Prove that for observations with arithmetic mean

MATHEMATICS · Subjective · CBSE · Mathematics · Statistics · Statistics

Problem

Prove that for

n

observations

x_1, x_2, \dots, x_n

with arithmetic mean

\bar{x}

, the variance can be expressed as

\sigma^2 = \frac{1}{n}\sum_{i=1}^{n} x_i^{2} - \bar{x}^{2}.