# How to Calculate Variance ?

How to Find the Sample Variance of a Data Set?

## Sample Variance Calculation

Variance can be defined as the average of the squared differences from the mean. The variance of a set of data that is selected from a statistical population is termed as the sample variance. It is represented using the symbol Ïƒ2 Formula:
Sample Variance = Î£(Xi- X)2 / (N - 1)
Where,
Xi= Ith Element of Sample
X = Mean of N elements
N = Number of Elements Step 1: Let us consider the set of data :
3, 7, 11, 2, 29, 31 Step 2: Substituting the values in the mean formula,
Mean (X) = (3+7+11+2+29+31) / 6
= 13.8333
X = 13.8333 Step 3: Substituting the mean and other values in the formula,
Perform the (Xi-X)2 operation for all values of i (from 1 to n)
Sample Variance
= [(13.833 - 3)2+ (13.833 - 7)2+ (13.833 - 11)2 + (13.833 - 2)2 + (13.833 - 29)2 + (13.833 - 31)2 ]/ (6-1)
= [(10.833)2 + (6.833)2+ (2.833)2 + (11.833)2+(-15.167)2+ (-17.161)2/ (5)
= (117.353 + 46.689 + 8.025 + 140.019 + 230.03 + 294.49) / 5
= 836.606 / 5
= 167.3
Hence, the sample variance of a given data set is 167.3 Find variance of given sample data using Sample Variance Calculator.