# Measure of variation standard deviation s q n x 2 x 2

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Measure of Variation: Standard deviations=qn(x)2-(x)2n(n-1)Example:Use the short-cut formula to findsof the data 1, 3, 14Step 1:x(x)2112= 1332= 914142= 196x= 18(x)2= 206Step 2:s=sn(x)2-(x)2n(n-1)=s3·(206)-1823·(3-1)
Measure of Variation: Standard deviations=qn(x)2-(x)2n(n-1)Example:Use the short-cut formula to findsof the data 1, 3, 14Step 1:x(x)2112= 1332= 914142= 196x= 18(x)2= 206Step 2:s=sn(x)2-(x)2n(n-1)=s3·(206)-1823·(3-1)=r2946= 7
Measure of Variation: Standard deviationProperties of standard deviation:IThe standard deviation is a measure of variation of all valuesfrom the mean.IThe value of the standard deviationsis usually positive. It iszero, when all the data value are repeated.scan never be a negative number.IThe value of the standard deviationscan increasedramatically with the inclusion of one or more outliers (datavalues far away from all others).IThe units of the standard deviation s are the same as theunits of the original data values.
Remember the notation:PopulationSampleMeanμxStandard deviationσsVarianceσ2s2
Example:Find the standard deviation of the data set (sample)57,58,59,60,61,62,63
Example:Find the standard deviation of the data set (sample)57,58,59,60,61,62,63We use the short-cut formulae:
Example:Find the standard deviation of the data set (sample)57,58,59,60,61,62,63We use the short-cut formulae: Noten= 7.
Example:Find the standard deviation of the data set (sample)57,58,59,60,61,62,63We use the short-cut formulae: Noten= 7.x(x)257572= 324958582= 336459592= 348160602= 360061612= 372162622= 384463632= 3969x= 420(x)2= 25228
Example:Find the standard deviation of the data set (sample)57,58,59,60,61,62,63We use the short-cut formulae: Noten= 7.x(x)257572= 324958582= 336459592= 348160602= 360061612= 372162622= 384463632= 3969x= 420(x)2= 25228s=sn(x)2-(x)2n(n-1)
Example:Find the standard deviation of the data set (sample)57,58,59,60,61,62,63We use the short-cut formulae: Noten= 7.x(x)257572= 324958582= 336459592= 348160602= 360061612= 372162622= 384463632= 3969x= 420(x)2= 25228s=sn(x)2-(x)2n(n-1)=s7·(25228)-42027(7-1)
Example:Find the standard deviation of the data set (sample)57,58,59,60,61,62,63We use the short-cut formulae: Noten= 7.