Which of the following expressions represents the population variance for an…

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

Problem

Which of the following expressions represents the population variance σ2\sigma^{2} for an ungrouped data set x1,x2,…,xnx_{1},x_{2},\ldots ,x_{n} having mean xˉ\bar{x}? (a) 1n−1∑i=1n(xi−xˉ)2\displaystyle \frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2} (b) 1n∑i=1nxi2\displaystyle \frac{1}{n}\sum_{i=1}^{n}x_{i}^{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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