For observations having arithmetic mean

MATHEMATICS · Single correct · CBSE · Mathematics · Statistics · Statistics

Problem

For nn observations x1,x2,…,xnx_1,x_2,\ldots ,x_n having arithmetic mean xˉ\bar{x}, which of the following expressions represents the variance σ2\sigma^2 of the data? (a) 1n∑i=1n(xi−xˉ)2\displaystyle \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2} (b) 1n−1∑i=1n(xi−xˉ)2\displaystyle \frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2 (c) 1n∑i=1n(xi−xˉ)2\displaystyle \frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2 (d) 1n∑i=1n∣xi−xˉ∣\displaystyle \frac{1}{n}\sum_{i=1}^{n}|x_i-\bar{x}|

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