Question

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 $P-O=$

• A. 0.3
• B. 0.32
• C. 0.23
• D. 0.2

Answer 1

Answer: (B)

First 5 odd natural numbers $=1,3,5,7,9$
Mean of 5 odd natural numbers
$=\frac{1+3+5+7+9}{5}=5$
Deviation $=⟨4,2,0,2,4⟩$
$=⟨|1-5|,|3-5|,|5-5|,|7-5|,|9-5|⟩$
$\therefore O=\text{ Mean deviation }=\frac{4+2+0+2+4}{5}=24$
First 5 prime numbers $=2,3,5,7,11$
Mean $=\frac{2+3+5+7+11}{5}=5.6$
Deviation $=3.6,2.6,0.6,1.4,5.4$
$P=$ Mean deviation
$=\frac{3.6+26+0.6+1.4+5.4}{5}=2.72$
$P-O=2.72-2.4=0.32$