Variance sigma^2 of data is . . . . . . xᵢ 0 1 5 6 10 12 17 fᵢ 3 2 3 2 6 3 3

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13.Statistics

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The variance $\sigma^2$ of the data is $ . . . . . .$

$x_i$ $0$ $1$ $5$ $6$ $10$ $12$ $17$

$f_i$ $3$ $2$ $3$ $2$ $6$ $3$ $3$

A

$28$

B

$29$

C

$27$

D

$25$

(JEE MAIN-2024)

Solution

$x_i$	$f_i$	$f_ix_i$	$f_ix_i^2$
$0$	$3$	$0$	$0$
$1$	$2$	$2$	$2$
$5$	$3$	$15$	$75$
$6$	$2$	$12$	$72$
$10$	$6$	$60$	$600$
$12$	$3$	$36$	$432$
$17$	$3$	$51$	$867$
	$\sum f_i = 22$		$\sum f_ix_i^2 = 2048$

$ \therefore \quad \sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}=176$

$ \text { So } \overline{\mathrm{x}}=\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}}=\frac{176}{22}=8 $

$ \text { for } \sigma^2=\frac{1}{\mathrm{~N}} \sum \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}^2-(\overline{\mathrm{x}})^2 $

$ \quad=\frac{1}{22} \times 2048-(8)^2$

$ \quad=93.090964 $

$\quad=29.0909$

Standard 11

Mathematics

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