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

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

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

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

$5$

$8$

$7$

$6$

(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

If the mean and variance of five observations are $\frac{24}{5}$ and $\frac{194}{25}$ respectively and the mean of first four observations is $\frac{7}{2}$, then the variance of the first four observations in equal to

hard

(JEE MAIN-2024)

If the mean and variance of the following data:

$6,10,7,13, a, 12, b, 12$ are 9 and $\frac{37}{4}$ respectively, then $(a-b)^{2}$ is equal to:

medium

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The mean and variance of eight observations are $9$ and $9.25,$ respectively. If six of the observations are $6,7,10,12,12$ and $13,$ find the remaining two observations.

hard

If the mean of the frequency distribution

Class: $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequency $2$ $3$ $x$ $5$ $4$

is $28$ , then its variance is $……..$.

hard

(JEE MAIN-2023)

Consider the statistics of two sets of observations as follows :

Size Mean Variance

Observation $I$ $10$ $2$ $2$

Observation $II$ $n$ $3$ $1$

If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ….. .

hard

(JEE MAIN-2021)

Class:	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$2$	$3$	$x$	$5$	$4$

	Size	Mean	Variance
Observation $I$	$10$	$2$	$2$
Observation $II$	$n$	$3$	$1$

If the variance of the frequency distribution is $160$ , then the value of $\mathrm{c} \in \mathrm{N}$ is $X$ $c$ $2c$ $3c$ $4c$ $5c$ $6c$ $f$ $2$ $1$ $1$ $1$ $1$ $1$

Solution

Similar Questions

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

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

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

If the mean and variance of the following data:

$6,10,7,13, a, 12, b, 12$ are 9 and $\frac{37}{4}$ respectively, then $(a-b)^{2}$ is equal to:

If the mean of the frequency distribution

Class: $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequency $2$ $3$ $x$ $5$ $4$

is $28$ , then its variance is $……..$.

Consider the statistics of two sets of observations as follows :

Size Mean Variance

Observation $I$ $10$ $2$ $2$

Observation $II$ $n$ $3$ $1$

If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ….. .