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 |
To find median, Assume
Σfi = N = Sum of frequencies,
h = length of median class,
l = lower boundary of the median class,
f = frequency of median class
and Cf = cumulative frequency
Lets form a table and convert it into exclusive - type by adjusting from both ends of a class.
WAGES PER DAY(Rs.) | NUMBER OF WOMEN WOKERS(fi) | Cf |
60.5 - 70.5 | 5 | 5 |
70.5 - 80.5 | 15 | 5 + 15 = 20 |
80.5 - 90.5 | 20 | 20 + 20 = 40 |
90.5 - 100.5 | 30 | 40 + 30 = 70 |
100.5 - 110.5 | 20 | 70 + 20 = 90 |
110.5 - 120.5 | 8 | 90 + 8 = 98 |
TOTAL | 98 |
So, N = 98
⇒ N/2 = 98/2 = 49
The cumulative frequency just greater than (N/2 = )49 is 70, so the corresponding median class is 90.5 - 100.5 and accordingly we get Cf = 40(cumulative frequency before the median class).
Now, since median class is 90.5 - 100.5.
∴ l = 90.5, h = 10, f = 30, N/2 = 49 and Cf = 40
Median is given by,
⇒ 
= 90.5 + 3
= 93.5
Thus, median is Rs. 93.5.