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(D) Given: $n_{1}=10, n_{2}=10$Means: $m_{1}=60, m_{2}=40$Standard deviations: $\sigma_{1}=4, \sigma_{2}=6$The formula for the combined standard devia

Vedclass · Accepted Answer

$11.2$

Vedclass · Answer

(D) Given: $n_{1}=10, n_{2}=10$Means: $m_{1}=60, m_{2}=40$Standard deviations: $\sigma_{1}=4, \sigma_{2}=6$The formula for the combined standard deviation $\sigma$ is:$\sigma=\sqrt{\frac{n_{1} \sigma_{1}^{2}+n_{2} \sigma_{2}^{2}}{n_{1}+n_{2}}+\frac{n_{1} n_{2}(m_{1}-m_{2})^{2}}{(n_{1}+n_{2})^{2}}}$Substituting the values:$\sigma=\sqrt{\frac{10 	imes 4^{2}+10 	imes 6^{2}}{10+10}+\frac{10 	imes 10(60-40)^{2}}{(10+10)^{2}}}$$\sigma=\sqrt{\frac{160+360}{20}+\frac{100(20)^{2}}{400}}$$\sigma=\sqrt{\frac{520}{20}+\frac{100 	imes 400}{400}}$$\sigma=\sqrt{26+100}=\sqrt{126} \approx 11.22$

$X$	$35$	$54$	$52$	$53$	$56$	$58$	$52$	$50$	$51$	$49$
$Y$	$108$	$107$	$105$	$105$	$106$	$107$	$104$	$103$	$104$	$101$

$x_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$f_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$

The average marks of $10$ students in a class was $60$ with a standard deviation of $4$,while the average marks of another $10$ students was $40$ with a standard deviation of $6$. If all the $20$ students are taken together,their combined standard deviation will be:

Similar Questions

From the prices of shares $X$ and $Y$ below,find out which is more stable in value:

$X$ $35$ $54$ $52$ $53$ $56$ $58$ $52$ $50$ $51$ $49$

$Y$ $108$ $107$ $105$ $105$ $106$ $107$ $104$ $103$ $104$ $101$

The standard deviation of the data $6, 7, 8, 9, 10$ is

The variance of the following data is
$x_{i}$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$f_{i}$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$

If the mean and variance of the following data: $6, 10, 7, 13, a, 12, b, 12$ are $9$ and $\frac{37}{4}$ respectively,then $(a-b)^{2}$ is equal to:

Statement-$1$: The variance of the first $n$ even natural numbers is $\frac{n^2 - 1}{3}$.
Statement-$2$: The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n(4n^2 - 1)}{3}$.

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