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Question

Mathematics Question on Standard deviation

Which of the following is correct for standard deviation, where Xˉ\bar{X} = mean

A

σ=∑i=1n(Xi−Xˉ)2n\sigma = \sqrt{\frac{ \sum_{i=1}^n (X_i - \bar{X})^2 }{n}}

B

σ=∑i=1n(Xi−Xˉ)2n\sigma = \sqrt{\frac{\sum_{i=1}^n (X_i - \bar{X})^2 }{n}}

C

σ=∑i=1n((Xi−Xˉ)2n)\sigma = \sqrt{ \sum_{i=1}^n \left(\frac{(X_i - \bar{X})^2}{n}\right) }

D

σ=∑i=1nXi−Xˉn\sigma = \sqrt{ \frac{\sum_{i=1}^n X_i - \bar{X}}{n} }

Answer

σ=∑i=1n(Xi−Xˉ)2n\sigma = \sqrt{\frac{\sum_{i=1}^n (X_i - \bar{X})^2 }{n}}

Explanation

Solution

The correct option is (B) :σ=∑i=1n(Xi−Xˉ)2n\sigma = \sqrt{\frac{\sum_{i=1}^n (X_i - \bar{X})^2 }{n}}