If variance of frequency distribution is 3 then α is ...... Xᵢ 2 3 4 5 6 7 8 Frequency fᵢ 3 6 1

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13.Statistics

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

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

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

A

$5$

B

$4$

C

$3$

D

$2$

(JEE MAIN-2023)

Solution

$x_i$	$f_i$	$d_i=x_i-5$	$f _{ i } d _{ i }^2$	$f _{ i } d _{ i }$
$2$	$3$	$-3$	$27$	$-9$
$3$	$6$	$-2$	$24$	$-12$
$4$	$16$	$-1$	$16$	$-16$
$5$	$\alpha$	$0$	$0$	$0$
$6$	$9$	$1$	$9$	$9$
$7$	$5$	$2$	$20$	$10$
$8$	$6$	$3$	$54$	$18$

$\sigma_{ x }^2=\sigma_{ d }^2=\frac{\sum f _{ i } d _{ i }^2}{\sum f _{ i }}-\left(\frac{\sum f _{ i } d _{ i }}{\sum f _{ i }}\right)^2$

$=\frac{150}{45+\alpha}-0=3$

$\Rightarrow 150=135+3 \alpha$

$\Rightarrow 3 \alpha=15 \Rightarrow \alpha=5$

Standard 11

Mathematics

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