13.Statistics
medium

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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