The standard deviation of the first 10 multip | vedclass

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(C) The first $10$ multiples of $4$ are $4, 8, 12, 16, 20, 24, 28, 32, 36, 40$.Let $X = 4i$ where $i = 1, 2, \dots, 10$.The standard deviation of the

Vedclass · Accepted Answer

$11.5$

Vedclass · Answer

(C) The first $10$ multiples of $4$ are $4, 8, 12, 16, 20, 24, 28, 32, 36, 40$.Let $X = 4i$ where $i = 1, 2, \dots, 10$.The standard deviation of the first $n$ natural numbers is $\sigma_n = \sqrt{\frac{n^2 - 1}{12}}$.Since each term is multiplied by $4$,the standard deviation of the multiples is $4 	imes \sigma_{10}$.$\sigma_{10} = \sqrt{\frac{10^2 - 1}{12}} = \sqrt{\frac{99}{12}} = \sqrt{8.25}$.Standard deviation $= 4 	imes \sqrt{8.25} = \sqrt{16 	imes 8.25} = \sqrt{132} \approx 11.489 \approx 11.5$.

Marks	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Group $A$	$9$	$17$	$32$	$33$	$40$	$10$	$9$
Group $B$	$10$	$20$	$30$	$25$	$43$	$15$	$7$

The standard deviation of the first $10$ multiples of $4$ is:

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