The mean and standard deviation of 20 observa | vedclass

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Question

Given :

Mean $(\bar{x})=\frac{\Sigma x_{i}}{20}=10$

or $\Sigma \mathrm{x}_{\mathrm{i}}=200$ (incorrect)

or $200-25+35=210=\Sigma \mathrm{x}_{

Vedclass · Accepted Answer

$(10.5,26)$

Vedclass · Answer

Given :

Mean $(\bar{x})=\frac{\Sigma x_{i}}{20}=10$

or $\Sigma \mathrm{x}_{\mathrm{i}}=200$ (incorrect)

or $200-25+35=210=\Sigma \mathrm{x}_{\mathrm{i}}$ (Correct)

Now correct $\bar{x}=\frac{210}{20}=10.5$

again given $S . D=2.5(\sigma)$

$\sigma^{2}=\frac{\Sigma \mathrm{x}_{\mathrm{i}}^{2}}{20}-(10)^{2}=(2.5)^{2}$

or $\Sigma \mathrm{x}_{\mathrm{i}}^{2}=2125$ (incorrect)

or $\Sigma \mathrm{x}_{\mathrm{i}}^{2}=2125-25^{2}+35^{2}$ $=2725$ (Correct)

$	herefore$ correct $\sigma^{2}=\frac{2725}{20}-(10.5)^{2}$

$\underline{\underline{\sigma}}^{2}=26$

or $\sigma=26$

$	herefore \underline{\alpha}=10.5, \beta=26$

class	$0-10$	$10-20$	$20-30$	$30-40$
Freq	$1$	$3$	$4$	$2$

	Size	Mean	Variance
Observation $I$	$10$	$2$	$2$
Observation $II$	$n$	$3$	$1$

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