Gujarati
13.Statistics
medium

निम्नलिखित श्रेणी का मानक विचलन है

Measurements

0-10

10-20

20-30

30-40

Frequency

1

3

4

2

A

$81$

B

$7.6$

C

$9$

D

$2.26$

Solution

(c)

$Class$

$f_i$

$y_i$

$d = {y_i} – A$

$A = 25$

$f_id_i$

$f_id_i^2$

$0-10$

$1$

$5$

$-20$

$-20$

$400$

$10-20$

$3$

$15$

$-10$

$-30$

$300$

$20-30$

$4$

$25$

$0$

$0$

$0$

$30-40$

$2$

$35$

$10$

$20$

$200$

$Total$

$10$

 

 

$-30$

$900$

 

${\sigma ^2} = \frac{{\sum {f_i}d_i^2}}{{\sum {f_i}}} – {\left( {\frac{{\sum {f_i}{d_i}}}{{\sum {f_i}}}} \right)^2}$

$= \frac{{900}}{{10}} – {\left( {\frac{{ – 30}}{{10}}} \right)^2}$

${\sigma ^2} = 90 – 9 = 81$

==> $\sigma$ = $9$.

Standard 11
Mathematics

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