Question

Find the mean, using direct method:

Marks	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Number of students	6	8	13	7	3	2	1

Answer 1

Class	Frequency $\left(f_i\right)$	Mid Values $\left(x_i\right)$	$(f_i\times x_i)$
10-20	6	15	90
20-30	8	25	200
30-40	13	35	455
40-50	7	45	315
50-60	3	55	165
60-70	2	65	130
70-80	1	75	75
	$\sum f_i=40$		$\sum (f_i\times x_i)=1430$

$$\begin{gathered} \therefore \text{Mean,}\overline{x}=\frac{{\displaystyle \sum (f_i\times x_i)}}{{\displaystyle \sum f_i}} \\ \text{=}\frac{1430}{40} \\ \text{=35}\text{.75} \\ \therefore \overline{x}=35.75 \end{gathered}$$