If variance of frequency distribution is 160 , then value of mathrm{c} ∈ mathrm{N} is X c 2c 3c 4c

English

Gujarati

Hindi

13.Statistics

medium

If the variance of the frequency distribution is $160$ , then the value of $\mathrm{c} \in \mathrm{N}$ is

$X$ $c$ $2c$ $3c$ $4c$ $5c$ $6c$

$f$ $2$ $1$ $1$ $1$ $1$ $1$

A

$5$

B

$8$

C

$7$

D

$6$

(JEE MAIN-2024)

Solution

$x$	$C$	$2C$	$3C$	$4C$	$5C$	$6C$
$f$	$2$	$1$	$1$	$1$	$1$	$1$

$\bar{x}=\frac{(2+2+3+4+5+6) C}{7}=\frac{22 C}{7}$

$ \operatorname{Var}(\mathrm{x})=\frac{\mathrm{c}^2\left(2+2^2+3^2+4^2+5^2+6^2\right)}{7} $

$ -\left(\frac{22 c}{7}\right)^2 $

$ =\frac{92 c^2}{7}-\mathrm{c}^2 \times \frac{484}{49} $

$ =\frac{(644-484) c^2}{49}=\frac{160 c^2}{49} $

$ 160=\frac{160 \times c^2}{49} \Rightarrow c=7$

Standard 11

Mathematics

Share

Similar Questions

Let the mean and variance of the frequency distribution

$\mathrm{x}$ $\mathrm{x}_{1}=2$ $\mathrm{x}_{2}=6$ $\mathrm{x}_{3}=8$ $\mathrm{x}_{4}=9$

$\mathrm{f}$ $4$ $4$ $\alpha$ $\beta$

be $6$ and $6.8$ respectively. If $x_{3}$ is changed from $8$ to $7 ,$ then the mean for the new data will be:

easy

(JEE MAIN-2021)

There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test:

$\begin{array}{|l|l|l|l|l|l|l|} \hline \text { Marks } & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Frequency } & x-2 & x & x^{2} & (x+1)^{2} & 2 x & x+1 \\ \hline \end{array}$

where $x$ is a positive integer. Determine the mean and standard deviation of the marks.

hard

The mean and variance of $7$ observations are $8$ and $16,$ respectively. If five of the observations are $2,4,10,12,14 .$ Find the remaining two observations.

hard

Find the mean and variance for the first $n$ natural numbers

hard

Let sets $A$ and $B$ have $5$ elements each. Let the mean of the elements in sets $A$ and $B$ be $5$ and $8$ respectively and the variance of the elements in sets $A$ and $B$ be $12$ and $20$ respectively $A$ new set $C$ of $10$ elements is formed by subtracting $3$ from each element of $A$ and adding 2 to each element of B. Then the sum of the mean and variance of the elements of $C$ is $…….$.

hard

(JEE MAIN-2023)