Calculate the mean and the median for the following distribution :

Number	Frequency
5	1
10	2
15	5
20	6
25	3
30	2
35	1

The given numbers are already in ascending order. We construct the cumulative frequency table as under :

Here, n (no. of observations) = 20, which is even.

$\therefore \text{Median} = \dfrac{\dfrac{n}{2} \text{th observation} + \big(\dfrac{n}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\dfrac{20}{2} \text{th observation} + \big(\dfrac{20}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\text{ 10th observation + 11th observation}}{2} \\[1em]$

All observations from 9th to 14th are equal, each = 20.

Hence, median

$= \dfrac{20 + 20}{2} \\[1em] = \dfrac{40}{2} \\[1em] = 20.$

Now calculating mean,

$\text{ Mean} = \dfrac{∑f$ixi}{∑f_i} \\[1em] = \dfrac{390}{20} \\[1em] = 19.5

Hence, mean = 19.5 and median = 20.