If the variance of the frequency distribution | vedclass

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Question

$x$
			$C$
			$2C$
			$3C$
			$4C$
			$5C$
			$6C$
		
		
			$f$
			$2$
			$1$
			$1$
			$1$
			$1$
			$1$
		
	


$\bar

Vedclass · Accepted Answer

$7$

Vedclass · Answer

$x$
			$C$
			$2C$
			$3C$
			$4C$
			$5C$
			$6C$
		
		
			$f$
			$2$
			$1$
			$1$
			$1$
			$1$
			$1$
		
	


$\bar{x}=\frac{(2+2+3+4+5+6) C}{7}=\frac{22 C}{7}$

$ \operatorname{Var}(\mathrm{x})=\frac{\mathrm{c}^2\left(2+2^2+3^2+4^2+5^2+6^2ight)}{7} $

$ -\left(\frac{22 c}{7}ight)^2 $

$ =\frac{92 c^2}{7}-\mathrm{c}^2 	imes \frac{484}{49} $

$ =\frac{(644-484) c^2}{49}=\frac{160 c^2}{49} $

$ 160=\frac{160 	imes c^2}{49} \Rightarrow c=7$

Classes	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
${f_i}$	$3$	$7$	$12$	$15$	$8$	$3$	$2$

Subject	Mathematics	Physics	Chemistty
Mean	$42$	$32$	$40.9$
Standard deviation	$12$	$15$	$20$

If the variance of the frequency distribution is $160$ , then the value of $\mathrm{c} \in \mathrm{N}$ is

$X$ $c$ $2c$ $3c$ $4c$ $5c$ $6c$

$f$ $2$ $1$ $1$ $1$ $1$ $1$

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