If both the means and the standard deviation | vedclass

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Question

Mean $\left( \mu  \right) = \frac{{\sum {{x_i}} }}{{50}} = 16$

Standard deviation $\left( \sigma  \right) = \sqrt {\frac{{\sum

Vedclass · Accepted Answer

$400$

Vedclass · Answer

Mean $\left( \mu  ight) = \frac{{\sum {{x_i}} }}{{50}} = 16$

Standard deviation $\left( \sigma  ight) = \sqrt {\frac{{\sum {x_i^2} }}{{50}} - {{\left( \mu  ight)}^2}}  = 16$

$ \Rightarrow \left( {256} ight) 	imes 2 = \frac{{\sum {x_i^2} }}{{50}}$

$\Rightarrow$ New mean

$ = \frac{{\sum {{{\left( {{x_i} - 4} ight)}^2}} }}{{50}} = \frac{{\sum {x_i^2 + 16 	imes 50 - 8\sum {{x_i}} } }}{{50}}$

$ = \left( {256} ight) 	imes 2 + 16 - 8 	imes 16 = 400$

Class:	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$2$	$3$	$x$	$5$	$4$

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