The following table shows the daily wages of workers in a factory:
Daily wages (in RS.) | 0 - 100 | 100 - 200 | 200 - 300 | 300 - 400 | 400 - 500 |
Number of workers | 40 | 32 | 48 | 22 | 8 |
Find the median daily wage income of the workers.
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.
DAILY WAGES(Rs.) | NUMBER OF WORKERS(fi) | Cf |
0 - 100 | 40 | 40 |
100 - 200 | 32 | 40 + 32 = 72 |
200 - 300 | 48 | 72 + 48 = 120 |
300 - 400 | 22 | 120 + 22 = 142 |
400 - 500 | 8 | 142 + 8 = 150 |
TOTAL | 150 |
So, N = 150
⇒ N/2 = 150/2 = 75
The cumulative frequency just greater than (N/2 = ) 75 is 120, so the corresponding median class is 200 - 300 and accordingly we get Cf = 72(cumulative frequency before the median class).
Now, since median class is 200 - 300.
∴ l = 200, h = 100, f = 48, N/2 = 75 and Cf = 72
Median is given by,
⇒ 
= 200 + 6.25
= 206.25
Thus, median wage is Rs. 206.25.