(C) Let the first distribution be $X$ with values $x_i$ and frequencies $f_i$. The variance is given by $\sigma_X^2 = 45.8$.The second distribution $Y

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(C) Let the first distribution be $X$ with values $x_i$ and frequencies $f_i$. The variance is given by $\sigma_X^2 = 45.8$.The second distribution $Y$ has values $y_i$ where $y_i = 2x_i + 2$.We know that if $Y = aX + b$,then the variance $\sigma_Y^2 = a^2 \sigma_X^2$.In this case,$y_i = 2x_i + 2$,so $a = 2$.Therefore,$\sigma_Y^2 = 2^2 \times \sigma_X^2 = 4 \times 45.8$.$\sigma_Y^2 = 183.2$.

Class 11 Mathematics Statistics Variance and Standard Deviation

Medium

If the variance of the distribution is $45.8$,then find the variance of the distribution given below:

$x_i$ $4$ $8$ $11$ $17$ $20$ $24$ $32$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

$y_i$ $10$ $18$ $24$ $36$ $42$ $50$ $66$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

$x_i$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

$y_i$	$10$	$18$	$24$	$36$	$42$	$50$	$66$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

AP EAMCET 2018 All AP EAMCET

A
$93.6$
B
$\sqrt{93.9}$
C
$183.2$
D
$\sqrt{183.2}$

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Variance and Standard Deviation

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The variance of $10$ observations is $16$. If each observation is doubled,then the standard deviation of the new data will be -

Medium

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Find the standard deviation for the following data:

${x_i}$ $3$ $8$ $13$ $18$ $23$

${f_i}$ $7$ $10$ $15$ $10$ $6$

Medium

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If $x_1, x_2, ..., x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 100$,then which of the following is a possible value of $n$?

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The mean and variance of $10$ observations were calculated as $15$ and $15$ respectively by a student who took by mistake $25$ instead of $15$ for one observation. Then,the correct standard deviation is $.....$

MediumJEE MAIN 2022

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The variance of the following continuous frequency distribution is
$\begin{array}{|l|c|c|c|c|}\hline \text{Class interval} & 0-4 & 4-8 & 8-12 & 12-16 \\ \hline \text{Frequency} & 2 & 3 & 2 & 1 \\ \hline\end{array}$

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If the variance of the distribution is $45.8$,then find the variance of the distribution given below: $x_i$ $4$ $8$ $11$ $17$ $20$ $24$ $32$ $f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$ $y_i$ $10$ $18$ $24$ $36$ $42$ $50$ $66$ $f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

Similar Questions

The variance of $10$ observations is $16$. If each observation is doubled,then the standard deviation of the new data will be -

Find the standard deviation for the following data: ${x_i}$ $3$ $8$ $13$ $18$ $23$ ${f_i}$ $7$ $10$ $15$ $10$ $6$

If $x_1, x_2, ..., x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 100$,then which of the following is a possible value of $n$?

The mean and variance of $10$ observations were calculated as $15$ and $15$ respectively by a student who took by mistake $25$ instead of $15$ for one observation. Then,the correct standard deviation is $.....$

The variance of the following continuous frequency distribution is$\begin{array}{|l|c|c|c|c|}\hline \text{Class interval} & 0-4 & 4-8 & 8-12 & 12-16 \\ \hline \text{Frequency} & 2 & 3 & 2 & 1 \\ \hline\end{array}$

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If the variance of the distribution is $45.8$,then find the variance of the distribution given below:

$x_i$ $4$ $8$ $11$ $17$ $20$ $24$ $32$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

$y_i$ $10$ $18$ $24$ $36$ $42$ $50$ $66$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

Find the standard deviation for the following data:

${x_i}$ $3$ $8$ $13$ $18$ $23$

${f_i}$ $7$ $10$ $15$ $10$ $6$

The variance of the following continuous frequency distribution is
$\begin{array}{|l|c|c|c|c|}\hline \text{Class interval} & 0-4 & 4-8 & 8-12 & 12-16 \\ \hline \text{Frequency} & 2 & 3 & 2 & 1 \\ \hline\end{array}$