Find the mean and the median of the following set of numbers :

8, 0, 5, 3, 2, 9, 1, 5, 4, 7, 2, 5.

By formula,

Mean = $\dfrac{\text{Sum of observations}}{\text{No. of observations}}$

Sum of observations = 8 + 0 + 5 + 3 + 2 + 9 + 1 + 5 + 4 + 7 + 2 + 5 = 51.

$\text{Mean} = \dfrac{51}{12} = 4.25$

By arranging data in ascending order, we get :

0, 1, 2, 2, 3, 4, 5, 5, 5, 7, 8, 9

Here, n = 12 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,

$\text{Median} = \dfrac{\dfrac{12}{2}\text{th observation} + \Big(\dfrac{12}{2} + 1\Big)\text{th observation}}{2} \\[1em] = \dfrac{\text{6th observation + 7th observation}}{2} \\[1em] = \dfrac{4 + 5}{2} \\[1em] = \dfrac{9}{2} \\[1em] = 4.5$

Hence, mean = 4.25 and median = 4.5