The median of class frequency distribution is:
| Class: | 0 – 25 | 25 – 50 | 50 – 75 | 75 – 100 | Total |
| Frequency: | 25 | 32 | 15 | 16 | 88 |
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 39.84
The median is the middle value, the \(\frac{N}{2}\)th observation. For grouped data, find the class that holds it from the cumulative frequencies, then use \(\text{Median}=l+\frac{N/2-cf}{f}\times h\), where \(l\) is the lower limit of that class, \(cf\) the cumulative frequency of the class before it, \(f\) its frequency and \(h\) the class width.
The median class:
Total frequency \(N=88\), so the median is the 44th value
Cumulative frequencies: 25, 57, 72, 88
The 44th value lies in 25 – 50 (cumulative frequency 57 is the first above 44)
The median (\(l=25\), \(cf=25\), \(f=32\), \(h=25\)):
Putting in the values: \(\displaystyle\text{Median}=25+\frac{44-25}{32}\times25=25+\frac{475}{32}\)
So the median is \(25+14.84=39.84\)