Show that the two formulae for the standard deviation of ungrouped dat – InterviewSolution

1.	Show that the two formulae for the standard deviation of ungrouped dataσ=1n∑xi-X2 and σ'=1n∑xi2-X2 are equivalent, where X=1n∑xi
Answer» Show that the two formulae for the standard deviation of ungrouped data $σ = \sqrt{\frac{1}{n} \underset{}{\sum {(x_{i} - X)}^{2}}}$ and $σ' = \sqrt{\frac{1}{n} \underset{}{\sum x_{i}^{2} - X^{2}}}$ are equivalent, where $X = \frac{1}{n} \sum_{} x_{i}$

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