For a frequency distribution standard deviation is computed by applying formula

English

Gujarati

Hindi

13.Statistics

normal

For a frequency distribution standard deviation is computed by applying the formula

A$\sigma = \sqrt {\left( {\frac{{\sum \,fd}}{{\sum \,f}}} \right) - \frac{{\sum \,f{d^2}}}{{\sum \,f}}} $

B$\sigma = \sqrt {\frac{{\sum \,f{d^2}}}{{\sum \,f}} - {{\left( {\frac{{\sum \,f{d^2}}}{{\sum \,f}}} \right)}^2}} $

C$\sigma = \sqrt {{{\left( {\frac{{\sum \,fd}}{{\sum \,f}}} \right)}^2} - \frac{{\sum \,f{d^2}}}{{\sum \,f}}} $

D$\sigma = \sqrt {\frac{{\sum \,f{d^2}}}{{\sum \,f}} - {{\left( {\frac{{\sum \,fd}}{{\sum \,f}}} \right)}^2}} $

Solution

(d)It is obvious.

Standard 11

Mathematics

Share

Similar Questions

Find the mean and variance of the frequency distribution given below:

$\begin{array}{|l|l|l|l|l|} \hline x & 1 \leq x<3 & 3 \leq x<5 & 5 \leq x<7 & 7 \leq x<10 \\ \hline f & 6 & 4 & 5 & 1 \\ \hline \end{array}$

hard

The variance of $20$ observations is $5 .$ If each observation is multiplied by $2,$ find the new variance of the resulting observations.

hard

Suppose a class has $7$ students. The average marks of these students in the mathematics examination is $62$, and their variance is $20$ . A student fails in the examination if $he/she$ gets less than $50$ marks, then in worst case, the number of students can fail is

medium

(JEE MAIN-2022)

What is the standard deviation of the following series

class

0-10

10-20

20-30

30-40

Freq

1

3

4

2

medium

If $\mathop \sum \limits_{i = 1}^9 \left( {{x_i} – 5} \right) = 9$ and $\mathop \sum \limits_{i = 1}^9 {\left( {{x_i} – 5} \right)^2} = 45,$ then the standard deviation of the $9$ items ${x_1},{x_2},\;.\;.\;.\;,{x_9}$ is :

hard

(JEE MAIN-2018)