Find the mean and the median of all the (positive) factors of 48.

Positive factors of 48 :

1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

By formula,

$\text{Mean} = \dfrac{\text{Sum of positive factors of 48}}{\text{No. of factors}}$

Sum of positive factors of 48 = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 124.

Mean $= \dfrac{124}{10} = 12.4$

Here, n = 10 which is even.

By formula,

Median = $\dfrac{\dfrac{n}{2}\text{th observation} + \Big(\dfrac{n}{2} + 1\Big)\text{th observation}}{2}$

Substituting the values we get,

$\text{Median} = \dfrac{\dfrac{10}{2}\text{th observation} + \Big(\dfrac{10}{2} + 1\Big)\text{th observation}}{2} \\[1em] = \dfrac{\text{5th observation + 6th observation}}{2} \\[1em] = \dfrac{6 + 8}{2} \\[1em] = \dfrac{14}{2} \\[1em] = 7$

Hence, mean = 12.4 and median = 7.