Question

The following table gives the daily income of 50 workers of a factory:
$\begin{array}{cccccc}\text{Daily income(in Rs.)}& 100-120& 120-140& 140-160& 160-180& 180-200\\ \text{Number of workers}& 12& 14& 8& 6& 10\end{array}$
Find the mean, mode and median of the above data.

Answer 1

Let assumed mean A = 150 and h = 20

Class	Frequency fi	Midvalue xi	ui=((xi−A)/h)	fiui	C.F
100-120	12	110	-2	-24	12
120-140	14	130	-1	-14	26
140-160	8	150 = A	0	0	34
160-180	6	170	1	6	40
180-200	10	190	2	20	50
	N = 50			∑(fiui)=−12

(i) Mean

$\overline{x}$ = A+h(∑fiui/N)

= 150-24/5 = 150-4.8 = 145.2

(ii) N = 50, N/2 = 25

Cumulative frequency just after 25 is 26

Median class is 120-140

I = 120, h = 10, N = 50, c = 12, f = 14

Therefore,
Median
Me=I+h((N/2−c)/f)
=120+20(25−1214)

= 120+20 x 13/14
= 120+130/7
= 120+18.6 = 138.6

(iii) Mode = 3 x median - 2 x mean

= 3 x 138.6 - 2 x 145.2

= 415.8 - 190.4 = 125.4

Thus, mean = 145.2, median = 138.6, mode = 125.4