both ungrouped and grouped frequency distribution data. Box-and-whisker plots are also introduced as a graphical method to display the five number summary of a data set including minimum, quartiles, and maximum values.
This document discusses measures of central tendency, including the mean, median, and mode. It defines each measure and describes their characteristics and how to calculate them. The mean is the average value and is affected by outliers. The median is the middle value and is not affected by outliers. The mode is the most frequently occurring value. The document provides examples of calculating each measure from data sets and discusses their advantages and disadvantages.
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
1. The document discusses the concept of mode in statistics, including definitions, methods of computing mode in individual, discrete, and grouped series, merits and demerits, and uses.
2. Key methods discussed include computing mode by inspection when values are small, making discrete or grouped series when values are large, and using the formula Mode = 3Median - 2Mean.
3. The mode is the value that occurs most frequently in a data set and indicates the central tendency. It is useful when wanting a representative typical value.
The document provides objectives and instructions for calculating standard deviation, variance, and student's t-test. It defines standard deviation as the positive square root of the arithmetic mean of the squared deviations from the mean. Standard deviation is considered the most reliable measure of variability. Variance is defined as the square of the standard deviation. Student's t-test is used to compare means of two samples and determine if they are statistically different. The document provides examples of calculating standard deviation, variance, and performing matched pairs and independent samples t-tests on sets of data.
The mode is defined as the score that occurs most frequently in a data set. It is a measure of central tendency that indicates the most common value. For an ungrouped data set, the mode is simply the value that repeats most. For a grouped data set, the mode is calculated using a formula that finds the midpoint of the interval with the highest frequency while accounting for the differences in frequencies on either side of that interval. The mode is useful when wanting a quick approximation of central tendency or when trying to find the most typical value in a data set. Data sets can have one, two, or more modes depending on the number of most frequent values.
This document defines and provides the formula for calculating mean deviation, which is a measure of variation that uses all the scores in a distribution. It is more reliable than range. Mean deviation is calculated by finding the absolute difference between each score and the mean, summing the absolute differences, and dividing by the number of observations. Two examples of calculating mean deviation for sets of data are provided, along with exercises asking students to find the mean deviation of additional data sets and define standard deviation.
Measure of Central Tendency (Mean, Median, Mode and Quantiles)Salman Khan
A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most values in a distribution fall and are also referred to as the central location of a distribution. You can think of it as the tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method.
This document discusses various measures of dispersion in statistics including range, mean deviation, variance, and standard deviation. It provides definitions and formulas for calculating each measure along with examples using both ungrouped and grouped frequency distribution data. Box-and-whisker plots are also introduced as a graphical method to display the five number summary of a data set including minimum, quartiles, and maximum values.
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
Standard deviation measures how dispersed data values are from the average. It is the most reliable measure of dispersion and shows the average distance of each data point from the mean. While it is more difficult to calculate than other measures, standard deviation provides important information about how concentrated or spread out the data is. The presentation defines standard deviation, lists its merits and demerits, and shows how to calculate it for both populations and samples.
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.
This document discusses measures of central tendency including mean, median, and mode. It provides definitions and formulas for calculating each measure from both grouped and ungrouped data. For mean, it is the sum of all values divided by the number of values. Median is the middle value when values are arranged in order. Mode is the most frequently occurring value. The document also discusses requirements for a good measure of central tendency and provides examples calculating the measures from sample medical data sets to illustrate their use and assess skewness.
Topic: Variance
Student Name: Sonia Khan
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
This document discusses various measures of central tendency including the mean, median, and mode. It defines each measure and provides examples of how to calculate each from both ungrouped and grouped data. The mean is the average value and is calculated by summing all values and dividing by the total number of values. The median is the middle value when values are arranged in order and divides the data set in half. The mode is the most frequently occurring value.
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the sum of all values divided by the number of values and is the most widely used measure. The median is the middle value when data is arranged from lowest to highest. The mode is the value that occurs most frequently. Examples are given demonstrating how to calculate each measure for both individual values and grouped data.
This document defines mean or average deviation and provides information about calculating it. Mean deviation is the average of the absolute differences between each value in a data set and the mean. It is easier to understand and calculate than other measures of variation. Mean deviation is less affected by extreme observations than other measures. It is frequently used to analyze the distribution of personal wealth by considering both the rich and poor. The document outlines the steps to calculate mean deviation for individual, discrete, and continuous data series.
The document defines and provides examples for calculating the coefficient of variation, which is a measure used to compare the dispersion of data sets. It gives the formula for coefficient of variation as the standard deviation divided by the mean, expressed as a percentage. Two examples are shown comparing the stability of prices between two cities and production between two manufacturing plants, with the data set having the lower coefficient of variation considered more consistent or stable.
One of the three points that divide a data set into four equal parts. Or the values that divide data into quarters. Each group contains equal number of observations or data. Median acts as base for calculation of quartile.
The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population.
The document discusses various measures of central tendency and dispersion used in statistical analysis. It defines measures of central tendency like arithmetic mean, median and mode, and provides their formulas and properties. It also discusses measures of dispersion such as range, mean deviation, standard deviation, variance and their characteristics. The document provides examples and steps to calculate various averages and measures of dispersion for a given data set.
The document discusses various techniques for summarizing quantitative and categorical data in statistics. It describes measures of central tendency like mean, median and mode, as well as measures of variability such as range, variance and standard deviation. It also discusses derived scores, standard scores, frequency polygons, histograms, stem and leaf plots, the normal curve, correlation, frequency tables, bar graphs and pie charts as common techniques for summarizing different types of data. Worked examples are provided for finding descriptive statistics measures and visualizing data distribution using graphs and tables.
This document defines and provides examples for calculating the mode of data sets. It explains that the mode is the value that occurs most frequently in a data set. For ungrouped data, the mode is simply the value that repeats the most. For grouped data, formulas are provided to calculate the mode using the median, mean, class intervals and frequencies. Examples are given to demonstrate calculating the mode for grouped data. The document also lists some merits and shortcomings of the mode as a measure of central tendency.
The range is the simplest measure of variability, defined as the difference between the highest and lowest values in a data set. It is quick to calculate but does not provide a full picture of the data distribution and can be strongly influenced by outliers. Other measures of variability include the average deviation, which calculates the average amount each score deviates from the mean, and the interquartile range, which is less influenced by outliers than the range. The interquartile range only considers data between the first and third quartiles and ignores half the data points.
This document defines and explains several common measures of dispersion used in statistics including range, mean absolute deviation, variance, standard deviation, and coefficient of variation. Range is the difference between the highest and lowest values. Mean absolute deviation measures the average distance between values and the mean. Variance and standard deviation both measure how spread out numbers are by taking the average of the squared distances from the mean, with standard deviation being the square root of variance. Coefficient of variation expresses standard deviation as a percentage of the mean to allow comparison between data sets with different means.
This document provides definitions and explanations of key statistical concepts including:
1. Statistics is defined as the science of collecting, classifying, presenting, and interpreting data. Central tendency measures like mean, median, and mode are used to summarize data.
2. Measures of dispersion like range, interquartile range, mean deviation, and standard deviation describe how spread out the data is from the central tendency. Standard deviation is the most accurate measure as it considers both the deviation from the mean and the mathematical signs.
3. Examples are provided to demonstrate calculating the mean, median, mode, and standard deviation for both ungrouped and grouped data series. The standard deviation provides the best estimation of the population mean when
Dr. R.K. Rao presented a seminar on standard deviation. The seminar covered the definition of standard deviation as the positive square root of the arithmetic mean of the squared deviations from the mean. It discussed various methods for calculating standard deviation for individual data series, discrete series, and grouped series. The seminar also reviewed the uses and merits of standard deviation as a statistical measure of dispersion.
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
Standard deviation measures how dispersed data values are from the average. It is the most reliable measure of dispersion and shows the average distance of each data point from the mean. While it is more difficult to calculate than other measures, standard deviation provides important information about how concentrated or spread out the data is. The presentation defines standard deviation, lists its merits and demerits, and shows how to calculate it for both populations and samples.
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.
This document discusses measures of central tendency including mean, median, and mode. It provides definitions and formulas for calculating each measure from both grouped and ungrouped data. For mean, it is the sum of all values divided by the number of values. Median is the middle value when values are arranged in order. Mode is the most frequently occurring value. The document also discusses requirements for a good measure of central tendency and provides examples calculating the measures from sample medical data sets to illustrate their use and assess skewness.
Topic: Variance
Student Name: Sonia Khan
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
This document discusses various measures of central tendency including the mean, median, and mode. It defines each measure and provides examples of how to calculate each from both ungrouped and grouped data. The mean is the average value and is calculated by summing all values and dividing by the total number of values. The median is the middle value when values are arranged in order and divides the data set in half. The mode is the most frequently occurring value.
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the sum of all values divided by the number of values and is the most widely used measure. The median is the middle value when data is arranged from lowest to highest. The mode is the value that occurs most frequently. Examples are given demonstrating how to calculate each measure for both individual values and grouped data.
This document defines mean or average deviation and provides information about calculating it. Mean deviation is the average of the absolute differences between each value in a data set and the mean. It is easier to understand and calculate than other measures of variation. Mean deviation is less affected by extreme observations than other measures. It is frequently used to analyze the distribution of personal wealth by considering both the rich and poor. The document outlines the steps to calculate mean deviation for individual, discrete, and continuous data series.
The document defines and provides examples for calculating the coefficient of variation, which is a measure used to compare the dispersion of data sets. It gives the formula for coefficient of variation as the standard deviation divided by the mean, expressed as a percentage. Two examples are shown comparing the stability of prices between two cities and production between two manufacturing plants, with the data set having the lower coefficient of variation considered more consistent or stable.
One of the three points that divide a data set into four equal parts. Or the values that divide data into quarters. Each group contains equal number of observations or data. Median acts as base for calculation of quartile.
The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population.
The document discusses various measures of central tendency and dispersion used in statistical analysis. It defines measures of central tendency like arithmetic mean, median and mode, and provides their formulas and properties. It also discusses measures of dispersion such as range, mean deviation, standard deviation, variance and their characteristics. The document provides examples and steps to calculate various averages and measures of dispersion for a given data set.
The document discusses various techniques for summarizing quantitative and categorical data in statistics. It describes measures of central tendency like mean, median and mode, as well as measures of variability such as range, variance and standard deviation. It also discusses derived scores, standard scores, frequency polygons, histograms, stem and leaf plots, the normal curve, correlation, frequency tables, bar graphs and pie charts as common techniques for summarizing different types of data. Worked examples are provided for finding descriptive statistics measures and visualizing data distribution using graphs and tables.
This document defines and provides examples for calculating the mode of data sets. It explains that the mode is the value that occurs most frequently in a data set. For ungrouped data, the mode is simply the value that repeats the most. For grouped data, formulas are provided to calculate the mode using the median, mean, class intervals and frequencies. Examples are given to demonstrate calculating the mode for grouped data. The document also lists some merits and shortcomings of the mode as a measure of central tendency.
The range is the simplest measure of variability, defined as the difference between the highest and lowest values in a data set. It is quick to calculate but does not provide a full picture of the data distribution and can be strongly influenced by outliers. Other measures of variability include the average deviation, which calculates the average amount each score deviates from the mean, and the interquartile range, which is less influenced by outliers than the range. The interquartile range only considers data between the first and third quartiles and ignores half the data points.
This document defines and explains several common measures of dispersion used in statistics including range, mean absolute deviation, variance, standard deviation, and coefficient of variation. Range is the difference between the highest and lowest values. Mean absolute deviation measures the average distance between values and the mean. Variance and standard deviation both measure how spread out numbers are by taking the average of the squared distances from the mean, with standard deviation being the square root of variance. Coefficient of variation expresses standard deviation as a percentage of the mean to allow comparison between data sets with different means.
This document provides definitions and explanations of key statistical concepts including:
1. Statistics is defined as the science of collecting, classifying, presenting, and interpreting data. Central tendency measures like mean, median, and mode are used to summarize data.
2. Measures of dispersion like range, interquartile range, mean deviation, and standard deviation describe how spread out the data is from the central tendency. Standard deviation is the most accurate measure as it considers both the deviation from the mean and the mathematical signs.
3. Examples are provided to demonstrate calculating the mean, median, mode, and standard deviation for both ungrouped and grouped data series. The standard deviation provides the best estimation of the population mean when
Dr. R.K. Rao presented a seminar on standard deviation. The seminar covered the definition of standard deviation as the positive square root of the arithmetic mean of the squared deviations from the mean. It discussed various methods for calculating standard deviation for individual data series, discrete series, and grouped series. The seminar also reviewed the uses and merits of standard deviation as a statistical measure of dispersion.
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, 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.
This document discusses various measures of dispersion used in statistics to quantify how spread out or varied a set of data values are. It defines dispersion as the state of being dispersed or spread out, and explains that measures of dispersion help interpret the variability in data by showing how squeezed or scattered the values are. The document then describes several common measures of absolute and relative dispersion, including range, quartile deviation, mean deviation, standard deviation, and coefficient of variation. For each measure, it provides a definition and formula to calculate it from a raw data set.
The document discusses different measures of central tendency including the mean, median and mode. It provides definitions and formulas for calculating different types of means:
- The arithmetic mean is calculated by summing all values and dividing by the total number of values. It can be calculated using direct or short-cut methods for both individual observations and grouped data.
- Other means include the geometric mean and harmonic mean, which are called special averages.
- The median is the middle value when values are arranged in order. The mode is the value that occurs most frequently.
- Data can be in the form of individual observations, discrete series or continuous series. Formulas are provided for calculating the mean of grouped or ungrouped data
This document defines and explains various measures of dispersion used in statistics, including range, quartile deviation, mean deviation, standard deviation, and Lorenz curve. It provides formulas for calculating each measure and includes examples to demonstrate how to apply the formulas. The key measures discussed are standard deviation, which is considered the most useful and popular, and measures of skewness, which quantify the symmetry of a distribution based on comparing the mean and third central moment.
Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdfRavinandan A P
Biostatistics, Unit-I, Measures of Dispersion, Dispersion
Range
variation of mean
standard deviation
Variance
coefficient of variation
standard error of the mean
Measure of Dispersion, Range, Mean and Standard Deviation, Correlation and Re...Parth Chuahan
It is simply the difference between the maximum value and the minimum value given in a data set. Example: 1, 3,5, 6, 7 => Range = 7 -1= 6
Standard Deviation: The square root of the variance is known as the standard deviation i.e. S.D. = √σ
Mean and Mean Deviation: The average of numbers is known as the mean and the arithmetic mean of the absolute deviations of the observations from a measure of central tendency is known as the mean deviation (also called mean absolute deviation).
There are two main types of dispersion methods in statistics which are:
Absolute Measure of Dispersion
Relative Measure of Dispersion
The most commonly used techniques for investigating the relationship between two quantitative variables are correlation and linear regression. Correlation quantifies the strength of the linear relationship between a pair of variables, whereas regression expresses the relationship in the form of an equation.
This document provides an overview of measures of dispersion, including range, quartile deviation, mean deviation, standard deviation, and variance. It defines dispersion as a measure of how scattered data values are around a central value like the mean. Different measures of dispersion are described and formulas are provided. The standard deviation is identified as the most useful measure as it considers all data values and is not overly influenced by outliers. Examples are included to demonstrate calculating measures of dispersion.
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
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.
This document discusses standard deviation and related statistical concepts. It defines standard deviation as a measure of variability around the mean and explains how to calculate it from both ungrouped and grouped data. It also defines related terms like variance, standard error of the mean, and confidence limits of the mean. Standard deviation is calculated using the formula that sums the squared deviations from the mean, divided by n-1. Standard error is the standard deviation divided by the square root of the sample size, and confidence limits refer to ranges around the mean within which we can be certain the population mean falls.
Dispersion- It is a statistical term that describes the size of the distribution of values expected for a particular variable and can be measured by several different statistics, such as Range, Variance and standard deviation.
Method of Dispersion-A measure of dispersion indicates the scattering of data. It explains the disparity of data from one another, delivering a precise view of their distribution.
Methods of Dispersion.
1.Relative Dispersion
a. Coefficient of Mean Deviation
b. Coefficient of Quartile Deviation
c. Coefficient of Range
d. Coefficient of Variation
2. Absolute Dispersion
a. Range
b. Quartile range
c. Standard deviation
d. Mean Deviation
Range- It is the difference between smallest & largest values in the dataset. Also the relative measure of range is known as Coefficient of Range.
Advantages and disadvantages of Range.
Calculation of Range by different Methods.
b. Quartile Range- The interquartile range of a group of observations is the interval between the values of upper quartile and the lower quartile for that group.
Advantages and Disadvantages of Quartile Range.
Calculation of Quartile Range by different Methods.
c. Standard Deviation- It measures the absolute dispersion (or) variability of a distribution. A small standard deviation means a high degree of uniformity of the observations as well as homogeneity in the series.
Advantages and Disadvantages of Quartile Range.
Calculation of Standard Deviation using.
i) Direct Method
ii) Short-cut Method
iii) Step Deviation Method.
The document discusses measures of central tendency and variability used in statistics. It defines mean, median and mode as the three main measures of central tendency, and how to compute each for both ungrouped and grouped data. For measures of variability, it defines range, variance and standard deviation, and provides examples of computing each for ungrouped and grouped data. The goal is for students to understand and be able to apply these fundamental statistical concepts and calculations.
The document discusses various measures of dispersion used to quantify how data values are spread around the average value. It describes measures such as range, interquartile range, mean deviation, standard deviation, variance, and coefficient of variation. Standard deviation is highlighted as the most important measure of dispersion as it is widely used and capable of further algebraic treatment. Different methods for calculating standard deviation for individual series, discrete series, and continuous series are provided along with examples. The key properties and appropriate uses of each measure are also outlined.
This document discusses various measures of dispersion used in statistics. It defines dispersion as the lack of uniformity or spread in a data set. The objectives of measuring dispersion are outlined as determining reliability of averages, comparing variability between data sets, and facilitating other statistical measures. Common measures of dispersion discussed include range, quartile deviation, mean deviation, standard deviation, and variance. Formulas and calculations for each measure are provided. The properties of a good measure of dispersion and different methods of calculating standard deviation are also summarized.
OBJECTIVES:
Run the test of hypothesis for mean difference using paired samples. Construct a confidence interval for the difference in population means using paired samples.
Observation of interest will be the difference in the readings
before and after intervention called paired difference observation.
Paired t test:
A paired t-test is used to compare two means where you have two samples in which observations in one sample can be paired with observations in the other sample.
Examples of where this might occur are:
Before-and-after observations on the same subjects (e.g. students’ test
results before and after a particular module or course).
A comparison of two different methods of measurement or two different treatments where the measurements/treatments are applied to the same subjects (e.g. blood pressure measurements using a sphygmomanometer and a dynamap).
When there is a relationship between the groups, such as identical twins.
This test is concerned with the pair-wise differences
between sets of data.
This means that each data point in one group has a related data point in the other group (groups always have equal numbers).
ASSUMPTIONS:
The sample or samples are randomly selected
The sample data are dependent
The distribution of differences is approximately normally
distributed.
Note: The under root is onto the entire numerator and denominator, so you should take the root after solving it entirely
where “t” has (n-1) degrees of freedom and “n” is
the total number of pairs.
The document discusses referencing and citation styles. It provides definitions of citations and explains their purposes, which include avoiding plagiarism and allowing readers to verify sources. The document outlines several common referencing styles like APA, MLA, Chicago and their origins. It also compares the key differences between APA and MLA formats for formatting papers, in-text citations, references, and citing various sources like books, websites, social media posts etc. Finally, it discusses patterns of in-text citations using ibid and loc. cit. and how to add and customize footnotes.
The document describes Robert Glaser's basic model of teaching which includes five components: instructional objectives, entering behavior, instructional procedures, performance assessment, and feedback loops. The model shows how performance assessment feeds back to each component to improve the teaching process. The components are then defined in more detail, with entering behavior describing students' prior knowledge and skills, instructional procedures outlining the teaching methods used, and performance assessment evaluating how well students achieved the objectives.
- Introduction skills are used to connect students' prior knowledge to new knowledge being taught through questions, statements, and teaching aids.
- A micro-teaching lesson plan format is provided that includes objectives, components, pupil-teacher statements, student responses, and evaluation.
- The purpose of introduction skills is to motivate students and build their interest and attention in the lesson through properly extending terminology and chaining ideas.
- This document discusses internal and external evaluations of projects and programs.
- Internal evaluations are carried out by project team members, while external evaluations are done by those outside the project team.
- Both types of evaluations have advantages and disadvantages - internal evaluations have better implementation understanding but less impartiality, while external evaluations have greater impartiality but less understanding of implementation issues.
Post init hook in the odoo 17 ERP ModuleCeline George
In Odoo, hooks are functions that are presented as a string in the __init__ file of a module. They are the functions that can execute before and after the existing code.
How to Create a Stage or a Pipeline in Odoo 17 CRMCeline George
Using CRM module, we can manage and keep track of all new leads and opportunities in one location. It helps to manage your sales pipeline with customizable stages. In this slide let’s discuss how to create a stage or pipeline inside the CRM module in odoo 17.
How to Create User Notification in Odoo 17Celine George
This slide will represent how to create user notification in Odoo 17. Odoo allows us to create and send custom notifications on some events or actions. We have different types of notification such as sticky notification, rainbow man effect, alert and raise exception warning or validation.
Decolonizing Universal Design for LearningFrederic Fovet
UDL has gained in popularity over the last decade both in the K-12 and the post-secondary sectors. The usefulness of UDL to create inclusive learning experiences for the full array of diverse learners has been well documented in the literature, and there is now increasing scholarship examining the process of integrating UDL strategically across organisations. One concern, however, remains under-reported and under-researched. Much of the scholarship on UDL ironically remains while and Eurocentric. Even if UDL, as a discourse, considers the decolonization of the curriculum, it is abundantly clear that the research and advocacy related to UDL originates almost exclusively from the Global North and from a Euro-Caucasian authorship. It is argued that it is high time for the way UDL has been monopolized by Global North scholars and practitioners to be challenged. Voices discussing and framing UDL, from the Global South and Indigenous communities, must be amplified and showcased in order to rectify this glaring imbalance and contradiction.
This session represents an opportunity for the author to reflect on a volume he has just finished editing entitled Decolonizing UDL and to highlight and share insights into the key innovations, promising practices, and calls for change, originating from the Global South and Indigenous Communities, that have woven the canvas of this book. The session seeks to create a space for critical dialogue, for the challenging of existing power dynamics within the UDL scholarship, and for the emergence of transformative voices from underrepresented communities. The workshop will use the UDL principles scrupulously to engage participants in diverse ways (challenging single story approaches to the narrative that surrounds UDL implementation) , as well as offer multiple means of action and expression for them to gain ownership over the key themes and concerns of the session (by encouraging a broad range of interventions, contributions, and stances).
Brand Guideline of Bashundhara A4 Paper - 2024khabri85
It outlines the basic identity elements such as symbol, logotype, colors, and typefaces. It provides examples of applying the identity to materials like letterhead, business cards, reports, folders, and websites.
Cross-Cultural Leadership and CommunicationMattVassar1
Business is done in many different ways across the world. How you connect with colleagues and communicate feedback constructively differs tremendously depending on where a person comes from. Drawing on the culture map from the cultural anthropologist, Erin Meyer, this class discusses how best to manage effectively across the invisible lines of culture.
8+8+8 Rule Of Time Management For Better ProductivityRuchiRathor2
This is a great way to be more productive but a few things to
Keep in mind:
- The 8+8+8 rule offers a general guideline. You may need to adjust the schedule depending on your individual needs and commitments.
- Some days may require more work or less sleep, demanding flexibility in your approach.
- The key is to be mindful of your time allocation and strive for a healthy balance across the three categories.
2. • The concept of standard deviation was first introduced by Karl Pearson in 1893.
• Karl Pearson after observing all these things has given us a more scientific formula for calculating or measuring
dispersion. While calculating SD we take deviations of individual observations from their AM and then
each squares. The sum of the squares is divided by the Total number of observations. The square root of
this sum is knows as standard deviation.
• The standard deviation is the most useful and the most popular measure of dispersion. It is always calculated
from the arithmetic mean, median and mode is not considered.
• मानक विचलन की अिधारणा सबसे पहले 1893 में कालल वपयसलन ने पेश की थी। इन सभी बातों के अिलोकन के बाद कालल वपयसलन ने हमें फैलाि की गणना करने या मापने के वलए अवधक िैज्ञावनक सूत्र
वदया है। एसडी की गणना करते समय हम अपने एएम और वफर प्रत्येक िगों से व्यविगत विप्पवणयों के विचलन लेते हैं। िगों का योग विप्पवणयों की कुल संख्या से विभावित है। इस रावश का िगलमूल मानक
विचलन के रूप में िाना िाता है। मानक विचलन फैलाि का सबसे उपयोगी और सबसे लोकवप्रय उपाय है।
• इसकी गणना हमेशा अंकगवणतीय माध्य, मावध्यका और विधा से नहीं की िाती है।
Standard Deviation
4
3. .
Standard deviation = 𝜎=
𝑥 𝑖 -𝑥 2
𝑛
or =
𝑑2
𝑛 𝑤ℎ𝑒𝑟𝑒 𝑑 = 𝑥𝑖 −𝑥
𝑥𝑖=value of the variable of observation,
𝑥= arithmetic mean
𝑛= total number of observations.
DIRECT METHOD
7. S.D. of Continues Series can be calculated by any one of the methods discussed
for discrete frequency distribution But Step Deviation Method is mostly used.
Standard deviation=𝜎 =
𝑛
𝑓𝑑2
− f𝑑
𝑛
2
× 𝑖
Where𝑖 = common classinterval,
𝑑 = 𝒙−𝑨,
𝒊
𝐴 = is assumedmean
𝑓 = f is the respectivefrequency.
9. • Calculation is difficult not as easier as Range and QD
• It always depends onAM
• Extreme items gain great importance
The formula of SD is =
𝑑2
𝑛
Problem: Calculate Standard Deviation of the following series
X – 40, 44, 54, 60, 62, 64, 70, 80, 90, 96
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