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

English

Gujarati

Hindi

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 of $5$ observations is $4.4$ and their variance is $8.24$. If three observations are $1, 2$ and $6$, the other two observations are

medium

Mean and standard deviation of 100 items are 50 and $4,$ respectively. Then find the sum of all the item and the sum of the squares of the items.

hard

The mean and standard deviation of a group of $100$ observations were found to be $20$ and $3,$ respectively. Later on it was found that three observations were incorrect, which were recorded as $21,21$ and $18 .$ Find the mean and standard deviation if the incorrect observations are omitted.

medium

A data consists of $n$ observations

${x_1},{x_2},……,{x_n}.$ If $\sum\limits_{i – 1}^n {{{({x_i} + 1)}^2}} = 9n$ and $\sum\limits_{i – 1}^n {{{({x_i} – 1)}^2}} = 5n,$ then the standard deviation of this data is

hard

(JEE MAIN-2019)

While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

hard

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

The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three observations are $1, 2$ and $6$, the other two observations are

Mean and standard deviation of 100 items are 50 and $4,$ respectively. Then find the sum of all the item and the sum of the squares of the items.

The mean and standard deviation of a group of $100$ observations were found to be $20$ and $3,$ respectively. Later on it was found that three observations were incorrect, which were recorded as $21,21$ and $18 .$ Find the mean and standard deviation if the incorrect observations are omitted.

A data consists of $n$ observations ${x_1},{x_2},……,{x_n}.$ If $\sum\limits_{i – 1}^n {{{({x_i} + 1)}^2}} = 9n$ and $\sum\limits_{i – 1}^n {{{({x_i} – 1)}^2}} = 5n,$ then the standard deviation of this data is

While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

Start a Free Trial Now

A data consists of $n$ observations

${x_1},{x_2},……,{x_n}.$ If $\sum\limits_{i – 1}^n {{{({x_i} + 1)}^2}} = 9n$ and $\sum\limits_{i – 1}^n {{{({x_i} – 1)}^2}} = 5n,$ then the standard deviation of this data is