Question

Find the mean of the following data

Class	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	3	6	8	10	8	5	3

Answer 1

Mean of grouped data by direct method

mid point $=\frac{Higherlimit+lowerlimit}{2}$

Class	Frequency (f)	Mid-point (x)	fx
$10-20$	$3$	$\frac{10+20}{2}=\frac{30}{2}=15$	$3\times 15=45$
$20-30$	$6$	$\frac{20+30}{2}=\frac{50}{2}=25$	$6\times 25=150$
$30-40$	$8$	$\frac{30+40}{2}=\frac{70}{2}=35$	$8\times 35=280$
$40-50$	$10$	$\frac{40-50}{2}=\frac{90}{2}=45$	$10\times 45=450$
$50-60$	$8$	$\frac{50+60}{2}=\frac{110}{2}=55$	$8\times 55=440$
$60-70$	$5$	$\frac{60+70}{2}=\frac{130}{2}=65$	$5\times 65=325$
$70-80$	$3$	$\frac{70+80}{2}=\frac{150}{2}=75$	$3\times 75=225$
	$N=\sum f=43$		$\sum fx=1915$

Arithmetic mean of grouped Data by Direct method

Mean $=\frac{\sum fx}{\sum f}=\frac{\sum fx}{N}=\frac{1915}{43}$

$=44.5348$

$\cong 44.535$ ramded 3 decimal