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This power point explains the methods of median calculation in individual series, discrete series and continuous series.

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Skewness

1) Skewness is a measure of the lack of symmetry in a distribution. It indicates if the distribution is balanced around the mean.
2) There are several ways to calculate skewness including using the mean, median, mode, quartiles, or moments. Positive skewness means the mean is greater than the median, while negative skewness means the mean is less than the median.
3) Examples show how to calculate skewness using different formulas and interpret if a distribution is positively, negatively, or symmetrically skewed based on the resulting skewness value.

Median & mode

This document provides information about various statistical measures of central tendency including the median, mode, and quartiles. It defines each measure and provides examples of how to calculate them from both grouped and ungrouped data sets. Formulas are given for calculating the median, quartiles, deciles, and percentiles for grouped data. The mode is defined as the value that occurs most frequently in a data set, and a formula is provided for calculating it from grouped frequency distributions.

quartile deviation: An introduction

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.

Standard deviation quartile deviation

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.

Median

The median is the middlemost score when values are arranged from lowest to highest. It divides the data set into two equal groups, with scores above and below the median. The median is not affected by extreme values and can be used when the mean would be skewed. To find the median of ungrouped data, arrange values from highest to lowest and take the middle value. For grouped data, use the formula Median = Ll + cfb/f, where Ll is the lower limit of the class containing N/2, cfb is the cumulative frequency below the assumed median, and f is the corresponding frequency.

Coefficient of variation

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.

Rank correlation

This document discusses rank correlation and Spearman's coefficient of rank correlation. Rank correlation is used to measure the relationship between two variables when only rank orders are available rather than exact numerical values. Spearman's coefficient of rank correlation (rs) is calculated using the differences in ranks between two data sets. A higher rs value indicates a closer relationship between the rankings. The document provides two examples to demonstrate calculating rs and interpreting the results.

Correlation Analysis

This document discusses correlation and different types of correlation analysis. It defines correlation as a statistical analysis that measures the relationship between two variables. There are three main types of correlation: (1) simple and multiple correlation based on the number of variables, (2) linear and non-linear correlation based on the relationship between variables, and (3) positive and negative correlation based on the direction of change between variables. The degree of correlation is measured using correlation coefficients that range from -1 to +1. Common methods to study correlation include scatter diagrams and Karl Pearson's coefficient of correlation.

Skewness

1) Skewness is a measure of the lack of symmetry in a distribution. It indicates if the distribution is balanced around the mean.
2) There are several ways to calculate skewness including using the mean, median, mode, quartiles, or moments. Positive skewness means the mean is greater than the median, while negative skewness means the mean is less than the median.
3) Examples show how to calculate skewness using different formulas and interpret if a distribution is positively, negatively, or symmetrically skewed based on the resulting skewness value.

Median & mode

This document provides information about various statistical measures of central tendency including the median, mode, and quartiles. It defines each measure and provides examples of how to calculate them from both grouped and ungrouped data sets. Formulas are given for calculating the median, quartiles, deciles, and percentiles for grouped data. The mode is defined as the value that occurs most frequently in a data set, and a formula is provided for calculating it from grouped frequency distributions.

quartile deviation: An introduction

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.

Standard deviation quartile deviation

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.

Median

The median is the middlemost score when values are arranged from lowest to highest. It divides the data set into two equal groups, with scores above and below the median. The median is not affected by extreme values and can be used when the mean would be skewed. To find the median of ungrouped data, arrange values from highest to lowest and take the middle value. For grouped data, use the formula Median = Ll + cfb/f, where Ll is the lower limit of the class containing N/2, cfb is the cumulative frequency below the assumed median, and f is the corresponding frequency.

Coefficient of variation

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.

Rank correlation

This document discusses rank correlation and Spearman's coefficient of rank correlation. Rank correlation is used to measure the relationship between two variables when only rank orders are available rather than exact numerical values. Spearman's coefficient of rank correlation (rs) is calculated using the differences in ranks between two data sets. A higher rs value indicates a closer relationship between the rankings. The document provides two examples to demonstrate calculating rs and interpreting the results.

Correlation Analysis

This document discusses correlation and different types of correlation analysis. It defines correlation as a statistical analysis that measures the relationship between two variables. There are three main types of correlation: (1) simple and multiple correlation based on the number of variables, (2) linear and non-linear correlation based on the relationship between variables, and (3) positive and negative correlation based on the direction of change between variables. The degree of correlation is measured using correlation coefficients that range from -1 to +1. Common methods to study correlation include scatter diagrams and Karl Pearson's coefficient of correlation.

Arithmetic Mean, Geometric Mean, Harmonic Mean

This document discusses different types of means - arithmetic mean, geometric mean, and harmonic mean. It provides definitions and formulas for calculating each type of mean between two numbers. It also presents examples of calculating means and solving word problems involving arithmetic progressions and geometric/harmonic progressions. The key information covered includes definitions of arithmetic, geometric, and harmonic means; formulas for calculating each mean; and examples of applying the concepts to word problems.

To find mode ppt

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.

Measures of Central Tendency

This document discusses various measures of central tendency including arithmetic mean, median, and mode. It provides definitions and formulas for calculating each measure along with examples using raw data and grouped data. The three main points covered are:
1. Measures of central tendency (mean, median, mode) calculate the central or typical value in a data set and are used to describe data distributions.
2. The arithmetic mean is the sum of all values divided by the number of values, the median is the middle number when values are arranged in order, and the mode is the most frequent value.
3. Formulas and methods are provided for calculating each measure using both raw ungrouped data as well as grouped frequency distribution data

Measures of variability

This document defines and provides examples of key statistical concepts used to describe and analyze variability in data sets, including range, variance, standard deviation, coefficient of variation, quartiles, and percentiles. It explains that range is the difference between the highest and lowest values, variance is the average squared deviation from the mean, and standard deviation describes how distant scores are from the mean on average. Examples are provided to demonstrate calculating these measures from data sets and interpreting what they indicate about the spread of scores.

Relationship among mean, median and mode

This document discusses the relationship between mean, median, and mode for different types of distributions. It provides formulas for relating these measures in moderately skewed distributions. An example is given of a symmetrical distribution where the mean, median, and mode are equal. The distribution's frequencies are used to calculate each measure and confirm the distribution is symmetrical since all three values are the same.

Arithmetic mean

This document provides information about various measures of central tendency including arithmetic mean, median, mode, and quartiles. It defines each measure and provides formulas and examples for calculating them for different types of data series, including individual, discrete, frequency distribution, and cumulative frequency series. Formulas are given for calculating the arithmetic mean, median, quartiles, and mode of a data set, along with examples worked out step-by-step. Advantages and disadvantages of each measure are also discussed.

Skewness and kurtosis

This document discusses skewness and kurtosis, which are statistical measures of the distribution of a variable. Skewness measures the asymmetry of a distribution and can be positive, negative, or zero. Kurtosis measures the peakedness of a distribution and can be platykurtic (flatter than normal), mesokurtic (normal), or leptokurtic (more peaked than normal). The document provides formulas for calculating skewness using Pearson's, Bowley's, and Kelly's coefficients as well as calculating kurtosis using the fourth standardized moment. Examples of applying skewness and kurtosis to determine if a variable's distribution or resource use is normal are also discussed.

Arithmetic mean

This document discusses measures of central tendency, specifically the arithmetic mean. It provides examples and step-by-step solutions for calculating the arithmetic mean of individual data sets, discrete series with frequencies, and continuous series grouped into class intervals. For continuous series, the formula uses the mid-point of each class interval. The document also includes one problem that requires solving for a missing frequency given the calculated arithmetic mean.

Standard deviation :grouped data/Continuous data

Study material for S.E.E Students
Secondary Education Board, Nepal
Optional Mathematics: Statistics

Stats measures of location 1

This document defines and provides examples of three common measures of central tendency: the mean, median, and mode. The mean is the average found by adding all data points and dividing by the total number. The median is the middle number when data points are ordered from lowest to highest. The mode is the most frequently occurring data point in a dataset. Examples are provided to demonstrate how to calculate each measure using sample data sets.

Skewness.ppt

This document discusses concepts related to skewness and kurtosis of a distribution. It defines skewness as a measure of asymmetry of a distribution, and explains that a distribution is skewed if the mean, median and mode do not coincide. It also defines kurtosis as a measure of peakedness of a distribution, and classifies distributions as leptokurtic (peaked), mesokurtic or platykurtic (flat) based on the shape of their peaks. The document then discusses various statistical measures to quantify skewness and kurtosis, including Karl Pearson's coefficient of skewness, Bowley's coefficient of skewness, Kelly's coefficient of skewness, Karl Pearson

Mode

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.

Calculation of arithmetic mean

The document discusses different methods to calculate arithmetic mean from various types of data series.
It explains the direct and shortcut methods to find the arithmetic mean for individual, discrete and continuous data series.
For individual series, the direct method sums all data points and divides by the total number of data points. The shortcut method assumes a mean, calculates the differences from the assumed mean, and finds the mean as the assumed mean plus the sum of the differences divided by the total number of data points.

Measures of central tendency mean

This document provides an introduction to measures of central tendency in statistics. It defines measures of central tendency as statistical measures that describe the center of a data distribution. The three most commonly used measures are the mean, median, and mode. The document focuses on explaining the arithmetic mean in detail, including how to calculate the mean from individual data series, discrete data series, and continuous data series using different methods. It also discusses weighted means, combined means, and the relationship between the mean, median and mode. The objectives and advantages and disadvantages of the mean are provided.

Measures of central tendency

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.

Skewness & Kurtosis

This document discusses skewness and kurtosis in a financial context. It defines skewness as a measure of asymmetry in a distribution, with positive skewness indicating a long right tail and negative skewness a long left tail. Kurtosis is defined as a measure of the "peakedness" of a probability distribution, with positive excess kurtosis indicating flatness/long fat tails and negative excess kurtosis indicating peakedness. Formulas are provided for calculating skewness and kurtosis from a data set. Examples of positively and negatively skewed distributions are given to illustrate these concepts.

Measure of Central Tendency

The document discusses different measures of central tendency including the mean, median, and mode. The mean is the average value calculated by adding all values and dividing by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequently occurring value in the data set. The document provides examples of calculating each measure and discusses their advantages and disadvantages.

Quartile in Statistics

The document discusses quartiles, which divide a data set into four equal parts. The first quartile contains the smallest 25% of values, the second quartile contains values between the 25th and 50th percentiles, the third quartile contains values between the 50th and 75th percentiles, and the fourth quartile contains the largest 25% of values. Formulas are provided for calculating the lower quartile (Q1), median (Q2), and upper quartile (Q3). The quartile deviation is defined as half the distance between Q3 and Q1, while the interquartile range is the full distance between Q3 and Q1. Examples are given to illustrate quartile calculations.

Median

The median of a dataset is the middle value when the observations are arranged in ascending order. It is the value below which 50% of the observations lie. For an odd number of observations, the median is the middle value. For an even number, the median is the average of the two middle values. The median can be calculated for both grouped and ungrouped data using different formulas depending on whether the data is grouped by value or range. Examples are provided to demonstrate calculating the median for different types of datasets.

mean median mode

This document discusses measures of central tendency including the mean, median, and mode. It defines each measure and provides examples of calculating them using individual, discrete, and continuous data series. The mean is the average value obtained by dividing the sum of all values by the total number of values. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently. Formulas and examples are given for calculating each measure using different types of data sets. Merits and demerits of each measure are also outlined.

Group 3 measures of central tendency and variation - (mean, median, mode, ra...

This document discusses various measures of central tendency and variation. It defines central tendency as indicating where the center of a distribution tends to be, and mentions that measures of central tendency answer whether scores are generally high or low. It then discusses specific measures of central tendency - the mean, median, and mode - and how to calculate each one for both ungrouped and grouped data. It also discusses other measures of variation like range and standard deviation, and how to compute standard deviation for ungrouped and grouped data.

Measures of Central Tendency - Biostatstics

The current presentation will guide you for the basic bio-statistics. Measures of Central Tendency...

Arithmetic Mean, Geometric Mean, Harmonic Mean

This document discusses different types of means - arithmetic mean, geometric mean, and harmonic mean. It provides definitions and formulas for calculating each type of mean between two numbers. It also presents examples of calculating means and solving word problems involving arithmetic progressions and geometric/harmonic progressions. The key information covered includes definitions of arithmetic, geometric, and harmonic means; formulas for calculating each mean; and examples of applying the concepts to word problems.

To find mode ppt

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.

Measures of Central Tendency

This document discusses various measures of central tendency including arithmetic mean, median, and mode. It provides definitions and formulas for calculating each measure along with examples using raw data and grouped data. The three main points covered are:
1. Measures of central tendency (mean, median, mode) calculate the central or typical value in a data set and are used to describe data distributions.
2. The arithmetic mean is the sum of all values divided by the number of values, the median is the middle number when values are arranged in order, and the mode is the most frequent value.
3. Formulas and methods are provided for calculating each measure using both raw ungrouped data as well as grouped frequency distribution data

Measures of variability

This document defines and provides examples of key statistical concepts used to describe and analyze variability in data sets, including range, variance, standard deviation, coefficient of variation, quartiles, and percentiles. It explains that range is the difference between the highest and lowest values, variance is the average squared deviation from the mean, and standard deviation describes how distant scores are from the mean on average. Examples are provided to demonstrate calculating these measures from data sets and interpreting what they indicate about the spread of scores.

Relationship among mean, median and mode

This document discusses the relationship between mean, median, and mode for different types of distributions. It provides formulas for relating these measures in moderately skewed distributions. An example is given of a symmetrical distribution where the mean, median, and mode are equal. The distribution's frequencies are used to calculate each measure and confirm the distribution is symmetrical since all three values are the same.

Arithmetic mean

This document provides information about various measures of central tendency including arithmetic mean, median, mode, and quartiles. It defines each measure and provides formulas and examples for calculating them for different types of data series, including individual, discrete, frequency distribution, and cumulative frequency series. Formulas are given for calculating the arithmetic mean, median, quartiles, and mode of a data set, along with examples worked out step-by-step. Advantages and disadvantages of each measure are also discussed.

Skewness and kurtosis

This document discusses skewness and kurtosis, which are statistical measures of the distribution of a variable. Skewness measures the asymmetry of a distribution and can be positive, negative, or zero. Kurtosis measures the peakedness of a distribution and can be platykurtic (flatter than normal), mesokurtic (normal), or leptokurtic (more peaked than normal). The document provides formulas for calculating skewness using Pearson's, Bowley's, and Kelly's coefficients as well as calculating kurtosis using the fourth standardized moment. Examples of applying skewness and kurtosis to determine if a variable's distribution or resource use is normal are also discussed.

Arithmetic mean

This document discusses measures of central tendency, specifically the arithmetic mean. It provides examples and step-by-step solutions for calculating the arithmetic mean of individual data sets, discrete series with frequencies, and continuous series grouped into class intervals. For continuous series, the formula uses the mid-point of each class interval. The document also includes one problem that requires solving for a missing frequency given the calculated arithmetic mean.

Standard deviation :grouped data/Continuous data

Study material for S.E.E Students
Secondary Education Board, Nepal
Optional Mathematics: Statistics

Stats measures of location 1

This document defines and provides examples of three common measures of central tendency: the mean, median, and mode. The mean is the average found by adding all data points and dividing by the total number. The median is the middle number when data points are ordered from lowest to highest. The mode is the most frequently occurring data point in a dataset. Examples are provided to demonstrate how to calculate each measure using sample data sets.

Skewness.ppt

This document discusses concepts related to skewness and kurtosis of a distribution. It defines skewness as a measure of asymmetry of a distribution, and explains that a distribution is skewed if the mean, median and mode do not coincide. It also defines kurtosis as a measure of peakedness of a distribution, and classifies distributions as leptokurtic (peaked), mesokurtic or platykurtic (flat) based on the shape of their peaks. The document then discusses various statistical measures to quantify skewness and kurtosis, including Karl Pearson's coefficient of skewness, Bowley's coefficient of skewness, Kelly's coefficient of skewness, Karl Pearson

Mode

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.

Calculation of arithmetic mean

The document discusses different methods to calculate arithmetic mean from various types of data series.
It explains the direct and shortcut methods to find the arithmetic mean for individual, discrete and continuous data series.
For individual series, the direct method sums all data points and divides by the total number of data points. The shortcut method assumes a mean, calculates the differences from the assumed mean, and finds the mean as the assumed mean plus the sum of the differences divided by the total number of data points.

Measures of central tendency mean

This document provides an introduction to measures of central tendency in statistics. It defines measures of central tendency as statistical measures that describe the center of a data distribution. The three most commonly used measures are the mean, median, and mode. The document focuses on explaining the arithmetic mean in detail, including how to calculate the mean from individual data series, discrete data series, and continuous data series using different methods. It also discusses weighted means, combined means, and the relationship between the mean, median and mode. The objectives and advantages and disadvantages of the mean are provided.

Measures of central tendency

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.

Skewness & Kurtosis

This document discusses skewness and kurtosis in a financial context. It defines skewness as a measure of asymmetry in a distribution, with positive skewness indicating a long right tail and negative skewness a long left tail. Kurtosis is defined as a measure of the "peakedness" of a probability distribution, with positive excess kurtosis indicating flatness/long fat tails and negative excess kurtosis indicating peakedness. Formulas are provided for calculating skewness and kurtosis from a data set. Examples of positively and negatively skewed distributions are given to illustrate these concepts.

Measure of Central Tendency

The document discusses different measures of central tendency including the mean, median, and mode. The mean is the average value calculated by adding all values and dividing by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequently occurring value in the data set. The document provides examples of calculating each measure and discusses their advantages and disadvantages.

Quartile in Statistics

The document discusses quartiles, which divide a data set into four equal parts. The first quartile contains the smallest 25% of values, the second quartile contains values between the 25th and 50th percentiles, the third quartile contains values between the 50th and 75th percentiles, and the fourth quartile contains the largest 25% of values. Formulas are provided for calculating the lower quartile (Q1), median (Q2), and upper quartile (Q3). The quartile deviation is defined as half the distance between Q3 and Q1, while the interquartile range is the full distance between Q3 and Q1. Examples are given to illustrate quartile calculations.

Median

The median of a dataset is the middle value when the observations are arranged in ascending order. It is the value below which 50% of the observations lie. For an odd number of observations, the median is the middle value. For an even number, the median is the average of the two middle values. The median can be calculated for both grouped and ungrouped data using different formulas depending on whether the data is grouped by value or range. Examples are provided to demonstrate calculating the median for different types of datasets.

mean median mode

This document discusses measures of central tendency including the mean, median, and mode. It defines each measure and provides examples of calculating them using individual, discrete, and continuous data series. The mean is the average value obtained by dividing the sum of all values by the total number of values. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently. Formulas and examples are given for calculating each measure using different types of data sets. Merits and demerits of each measure are also outlined.

Arithmetic Mean, Geometric Mean, Harmonic Mean

Arithmetic Mean, Geometric Mean, Harmonic Mean

To find mode ppt

To find mode ppt

Measures of Central Tendency

Measures of Central Tendency

Measures of variability

Measures of variability

Relationship among mean, median and mode

Relationship among mean, median and mode

Arithmetic mean

Arithmetic mean

Skewness and kurtosis

Skewness and kurtosis

Arithmetic mean

Arithmetic mean

Standard deviation :grouped data/Continuous data

Standard deviation :grouped data/Continuous data

Stats measures of location 1

Stats measures of location 1

Skewness.ppt

Skewness.ppt

Mode

Mode

Calculation of arithmetic mean

Calculation of arithmetic mean

Measures of central tendency mean

Measures of central tendency mean

Measures of central tendency

Measures of central tendency

Skewness & Kurtosis

Skewness & Kurtosis

Measure of Central Tendency

Measure of Central Tendency

Quartile in Statistics

Quartile in Statistics

Median

Median

mean median mode

mean median mode

Group 3 measures of central tendency and variation - (mean, median, mode, ra...

This document discusses various measures of central tendency and variation. It defines central tendency as indicating where the center of a distribution tends to be, and mentions that measures of central tendency answer whether scores are generally high or low. It then discusses specific measures of central tendency - the mean, median, and mode - and how to calculate each one for both ungrouped and grouped data. It also discusses other measures of variation like range and standard deviation, and how to compute standard deviation for ungrouped and grouped data.

Measures of Central Tendency - Biostatstics

The current presentation will guide you for the basic bio-statistics. Measures of Central Tendency...

Central tendency and Variation or Dispersion

The document discusses various measures of central tendency and variation. It defines mean, median and mode as the three main measures of central tendency. It provides formulas and examples to calculate mean, median and mode for discrete, continuous and grouped data. The document also discusses measures of variation such as range and standard deviation. It provides the formula to calculate standard deviation and an example to demonstrate calculating standard deviation for a set of data.

Analysis and interpretation of Assessment.pptx

The document provides information on statistics, frequency distributions, measures of central tendency (mean, median, mode), and how to calculate and interpret them. It defines statistics, descriptive and inferential statistics, and frequency distributions. It outlines the steps to construct a frequency distribution and calculate the mean, median, and mode for both ungrouped and grouped data. Examples are provided to demonstrate calculating each measure of central tendency.

Central tendency

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.

Measures of central tendency

The document provides information about various measures of central tendency including arithmetic mean, median, mode, geometric mean, and harmonic mean. It defines each measure and provides examples of calculating them using data from frequency distributions. The arithmetic mean is the most common average 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. The mode is the most frequent value. The geometric mean is calculated by taking the nth root of the product of n values. The harmonic mean gives the greatest weight to the smallest values and is used to average rates.

statistics 10th (1) (3).pdf

1) The document discusses various measures of central tendency including mean, median, and mode for grouped and ungrouped data. It provides formulas to calculate mean, median, and mode for different data sets.
2) Formulas are given to find the mean, median, and mode of grouped data using class boundaries and frequencies. The direct method and assumed mean method for calculating the mean of grouped data are described.
3) Relationships between mean, median and mode are discussed. The document also covers topics like cumulative frequency, modal class, and finding measures of central tendency for discrete data series.

central tendency.pptx

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

Measures of central tendency.pptx

1. Measures of central tendency include the mean, median, and mode.
2. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged in order. The mode is the value that appears most frequently.
3. For grouped data, the mean is calculated using the sum of the frequency multiplied by the class midpoint divided by the total frequency. The median class is identified which has a cumulative frequency above and below half the total. The mode is the class with the highest frequency.

Measures of Central Tendancy

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 average value and is calculated by summing all values and dividing by the total number of items. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently in a data set. Examples are provided to demonstrate calculating each measure for both grouped and ungrouped data. The advantages and disadvantages of each measure are also briefly discussed.

MEDIAN.pptx

Median
Middle value in a distribution is known as Median.
Calculation of median.
1. Calculation of median in a series of individual observations or Calculation of median for ungrouped data
2. Calculation of median for grouped data
a) Calculation of median in a discrete series.
b) Calculation of median in a continuous series.
c) Calculation of median in unequal class intervals.
d) Calculation of median in open-end classes.
Merits and Demerits of Median.

MEASURES OF CENTRAL TENDENCY

MEASURES OF CENTRAL TENDENCY
(Mean , Median , Mode)
“An average is a single figure that represents the whole group.’’ clark

statistical tools for data analysis mean mode

Statistical tools

Biostatistics community medicine or Psm.pptx

Biostatistics- mean median mode

CAVENDISH COLLEGE LESSON NOTE FOR FIRST TERM ECONOMICS SSS2 UPDATED..docx

The document provides information about measures of central tendency and dispersion from economics lessons at Cavendish College. It defines terms like mean, median, mode, range, variance, and standard deviation. For measures of central tendency, it gives the formulas to calculate each measure and provides an example using exam marks. For measures of dispersion, it similarly defines terms like range, mean deviation, variance, and standard deviation and gives the relevant formulas. It also includes an example using student weights to demonstrate calculating these measures.

Qt notes

This document provides an overview of descriptive statistics and statistical inference. It discusses key concepts such as populations, samples, census surveys, sample surveys, raw data, frequency distributions, measures of central tendency including the arithmetic mean, median, and mode. It provides examples and formulas for calculating averages from both grouped and ungrouped data. The arithmetic mean can be used to find the combined mean of two groups or a weighted mean when values have different levels of importance. The median divides a data set into two equal halves.

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The 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 average and is calculated by adding all values and dividing by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently in the data set. Examples are provided to demonstrate calculating each measure using both raw and grouped data.

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Measure of central tendency

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- 1. Calculation of Median SUBMITTED BY DR. SUNITA OJHA ASSISTANT PROFESSOR SURESH GYAN VIHAR UNIVERSITY
- 2. Median • The median is usually defined as that value which divides a distribution so that equal number of items occur on either side of it. • In other words 50 percent of the observations will be smaller than the median and 50 percent of the observations will be greater than the median. 1. Calculation of median in a series of individual observations: • Arrange the data in the ascending or descending order • Median is located by finding the size of the (n+1/2)th item. 𝑴 = 𝒏 + 𝟏 𝟐 𝒕𝒉 𝒊𝒕𝒆𝒎 M= Median n= number of observations Example 1. Find out the median from the data recorded on the number of clusters per plant in a pulse crop: 10,18, 17, 19, 10, 15, 11, 17, 12
- 3. S. No. Data arranged in ascending order 1 10 2 10 3 11 4 12 5 15 6 17 7 17 8 18 9 19 Median = Size of (n+1)/2 th item = (9+1)2 th item =5th item Median = 15 2. Calculation of median in a discrete series • Data should be arranged in ascending or descending order of magnitude • Find out the cumulative frequencies • Median= size of the (n+1)/2 th item • Find out the (n+1)/2 th item. It can be found by first locating the cumulative frequency which is equal to (n+1)/2 or the next higher to this and then determine the value corresponding to it. This will be the value of median.
- 4. Example 1. Find out the median of the following data No. of angular seeded plants 12 8 17 10 11 16 18 14 6 7 No. of plants 39 33 42 40 47 42 60 50 22 25 No. of angular seeded plants No. of plants Cumulative Frequency 6 22 22 7 25 47 8 33 80 10 40 120 11 47 167 12 39 206 14 50 256 16 42 298 17 42 340 18 60 400 Median = (400+1)/2 th item =200.5th item Median=12
- 5. 3. Calculation of median in a continuous series • While computing the value of the median in a continuous series, first determine the particular class in which the value of the median lies. • Use n/2 as the rankof the median and not (n+1)/2 𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑳 + 𝒏 𝟐 − 𝒄𝒇 𝒇 × 𝒊 L= lower limit of the median class cf= cumulative frequency of the class preceding the median class f=frequency of the median class i= class interval
- 6. No. of grains per earhead classes Frequency Cumulative frequency 5-10 2 2 10-15 27 29 15-20 52 81 20-25 118 199 25-30 57 256 30-35 27 283 35-40 13 296 40-45 4 300 Example 1. Calculate the value of the median from the data recorded on the number of grains per earhead on 300 wheat earhead. Solution: Median= Size of (n/2)th item= 300/2= 150 Median lies in the class=20-25 L=20; n/2= 150; cf=81; i=5; f=118 Median=20+(69/118)*5 =20+2.92 =22.92
- 7. 4. Calculation of median in unequal class- intervals • In unequal class-interval frequencies need not be adjusted to make the class intervals equal and the formula can be used here. 𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑳 + 𝒏 𝟐 − 𝒄𝒇 𝒇 × 𝒊 n/2=70/2= 35 Median= 30+ ((35-21)/10)*10 = 30+(140/10)*10 =30+14 =44 Classes Frequency Cumulative Frequency 0-10 5 5 10-30 16 21 30-60 30 51 60-80 12 63 80-90 6 69 90-100 1 70 Classes Frequency Cumulative Frequency 0-10 5 5 10-20 8 13 20-30 8 21 30-40 10 31 40-50 10 41 50-60 10 51 60-70 6 57 70-80 6 63 80-90 6 69 90-100 1 70
- 8. 5. Calculation of median in open-end classes • Since the median is not affected by the values of extreme ends we are not concerned with the extreme values for the calculation of median in open-end classes. Size of item classes Frequency Cumulative Frequency Less than 10 4 4 10-20 8 12 20-30 14 26 30-40 6 32 40 and above 4 36 Example 1. Calculate the median in open –end series. Solution: 𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑳 + 𝒏 𝟐 − 𝒄𝒇 𝒇 × 𝒊 n/2= 36/2= 18th item Median lies in the class 20-30 Median= 20+((18-12)/14)*10 =24.29
- 9. 6. Graphic Location of Median: • Draw two ogives one by less than method and the other by more than method. • From the point where the two curves intersect draw a perpendicular line to the X- axis. The point on the X-axis will give the median value.