QT1 - 03 - Measures of Central Tendency

Measures of Central Tendency and Dispersion Q U A N T T E C H I N T E U Q I A S E V I T 1 0 S

Contents ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Relative Frequency Distribution ,[object Object],[object Object]

Let us compare two sets of data mid term and end term marks for same students ,[object Object],[object Object],[object Object]

Summary Statistics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Measure of Central Tendency ,[object Object],[object Object],[object Object],[object Object]

Measure of Dispersion ,[object Object],[object Object],[object Object],[object Object]

Skewness ,[object Object],[object Object]

Kurtosis ,[object Object],[object Object],[object Object]

Measures of Central Tendency ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Arithmetic Mean ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],X = X =

Arithmetic Mean of Grouped Data ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],X = X =

Arithmetic Mean ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The weighted mean ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Weighted Mean <=> Grouped Data ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],The Weight is logically and mathematically equivalent to midpoint of the class. Since we assume that all members of the class have the same value So lower class boundary, upper class boundary and midpoint are all same !! X = X =

Median ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Median of Grouped Data ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Median ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Mode ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Measures of Dispersion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Range ,[object Object],[object Object],[object Object]

Fractile / Quartile / Percentile ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Interquartile Range ,[object Object],25% below this 75% below this

Variance & Standard Deviation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Variance & Standard Deviation ,[object Object],[object Object],[object Object],Here we use the formula provided by the spreadsheet

Significance of s ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Variance & Standard Deviation for Grouped Data ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Variance & Standard Deviation for Grouped Data ,[object Object],[object Object],[object Object]

Variance : Population and Sample ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Suspiciously similar but not quite ... why is this ? Population Statistics Sample Statistics

Population and Sample ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Population & Sample Formulae are different in a Spreadsheet sample population

Last two statistics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

QT1 - 03 - Measures of Central Tendency

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QT1 - 03 - Measures of Central Tendency