If the variance of the frequency distribution | vedclass

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Question

$x_i$
			$f_i$
			$d_i=x_i-5$
			$f _{ i } d _{ i }^2$
			$f _{ i } d _{ i }$
		
		
			$2$
			$3$
			$-3$
			$27$
			$-9$

Vedclass · Accepted Answer

$5$

Vedclass · Answer

$x_i$
			$f_i$
			$d_i=x_i-5$
			$f _{ i } d _{ i }^2$
			$f _{ i } d _{ i }$
		
		
			$2$
			$3$
			$-3$
			$27$
			$-9$
		
		
			$3$
			$6$
			$-2$
			$24$
			$-12$
		
		
			$4$
			$16$
			$-1$
			$16$
			$-16$
		
		
			$5$
			$\alpha$
			$0$
			$0$
			$0$
		
		
			$6$
			$9$
			$1$
			$9$
			$9$
		
		
			$7$
			$5$
			$2$
			$20$
			$10$
		
		
			$8$
			$6$
			$3$
			$54$
			$18$
		
	


$\sigma_{ x }^2=\sigma_{ d }^2=\frac{\sum f _{ i } d _{ i }^2}{\sum f _{ i }}-\left(\frac{\sum f _{ i } d _{ i }}{\sum f _{ i }}\right)^2$

$=\frac{150}{45+\alpha}-0=3$

$\Rightarrow 150=135+3 \alpha$

$\Rightarrow 3 \alpha=15 \Rightarrow \alpha=5$

If the variance of the frequency distribution is $3$ then $\alpha$ is ......

$X_i$ $2$ $3$ $4$ $5$ $6$ $7$ $8$

Frequency $f_i$ $3$ $6$ $16$ $\alpha$ $9$ $5$ $6$

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$X_i$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency $f_i$	$3$	$6$	$16$	$\alpha$	$9$	$5$	$6$

If the variance of the frequency distribution is $3$ then $\alpha$ is ...... $X_i$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ Frequency $f_i$ $3$ $6$ $16$ $\alpha$ $9$ $5$ $6$