Question

Find the mean, using direct method:

Class	0-100	100-200	200-300	300-400	400-500
Frequency	6	9	15	12	8

Answer 1

Class	Frequency $\left(f_i\right)$	Mid values $\left(x_i\right)$	$(f_i\times x_i)$
0-100	6	50	300
100-200	9	150	1350
200-300	15	250	3750
300-400	12	350	4200
400-500	8	450	3600
	$\sum f_i=50$		$\sum (f_i\times x_i)=13200$

$$\begin{gathered} \therefore \text{Mean,}\overline{x}=\frac{{\displaystyle \sum (f_i\times x_i)}}{{\displaystyle \sum f_i}} \\ \text{=}\frac{13200}{50} \\ \text{=264} \\ \therefore \overline{x}=264 \end{gathered}$$