Question :
| Age (in years) | Number of Policy Holders |
| Below 20 | 2 |
| Below 25 | 6 |
| Below 30 | 24 |
| Below 35 | 45 |
| Below 40 | 78 |
| Below 45 | 89 |
| Below 50 | 92 |
| Below 55 | 98 |
| Below 60 | 100 |
Solution :
We are given the cumulative frequency distribution.
So, we first construct a frequency table from the given cumulative frequency distribution and then we will make necessary computations to compute median.
Class Interval
Frequency
Cumulative Frequency
18 โ 20
2
2
20 โ 25
4
6
25 โ 30
18
24
30 โ 35
21
45
35 โ 40
33
78
40 โ 45
11
89
45 โ 50
3
92
50 โ 55
6
98
55 โ 60
2
100
Here, n = 100 So, \(n\over 2\) = 50
We see that the cumulative frequency just greater than \(n\over 2\), i.e. 50 is 78 and the corresponding class is (35 โ 40), So, it is the median class.
\(\therefore\) l = 35, cf = 45, f = 33 and h = 5.
Now, let us substitute these values in the formula
Median = l + (\({n\over 2} โ cf\over f\)) \(\times\) h = 35 + \(5\over 33\) \(\times\) 5
= 35 + 0.76 = 35.76
Hence, the median age is 35.76 years.
