(C) The variance of a set of observations $x_{i}$ is independent of the shift $p$. Let $y_{i} = x_{i} - p$.Given $\sum_{i=1}^{10} y_{i} = 3$ and $\sum

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(C) The variance of a set of observations $x_{i}$ is independent of the shift $p$. Let $y_{i} = x_{i} - p$.Given $\sum_{i=1}^{10} y_{i} = 3$ and $\sum_{i=1}^{10} y_{i}^{2} = 9$.The variance $\sigma^{2}$ is given by the formula:$\sigma^{2} = \frac{\sum y_{i}^{2}}{n} - \left( \frac{\sum y_{i}}{n} \right)^{2}$Substituting the given values with $n = 10$:$\sigma^{2} = \frac{9}{10} - \left( \frac{3}{10} \right)^{2}$$\sigma^{2} = 0.9 - 0.09 = 0.81$Standard deviation $\sigma = \sqrt{0.81} = 0.9 = \frac{9}{10}$.

Class 11 Mathematics Statistics Variance and Standard Deviation

Medium

Let $x_{i} (1 \leq i \leq 10)$ be ten observations of a random variable $X$. If $\sum_{i=1}^{10} (x_{i} - p) = 3$ and $\sum_{i=1}^{10} (x_{i} - p)^{2} = 9$,where $0 \neq p \in R$,then the standard deviation of these observations is:

JEE MAIN 2020 All JEE MAIN

A
$\sqrt{\frac{3}{5}}$
B
$\frac{7}{10}$
C
$\frac{9}{10}$
D
$\frac{4}{5}$

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Statistics

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If the variance of the numbers $9, 15, 21, \ldots, (6n+3)$ is $P$,then the variance of the first $n$ even numbers is

DifficultTS EAMCET 2025

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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,Chemistry

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 $\sigma_1$ and $\sigma_2$ be the standard deviations of two distributions $D_1$ and $D_2$ respectively,and $D_1$ be more consistent than $D_2$. If the means of $D_1$ and $D_2$ are the same,then the percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$ is:

EasyTS EAMCET 2018

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The mean of four observations is $3$. If the sum of the squares of these observations is $48$,then their standard deviation is

MediumAP EAMCET 2014

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If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$,then the variance of the data is:

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

Let $x_{i} (1 \leq i \leq 10)$ be ten observations of a random variable $X$. If $\sum_{i=1}^{10} (x_{i} - p) = 3$ and $\sum_{i=1}^{10} (x_{i} - p)^{2} = 9$,where $0 \neq p \in R$,then the standard deviation of these observations is:

Similar Questions

If the variance of the numbers $9, 15, 21, \ldots, (6n+3)$ is $P$,then the variance of the first $n$ even numbers is

Let $\sigma_1$ and $\sigma_2$ be the standard deviations of two distributions $D_1$ and $D_2$ respectively,and $D_1$ be more consistent than $D_2$. If the means of $D_1$ and $D_2$ are the same,then the percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$ is:

The mean of four observations is $3$. If the sum of the squares of these observations is $48$,then their standard deviation is

If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$,then the variance of the data is:

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