Following data relates to daily wages of persons working in a factory. Compute the median daily wage.
| Daily Wages (Rs) | Number of Workers |
| 20-25 | 14 |
| 25-30 | 28 |
| 30-35 | 33 |
| 35-40 | 30 |
| 40-45 | 20 |
| 45-50 | 15 |
| 50-55 | 13 |
| 55-60 | 7 |
Answer & explanation
Correct answer: option 4
The correct answer is option 4: 35.83
| Daily Wages (Rs) | Number of Workers | Cumulative Frequency |
| 20-25 | 14 | 14 |
| 25-30 | 28 | 42 |
| 30-35 | 33 | 75 |
| 35-40 | 30 | 105 |
| 40-45 | 20 | 125 |
| 45-50 | 15 | 140 |
| 50-55 | 13 | 153 |
| 55-60 | 7 | 160 |
In case of continuous series we have to locate the median class where N/2th item lies.
In the above question median class is the value of (N/2)th item (i.e.160/2) = 80th item of the series, which lies in 35–40 class interval.
The median can then be obtained as follows: Median =L + [(N/2- c.f)/f] * h
Where, L = lower limit of the median class
c.f. = cumulative frequency of the class preceding the median class,
f = frequency of the median class,
h = magnitude of the median class interval.
Putting the values in the formula,
Median = 35 + [(80-75)/30] * (40-35)
= 35 + (5*5)/30
= 35.83