Question

The marks obtained by 110 students in an examination are given below:

Marks:	30 – 35	35 – 40	40 – 45	45 – 50	50 – 55	55 – 60	60 – 65
Frequency:	14	16	28	23	18	8	3

Find the mean marks of the students.

Answer 1

Let the assumed mean, A be 47.5.

Here, h = 5

Marks	Mid-Values(xi)	Frequency (fi)	${\mathit{d}}_{\mathbf{i}}\mathbf{=}{\mathit{x}}_{\mathbf{i}}\mathbf{-}\mathbf{47}\mathbf{.}\mathbf{5}$	${\mathit{u}}_{\mathbf{i}}\mathbf{=}\frac{{\mathbf{x}}_{\mathbf{i}}\mathbf{-}\mathbf{47}\mathbf{.}\mathbf{5}}{\mathbf{5}}$	${\mathit{f}}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}$
30–35	32.5	14	−15	−3	−42
35–40	37.5	16	−10	−2	−32
40–45	42.5	28	−5	−1	−28
45–50	47.5	23	0	0	0
50–55	52.5	18	5	1	18
55–60	57.5	8	10	2	16
60–65	62.5	3	15	3	9
		$\sum _{}{f}_i=110$			$\sum _{}{f}_i{u}_i=-59$

We know

Mean $=A+h\times \left(\frac{{\displaystyle \sum _{}}{f}_i{u}_i}{{\displaystyle \sum _{}}{f}_i}\right)$
∴ Mean marks of the students

$$\begin{gathered} =47.5+5\times \left(\frac{-59}{110}\right) \\ =47.5-2.68 \\ =44.82 \end{gathered}$$

Hence, the mean marks of the students is 44.82.