Consider the following frequency distribution.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Frequency | 4 | 5 | 7 | 10 | 12 | 8 | 4 |
Find the median of the distribution?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 39
The median is the middle value of the data. For a grouped distribution, the class in which the \(\frac{N}{2}\)th value falls (the median class) is found from the cumulative frequencies, and then
\(\displaystyle \text{Median}=l+\frac{\frac{N}{2}-cf}{f}\times h\)
where \(l\) is the lower limit of the median class, \(cf\) the cumulative frequency of the class before it, \(f\) its frequency and \(h\) the class width.
The median class (from the cumulative frequencies):
Adding the frequencies one class at a time gives the cumulative frequencies: 4, 9, 16, 26, 38, 46, 50
\(N=50\) and \(\frac{N}{2}=25\)
The count passes 25 in the class 30-40 (16 before it, 26 up to its end), so it is the median class
Putting the values in the formula (from the median class and the one before it):
\(l=30\), \(cf=16\), \(f=10\), \(h=10\)
\(\displaystyle \text{Median}=30+\frac{25-16}{10}\times10=30+9=39\)