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subject: Square Of Standard Deviation [print this page]

Standard deviation is the statistical analysis of data, in which it is the measure of the variability or spread of the data set. Square of standard deviation is nothing but the value of variance. The standard deviation( 'sigma') is the square of the variance. This is done because the standard deviation may have the value in negative. The variance value will be always in positive so that only the standard deviation values are squared. Here some of the examples for the square of the standard deviation.

Definition on Square of Standard Deviation

Definition of standard deviation:

Standard Deviation is the measure or determination of describing the variability of the spread of the Data set It is take the measure for the average of the given numbers in the Data set. Standard Deviation is given by the square root for the sum of the total squared mean deviation value and it is divided by the total number of values subtracted by one.

Mean value is to be calculated for finding the standard deviation

'barx = (sum_(K=1) ^n (x_k))/N'

Formula for measuring standard deviation,

'sigma' =' sqrt((sum_(K=1) ^n (x - barx)) / (n-1))'

Where 'sigma'is the statistical variable, which is called for standard deviation.

Taking square for the sigma to calculate the square of standard deviation, Then the formula will be,

'sigma^2' =' (sum_(K=1) ^n (x - barx)) / (n-1)'

This is also called as the variance.

Steps for Measuring the Square of Standard Deviation:

Measure the mean value for the given data set from the mean formula.

Calculate the mean difference value to calculate the mean deviation.

Take the square for the mean difference to measure the mean deviation.

By using the mean deviation calculate the standard deviation from the formula.

Take the square for the value measured in the standard deviation

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Example Problems on Square of Standard Deviation:

Measure the square of standard deviation for the following data set. 556,563,565,568

Solution:

Mean: Measuring the value for mean

'barx = (sum_(K=1) ^n (x_k))/N'

'= (556+563+565+568)/ 4'

'= 2252/ 4'

'= 563'

Standard deviation: Measure the standard deviation using the formula,

'sigma' =' sqrt((sum_(K=1) ^n (x - barx)) / (n-1))'

= 'sqrt(((556-563)^2+(563-563)^2+(565-563)^2+(568-563)^2) / (4-1))'

= 'sqrt(78/3)'

= 'sqrt(26)'

= 5.0990195135928

Square of standard deviation: Take the square for the standard deviation

'sigma^2 =( 5.0990195135928 ) ^2'

'sigma^2 = 26'

Practice Problems on Square of Standard Deviation:

1. Measure the square of standard deviation for the given data. 934, 936, 938,937,939

Answer: Square of standard deviation = 3.7

2. Measure the square of standard deviation for the given data. 676, 683, 685, 688.

Answer: Square of standard deviation = 26

3. Measure the square of standard deviation for the given data. 350, 310, 325, 319,

Answer: Square of standard deviation = 294

by: nitinp

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