The marks obtained by 30 students in a class assessment of 5 marks is given below :

Marks	No. of students
0	1
1	3
2	6
3	10
4	5
5	5

Calculate the mean, median and mode of the above distribution.

The variates (marks) are already in ascending order. We construct the cumulative frequency table as under :

Mean = $\dfrac{∑f$ixi}{∑f_i} = \dfrac{90}{30} = 3.

Total number of observations = 30, which is even.

$\therefore \text{Median} = \dfrac{\dfrac{n}{2} \text{th observation} + \big(\dfrac{n}{2} + 1\big)\text{th observation}}{2} \\[1em] = \dfrac{\dfrac{30}{2} \text{th observation} + \big(\dfrac{30}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\text{ 15th observation + 16th observation}}{2} \\[1em]$

All observations from 11th to 20th are equal, each = 3.

Hence, median

$= \dfrac{3 + 3}{2} \\[1em] = \dfrac{6}{2} \\[1em] = 3.$

As the variate 3 has maximum frequency 10, so mode = 3.

Hence, mean = 3, median = 3 and mode = 3.