The median of frequency distribution is:
| Class : | 0 – 25 | 25 – 50 | 50 – 75 | 75 – 100 |
| Frequency : | 23 | 32 | 15 | 12 |
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 39.06
The median is the value with half the observations below it. It lies in the class where the cumulative frequency first passes \(\frac{N}{2}\), and inside that class it is found by \(\text{Median}=l+\displaystyle\frac{\frac{N}{2}-cf}{f}\times h\), where \(l\) is the lower limit of the class, \(cf\) the cumulative frequency before it, \(f\) its frequency and \(h\) its width.
The median class:
Total frequency \(N=23+32+15+12=82\), so half of it is \(\frac{N}{2}=41\)
Cumulative frequencies are 23, 55, 70, 82; the first to pass 41 is 55, so the median class is 25 – 50
The median (l = 25, cf = 23, f = 32, h = 25):
Putting the values in the formula: \(\text{Median}=25+\displaystyle\frac{41-23}{32}\times25\)
The 18 observations needed inside the class give \(\displaystyle\frac{18\times25}{32}=14.06\), so the median is \(25+14.06=\) 39.06