Find the mean and median of all the positive factors of 72.

The positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Mean = $\dfrac{\text{Sum of all observations }}{\text{Number of all observations }}$

= $\dfrac{1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 + 72}{12}$

= $\dfrac{195}{12}$

= 16.25

Hence, the mean is 16.25.

On arranging the given set of data in ascending order, we get :

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Number of observations, n = 12 (even)

Median = $\dfrac{1}{2}\Big[\text{the value of} \Big(\dfrac{n}{2}\Big)^{th} + \text{the value of} \Big(\dfrac{n}{2} + 1\Big)^{th}\Big]$ term

= $\dfrac{1}{2}\Big[\text{the value of} \Big(\dfrac{12}{2}\Big)^{th} + \text{the value of} \Big(\dfrac{12}{2} + 1\Big)^{th}\Big]$ term

= $\dfrac{1}{2}\Big[\text{the value of} (6)^{th} + \text{the value of} (6 + 1)^{th}\Big]$ term

= $\dfrac{1}{2}\Big[8 + 9\Big]$

= $\dfrac{1}{2}\Big[17\Big]$

= 8.5

Hence, the median is 8.5.