The standard deviation of 25 numbers is 40. I | vedclass

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(A) The standard deviation is a measure of dispersion,which represents how spread out the numbers are from their mean.If each observation $x_i$ in a d

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$40$

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(A) The standard deviation is a measure of dispersion,which represents how spread out the numbers are from their mean.If each observation $x_i$ in a dataset is transformed to $x_i + k$,where $k$ is a constant,the mean of the data increases by $k$,but the differences between the observations and the mean remain the same.Specifically,if $X'$ is the new set of numbers where $x'_i = x_i + 5$,the new mean $\bar{X}' = \bar{X} + 5$.The new standard deviation $\sigma'$ is given by $\sqrt{\frac{1}{n} \sum (x'_i - \bar{X}')^2} = \sqrt{\frac{1}{n} \sum ((x_i + 5) - (\bar{X} + 5))^2} = \sqrt{\frac{1}{n} \sum (x_i - \bar{X})^2} = \sigma$.Therefore,the standard deviation remains unchanged.Thus,the new standard deviation is $40$.

Class interval	$0-5$	$5-10$	$10-15$	$15-20$	$20-25$
Frequency	$4$	$1$	$10$	$3$	$2$

The standard deviation of $25$ numbers is $40$. If each of the numbers is increased by $5$,then the new standard deviation will be

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Class interval $0-5$ $5-10$ $10-15$ $15-20$ $20-25$
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