Question

Find the mean, using direct method:

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	7	5	6	12	8	2

Answer 1

Class	Frequency $\left(f_i\right)$	Mid Values $\left(x_i\right)$	$(f_i\times x_i)$
0-10	7	5	35
10-20	5	15	75
20-30	6	25	150
30-40	12	35	420
40-50	8	45	360
50-60	2	55	110
	${\sum }_{f_i}=40$		$\sum (f_i\times x_i)=1150$

$$\begin{gathered} \therefore \text{Mean,}\overline{x}=\frac{{\displaystyle \sum (f_i\times x_i)}}{{\displaystyle \sum f_i}} \\ \text{=}\frac{1150}{40} \\ \text{=28}\text{.75} \\ \therefore \overline{x}=\text{28}\text{.75} \end{gathered}$$