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

1.	Show that the two formulae for the standard deviation of ungrouped data . σ=√1n∑(xi−¯¯¯¯¯X)2 and σ′=√1n∑x2i−¯¯¯¯¯X2 are equivalent , where ¯¯¯¯¯X=1n∑xi
Answer» Show that the two formulae for the standard deviation of ungrouped data . $σ = \sqrt{\frac{1}{n} \sum (x_{i} - ¯ ¯¯¯ ¯ X)^{2}} a n d σ^{'} = \sqrt{\frac{1}{n} \sum x_{i}^{2} - {¯ ¯¯¯ ¯ X}^{2}}$ are equivalent , where $¯ ¯¯¯ ¯ X = \frac{1}{n} \sum x_{i}$

Show that the two formulae for the standard deviation of ungrouped data . σ=√1n∑(xi−¯¯¯¯¯X)2 and σ′=√1n∑x2i−¯¯¯¯¯X2 are equivalent , where ¯¯¯¯¯X=1n∑xi

Answer»

Show that the two formulae for the standard deviation of ungrouped data .

$σ = \sqrt{\frac{1}{n} \sum (x_{i} - ¯ ¯¯¯ ¯ X)^{2}} a n d σ^{'} = \sqrt{\frac{1}{n} \sum x_{i}^{2} - {¯ ¯¯¯ ¯ X}^{2}}$ are equivalent , where $¯ ¯¯¯ ¯ X = \frac{1}{n} \sum x_{i}$

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Show that the two formulae for the standard deviation of ungrouped data . σ=√1n∑(xi−¯¯¯¯¯X)2 and σ′=√1n∑x2i−¯¯¯¯¯X2 are equivalent , where ¯¯¯¯¯X=1n∑xi

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