Find the mean, median and mode of the following marks obtained by 16 students in a class test marked out of 10 marks :

0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7 and 8.

Total marks = 0 + 0 + 2 + 2 + 3 + 3 + 3 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 7 + 8 = 64.

By formula,

Mean = $\dfrac{\text{Total marks}}{\text{No. of students}} = \dfrac{64}{16}$ = 4.

Here, n = 16, which is even.

By formula,

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

Substituting values we get,

$= \dfrac{\dfrac{16}{2}\text{ th term} + \Big(\dfrac{16}{2} + 1\Big)\text{ th term}}{2} \\[1em] = \dfrac{\text{8th term + 9th term}}{2} \\[1em] = \dfrac{4 + 5}{2} \\[1em] = \dfrac{9}{2} \\[1em] = 4.5$

From above set of numbers : 5 occurs most of the time.

Mode = 5.

Hence, mean = 4, median = 4.5 and mode = 5.