Question

Find the median wages for the following frequency distribution:

Wages per day (in Rs)	61 – 70	71 – 80	81 – 90	91 – 100	101 – 110	111 – 120
No. of women workers	5	15	20	30	20	8

 

Answer 1

Class	Frequency (f)	Cumulative Frequency (cf)
60.5 – 70.5	5	5
70.5 – 80.5	15	20
80.5 – 90.5	20	40
90.5 – 100.5	30	70
100.5 – 110.5	20	90
110.5 – 120.5	8	98
	N = Σ𝑓 = 98

Now, N = 98
⇒ `N/2` = 49.
The cumulative frequency just greater than 49 is 70 and the corresponding class is 90.5 – 100.5.
Thus, the median class is 90.5 – 100.5.
Now, l = 90.5, h = 10, f = 30, cf = c.f. of preceding class = 40 and `N/2` = 49.
∴ Median, `M = l + {h×((N/2−f)/f)}`
                 `= 90.5 + {10 × ((49 − 40)/30)}`
                 = 90.5 + 3
                 = 93.5
Hence, median wages = Rs. 93.50.