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 σ²

Formula:
Sample Variance = Σ(X_i- X)² / (N - 1)
Where,
Xi= I^th 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.

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