The standard deviation of the numbers 31, 32, | vedclass

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Question

(C) The given numbers are $31, 32, 33, \ldots, 47$. Subtracting $30$ from each term,we get the sequence $1, 2, 3, \ldots, 17$. The standard deviation

Vedclass · Accepted Answer

$2 \sqrt{6}$

Vedclass · Answer

(C) The given numbers are $31, 32, 33, \ldots, 47$. Subtracting $30$ from each term,we get the sequence $1, 2, 3, \ldots, 17$. The standard deviation remains unchanged when a constant is subtracted from each term. The formula for the standard deviation of the first $n$ natural numbers is $SD = \sqrt{\frac{n^{2}-1}{12}}$. Here,$n = 17$. $SD = \sqrt{\frac{17^{2}-1}{12}} = \sqrt{\frac{289-1}{12}} = \sqrt{\frac{288}{12}}$. $SD = \sqrt{24} = 2 \sqrt{6}$.

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

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

The standard deviation of the numbers $31, 32, 33, \ldots, 46, 47$ is

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