Let O be the mean deviation of the first five | vedclass

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(B) The first five odd natural numbers are $1, 3, 5, 7, 9$. Their mean $\bar{x} = \frac{1+3+5+7+9}{5} = \frac{25}{5} = 5$.The mean deviation $O = \fra

Vedclass · Accepted Answer

$0.32$

Vedclass · Answer

(B) The first five odd natural numbers are $1, 3, 5, 7, 9$. Their mean $\bar{x} = \frac{1+3+5+7+9}{5} = \frac{25}{5} = 5$.The mean deviation $O = \frac{\sum |x_i - \bar{x}|}{5} = \frac{|1-5| + |3-5| + |5-5| + |7-5| + |9-5|}{5} = \frac{4+2+0+2+4}{5} = \frac{12}{5} = 2.4$.The first five prime numbers are $2, 3, 5, 7, 11$. Their mean $\bar{y} = \frac{2+3+5+7+11}{5} = \frac{28}{5} = 5.6$.The mean deviation $P = \frac{\sum |y_i - \bar{y}|}{5} = \frac{|2-5.6| + |3-5.6| + |5-5.6| + |7-5.6| + |11-5.6|}{5} = \frac{3.6 + 2.6 + 0.6 + 1.4 + 5.4}{5} = \frac{13.6}{5} = 2.72$.Therefore,$P - O = 2.72 - 2.4 = 0.32$.

$x_i$	$6$	$12$	$18$	$24$	$30$	$36$	$42$
$f_i$	$4$	$7$	$9$	$18$	$15$	$10$	$5$

Class interval	$0$-$10$	$10$-$20$	$20$-$30$	$30$-$40$	$40$-$50$	$50$-$60$	$60$-$70$
Frequency	$4$	$6$	$16$	$28$	$16$	$6$	$4$

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Freq	$6$	$7$	$15$	$16$	$4$	$2$

Let $O$ be the mean deviation of the first five odd natural numbers about their mean and $P$ be the mean deviation of the first five prime numbers about their mean. Then $P-O=$

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Calculate the mean deviation about the mean of the set of first $n$ natural numbers when $n$ is an odd number.

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