$\because \operatorname{var} .\left(2 \mathrm{x}_{\mathrm{i}}+7\right)=4 \operatorname{var}\left(\mathrm{x}_{\mathrm{i}}\right)=4\left(\frac{\Sigma \m

$\because \operatorname{var} .\left(2 \mathrm{x}_{\mathrm{i}}+7\right)=4 \operatorname{var}\left(\mathrm{x}_{\mathrm{i}}\right)=4\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}^{2}}{5}-\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}}{5}\right)^{2}\right)$ $=4\left(\frac{25}{5}-\left(\frac{5}{5}\right)^{2}\right)=4(5-1)=16$ $\therefore \mathrm{S} \mathrm{D}=\sqrt{16}=4$

13.StatisticsAdvanced

If $\sum_{i=1}^{5}(x_i-10)=5$ and $\sum_{i=1}^{5}(x_i-10)^2=5$ then standard deviation of observations $2x_1 + 7, 2x_2 + 7, 2x_3 + 7, 2x_4 + 7$ and $2x_5 + 7$ is equal to-

A
$8$
B
$16$
C
$4$
D
$2$

Std 11
Mathematics

Suppose values taken by a variable $x$ are such that $a \le {x_i} \le b$, where ${x_i}$ denotes the value of $x$ in the $i^{th}$ case for $i = 1, 2, ...n.$ Then..

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The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted a and $b$ are respectively mean and variance of remaining $6$ observation, then $a+3 b-5$ is equal to $..........$.

Difficult

[JEE MAIN 2023]

View Solution

The mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below:

Subject Mathematics Physics Chemistty

Mean $42$ $32$ $40.9$

Standard deviation $12$ $15$ $20$

Which of the three subjects shows the highest variability in marks and which shows the lowest?

Difficult

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Let $\mathrm{X}$ be a random variable with distribution.

$\mathrm{x}$ $-2$ $-1$ $3$ $4$ $6$

$\mathrm{P}(\mathrm{X}=\mathrm{x})$ $\frac{1}{5}$ $\mathrm{a}$ $\frac{1}{3}$ $\frac{1}{5}$ $\mathrm{~b}$

If the mean of $X$ is $2.3$ and variance of $X$ is $\sigma^{2}$, then $100 \sigma^{2}$ is equal to :

Difficult

[JEE MAIN 2021]

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The mean and standard deviation of the marks of $10$ students were found to be $50$ and $12$ respectively. Later, it was observed that two marks $20$ and $25$ were wrongly read as $45$ and $50$ respectively. Then the correct variance is $............$.

Difficult

[JEE MAIN 2023]

View Solution

Subject	Mathematics	Physics	Chemistty
Mean	$42$	$32$	$40.9$
Standard deviation	$12$	$15$	$20$

$\mathrm{x}$	$-2$	$-1$	$3$	$4$	$6$
$\mathrm{P}(\mathrm{X}=\mathrm{x})$	$\frac{1}{5}$	$\mathrm{a}$	$\frac{1}{3}$	$\frac{1}{5}$	$\mathrm{~b}$

If $\sum_{i=1}^{5}(x_i-10)=5$ and $\sum_{i=1}^{5}(x_i-10)^2=5$ then standard deviation of observations $2x_1 + 7, 2x_2 + 7, 2x_3 + 7, 2x_4 + 7$ and $2x_5 + 7$ is equal to-

Similar Questions

Suppose values taken by a variable $x$ are such that $a \le {x_i} \le b$, where ${x_i}$ denotes the value of $x$ in the $i^{th}$ case for $i = 1, 2, ...n.$ Then..

The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted a and $b$ are respectively mean and variance of remaining $6$ observation, then $a+3 b-5$ is equal to $..........$.

Let $\mathrm{X}$ be a random variable with distribution. $\mathrm{x}$ $-2$ $-1$ $3$ $4$ $6$ $\mathrm{P}(\mathrm{X}=\mathrm{x})$ $\frac{1}{5}$ $\mathrm{a}$ $\frac{1}{3}$ $\frac{1}{5}$ $\mathrm{~b}$ If the mean of $X$ is $2.3$ and variance of $X$ is $\sigma^{2}$, then $100 \sigma^{2}$ is equal to :

The mean and standard deviation of the marks of $10$ students were found to be $50$ and $12$ respectively. Later, it was observed that two marks $20$ and $25$ were wrongly read as $45$ and $50$ respectively. Then the correct variance is $............$.