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Q. The mein value of the median and mean of the odd divisors of $360$ is

Statistics

Solution:

$360 = 2^3 \,3^2\, 5^1 = 2^a\, 3^b\, 5^c$
Number of odd divisors of $360 = (b + 1) (c + 1)$
$= 3 \times 2= 6$
Sum of all odd divisors $= \frac{\text{Sum of odd divisors}}{\text{Number of odd divisors}}$
$= \frac{78}{6} = 13$
Again, odd divisors of $360$ are the factors of $3^{2} \times 5^{1} = 45$
i.e., odd divisors are $1$, $3$, $5$, $9$, $15$, $45$
Now median value of the divisor is
$\frac{\text{Value of $3^{rd}$ divisor + Value of $4^{th}$ divisor}}{2}$
$= \frac{5+9}{2}=7$
$\therefore $ Median $= 7$
$\therefore $ Mean of median and mean of odd divisors of $360$
$= \frac{13+7}{2} = 10$