The following table shows the daily wages of workers in a factory:
Daily eages (in Rs)0−100100−200200−300300−400400−500Number of workers403248228
Find the median daily wage income of the workers.
Sol:
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 = 75 and N/2=75
Median,M=l+((N/2−cf) /f)×h
Median=200+((75−720/48 )×100
Median=200+6.25
Median=206.25
Hence, the median daily wage income of the worker is Rs. 206.25 .