Question

The mean and S.D. of the odd divisors of 360 are respectively as

• A. 13, 15.01
• B. 78, 15.01
• C. 6, 78
• D. 13, 6

Answer 1

Answer: (A)

13, 15.01

$360=2^3\times 3^2\times 5^1=2^a{3}^b{5}^c$

Number of odd divisors $=(b+1)(c+1)=(2+1)$$(1+1)=6$
these six divisor are the factors of 45, which are 1, 3, 5, 9, 15, 45

$\therefore$ Mean, $\overline{x}=\frac{1+3+5+9+15+45}{6}=\frac{78}{6}=13$
and S.D $=\sqrt{\frac{\sum (x-\overline{x}{)}^2}{6}}=\sqrt{\frac{{12}^2+{10}^2+8^2+4^2+2^2+{32}^2}{6}}=15.01$