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in Statistics by (30.7k points)
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Show that the two formula for the standard deviation of ungrouped data

σ = \(\sqrt{\frac{1}{n}Σ(x_i - \bar{X})^2}\) and

σ' = \(\sqrt{\frac{1}{n}Σx_i^2 -\bar{X}^2 }\)are equivalent.

where \(\bar{ X} = \frac{1}{n}Σ_i\)

1 Answer

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Best answer

Taking square root both side

Hence, Proved

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