Question

Find the mean, using direct method:

Class	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	11	15	20	30	14	10

Answer 1

Class	Frequency $\left(f_i\right)$	Mid Values $\left(x_i\right)$	$\left(f_i\times x_i\right)$
10-20	11	15	165
20-30	15	25	375
30-40	20	35	700
40-50	30	45	1350
50-60	14	55	770
60-70	10	65	650
	$\sum f_i=100$		$\sum (f_i\times x_i)=4010$

$$\begin{gathered} \therefore \text{Mean,}\overline{x}=\frac{{\displaystyle \sum (f_i\times x_i)}}{{\displaystyle \sum f_i}} \\ \text{=}\frac{4010}{100} \\ \text{=40}\text{.1} \\ \therefore \overline{x}=40.1 \end{gathered}$$