Question

The following table shows the daily wages of workers in a factory:
$\begin{array}{cccccc}\text{Daily eages (in ₹)}& 0-100& 100-200& 200-300& 300-400& 400-500\\ \text{Number of workers}& 40& 32& 48& 22& 8\end{array}$
Find the median daily wage income of the workers.

• A.
  ₹202.25
• B.
  ₹204.25
• C.
  ₹206.25
• D.
  ₹208.25

Answer 1

The correct option is C

₹206.25

We prepare the cumulative frequency table, as shown:

Daily wages	Number of workers	Cumulative frequency
0-100	40	40
100-200	32	72
200-300	48	120
300-400	22	142
400-500	8	150
	N=Σf=150

N= 150

⇒N/2 = 75

The cumulative frequency greater than 75 is 120 and the corresponding class is 200-300.

Thus the median class is 200-300.

Therefore, l=200, h = 100, f = 48,
c.f. of preceding class = 72 and N/2=75

Median,M=l+((N/2−cf) /f)×h
Median=200+((75−72)/48 )×100
Median=200+6.25
Median=206.25

Hence, the median daily wage income of the workers is ₹206.25 .