If Σ_{i=1}^{5}(xᵢ-10)=5 and Σ_{i=1}^{5}(xᵢ-10)^2=5 then standard deviation of observatio

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13.Statistics

normal

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-

$8$

$16$

$4$

$2$

Solution

$\because \operatorname{var} .\left(2 \mathrm{x}_{\mathrm{i}}+7\right)=4 \operatorname{var}\left(\mathrm{x}_{\mathrm{i}}\right)=4\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}^{2}}{5}-\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}}{5}\right)^{2}\right)$

$=4\left(\frac{25}{5}-\left(\frac{5}{5}\right)^{2}\right)=4(5-1)=16$

$\therefore \mathrm{S} \mathrm{D}=\sqrt{16}=4$

Standard 11

Mathematics

The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38 \sigma^{2}$ is equal to$………$

hard

(JEE MAIN-2022)

Let $X$ be a random variable, and let $P(X=x)$ denote the probability that $X$ takes the value $x$. Suppose that the points $(x, P(X=x)), x=0,1,2,3,4$, lie on a fixed straight line in the $x y$-plane, and $P(X=x)=0$ for all $x \in R$ $\{0,1,2,3,4\}$. If the mean of $X$ is $\frac{5}{2}$, and the variance of $X$ is $\alpha$, then the value of $24 \alpha$ is. . . . .

normal

(IIT-2024)

In a series of $2n$ observation, half of them are equal to $'a'$ and remaining half observations are equal to $' -a'$. If the standard deviation of this observations is $2$ then $\left| a \right|$ equals

hard

(JEE MAIN-2013)

If the standard deviation of $0, 1, 2, 3, …..,9$ is $K$, then the standard deviation of $10, 11, 12, 13 …..19$ is

medium

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 :

hard

(JEE MAIN-2021)

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

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-

Solution

Similar Questions

In a series of $2n$ observation, half of them are equal to $'a'$ and remaining half observations are equal to $' -a'$. If the standard deviation of this observations is $2$ then $\left| a \right|$ equals

If the standard deviation of $0, 1, 2, 3, …..,9$ is $K$, then the standard deviation of $10, 11, 12, 13 …..19$ is

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 :

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