Standard deviation of following series class 0-10 10-20 20-30 30-40 Freq 1 3 4 2

English

Gujarati

Hindi

13.Statistics

medium

What is the standard deviation of the following series

class $0-10$ $10-20$ $20-30$ $30-40$

Freq $1$ $3$ $4$ $2$

A

$81$

B

$7.6$

C

$9$

D

$2.26$

Solution

Class	$f$	${y_i}$	$d = {y_i} – A,$ $A = 25$	${f_i}{d_i}$	${f_i}d_i^2$
$0-10$	$1$	$5$	$-20$	$-20$	$400$
$10-20$	$3$	$15$	$-10$	$-30$	$300$
$20-30$	$4$	$25$	$0$	$0$	$0$
$30-40$	$2$	$35$	$10$	$20$	$200$
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 $

$\Rightarrow \sigma=9$

Standard 11

Mathematics

Share

Similar Questions

If $x_1, x_2,…..x_n$ are $n$ observations such that $\sum\limits_{i = 1}^n {x_i^2} = 400$ and $\sum\limits_{i = 1}^n {{x_i}} = 100$ , then possible value of $n$ among the following is

normal

The mean and standard deviation of $20$ observations were calculated as $10$ and $2.5$ respectively. It was found that by mistake one data value was taken as $25$ instead of $35 .$ If $\alpha$ and $\sqrt{\beta}$ are the mean and standard deviation respectively for correct data, then $(\alpha, \beta)$ is :

hard

(JEE MAIN-2021)

If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to

hard

(JEE MAIN-2019)

The mean of the numbers $a, b, 8,5,10$ is $6$ and their variance is $6.8$. If $M$ is the mean deviation of the numbers about the mean, then $25\; M$ is equal to

hard

(JEE MAIN-2022)

The mean and $S.D.$ of $1, 2, 3, 4, 5, 6$ is

medium