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subject: Efficiency Variance Formula [print this page]

Introduction to efficiency variance formula:

This article is related the efficiency variance formula. Variance is the one of statistical distribution and the parameter to define the probability distribution. Variance is a squared deviation of variable from the mean. The variance of variable units is a squared unit of variable. Variance is non negative because values is positive or zero. Consider the steps for finding the efficiency variance.

Step to Find Variance of the Values - Efficiency Variance Formula :

Consider the following steps will be help to find out the efficiency variance. First find out the mean or expected value of the given data after that calculate the variance.

Step 1: Let take the values.

Step 2: Calculate the expected values.

Mean or expected value' (barx)' = sum of the values/total number of data.

Step 3: Finally find out the variance use the following efficiency variance formula.

Efficiency Variance '(sigma^2)' ='(sum ()(x-barx)^2)/n'

Following problems ralated to variation of a data:

Example 1: Find the variance of following values 5, 1, 8,6,15

Solution:

Mean '(barx)' = Some of the data set / total number of data

Mean = 5+1+8+6+15 / 5

Mean = 35 / 5

Mean = 7

Next consider efficiency variance formula

Efficiency Variance '(sigma^2)' = '(sum ()(x-barx)^2)/n '

Find out the '(x-barx)^2' let mean '( barx)' = 7

'( 5 - 7)^2' = '(-2)^2' = 4

'( 1-7)^2' = '(-6)^2' = 36

'(8- 7)^2' = 1

'( 6 - 7)^2' = 1

'(15 -7)^2' = 64

Variance 'sigma^2' ='(sum ()(x-barx)^2)/n'

'sigma^2' = 4+36+1+1+64 / 5

Variance 'sigma^2' = 106 / 5

Variance = 21.2

Example 2: To find out variance of the given 2,8,4,6,12

Solution :

Mean '(barx)' = Some of the data set / total number of data

Mean = 2+8+4+6+10 / 5

Mean = 30 / 5

Mean = 6

Efficiency Variance 'sigma^2' ='(sum ()(x-barx)^2)/n'

find the '(x-barx)^2'

'( 2 - 6)^2' =' (-4)^2' = 16

'( 8 - 6)^2' = 4

'(4-6)^2' = 4

'( 6 - 6)^2' = 0

'(12 - 6)^2' = 36

Variance 'sigma^2' ='(sum ()(x-barx)^2)/n'

'sigma^2' = 16+4+4+0+36 / 5

Variance 'sigma^2' = 60 / 5

Variance = 12

Practice Problem Related to Variance - Efficiency Variance Formula:

Problem 1: Solve variation of the given data 5, 3,4,2,1

Answer: Variance = 2

Problem 2: To Calculate the variance of the data 4,6,8,12,15

Answer: Variance = 16

by: Omkar Nayak

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