The mean and standard deviation of 15 observa | vedclass

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Question

Let the incorrect mean be $\mu^{\prime}$ and standard deviation be $\sigma^{\prime}$

We have

$\mu^{\prime}=\frac{\Sigma x_i}{15}=12 \Rightarrow

Vedclass · Accepted Answer

$2521$

Vedclass · Answer

Let the incorrect mean be $\mu^{\prime}$ and standard deviation be $\sigma^{\prime}$

We have

$\mu^{\prime}=\frac{\Sigma x_i}{15}=12 \Rightarrow \Sigma x_i=180$

As per given information correct $\Sigma x_i=180-10+12$

$\Rightarrow \mu(	ext { correct mean })=\frac{182}{15}$

Also

$ \sigma^{\prime}=\sqrt{\frac{\sum \mathrm{x}_{\mathrm{i}}^2}{15}-144}=3 \Rightarrow \Sigma \mathrm{x}_{\mathrm{i}}^2=2295 $

$	ext { Correct } \Sigma \mathrm{x}_{\mathrm{i}}^2=2295-100+144=2339 $

$ \sigma^2(	ext { correct variance })=\frac{2339}{15}-\frac{182 	imes 182}{15 	imes 15}$

Required value

$ =15\left(\mu+\mu^2+\sigma^2ight) $

$ =15\left(\frac{182}{15}+\frac{182 	imes 182}{15 	imes 15}+\frac{2339}{15}-\frac{182 	imes 182}{15 	imes 15}ight) $

$ =15\left(\frac{182}{15}+\frac{2339}{15}ight) $

$ =2521$

$\mathrm{x}$	$\mathrm{x}_{1}=2$	$\mathrm{x}_{2}=6$	$\mathrm{x}_{3}=8$	$\mathrm{x}_{4}=9$
$\mathrm{f}$	$4$	$4$	$\alpha$	$\beta$

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