Question

Calculate the median in the following frequency distribution

Wages	50-60	60-70	70-80	80-90	90-100
No. of labourers	5	10	15	20	25

• A. $90$
• B. $70$
• C. $83.75$
• D. $85$

Answer 1

Answer: (D)

$85$

Wages	mid point (m)	frequency (f)	(m-75)/10 (d)	fd	c.f.
50-60	55	5	-2	-10	5
60-70	65	10	-1	-10	15
70-80	75	15	0	0	30
80-90	85	20	1	20	50
90-100	95	25	2	50	75
		n=75		$\sum fd=50$

Median is given by $L+\frac{\frac{n}{2}-c.f.}{f}\times i$

where $L$ is the lower limit of the median class. (median class is the class where ${\frac{n}{2}}^{th}$ term is lying)

$c.f.$ is the cumulative frequency of the class preceding the median class

$f$ is the frequency of the median class

$i$ is the class interval of the median class.

From the above table,

$L=70$

$\frac{n}{2}=37.5$

$c.f.=15$

$f=15$

$i=10$

Therefore, $median=70+\frac{37.5-15}{15}\times 10=70+15=85$