The mean and standard deviation of 40 observa | vedclass

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Question

Wrong mean $=\mu_{1}=30$

Wrong $S.D$ $=\sigma_{1}=5$

$\frac{\sum x _{ i }}{40}=30$

$\sum x _{ i }=1200$

$\sigma_{1}^{2}=25$

$\frac{\sum

Vedclass · Accepted Answer

$238$

Vedclass · Answer

Wrong mean $=\mu_{1}=30$

Wrong $S.D$ $=\sigma_{1}=5$

$\frac{\sum x _{ i }}{40}=30$

$\sum x _{ i }=1200$

$\sigma_{1}^{2}=25$

$\frac{\sum x _{ i }^{2}}{40}-30^{2}=25$

$\sum x _{ i }^{2}=925 	imes 40=37000$

New sum $=\sum x _{ i }^{\prime}=1200-10-12=1178$

New mean $=\mu_{1}^{\prime}=\frac{1178}{38}=31$

New $\sum x _{ i }^{2}=37000-(10)^{2}-(12)^{2}=36756$

New $S.D$, $\sigma_{1}^{\prime}=\sqrt{\frac{36756}{38}-(31)^{2}}=\sigma$

$36756-(31)^{2} 	imes 38=38 \sigma^{2}$

$38 \sigma^{2}=238$

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

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