If the median of the following data is 32.5, find the missing frequencies.
Class interval: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | Total |
Frequency: | f1 | 5 | 9 | 12 | f2 | 3 | 2 | 40 |
Class interval | Frequency | Cumulative frequency |
0-10 | f1 | f1 |
10-20 | 5 | 5 + f1 |
20-30 | 9 | 14 + f1 (F) |
30-40 | 12 (f) | 26 + f1 |
40-50 | f2 | 26 + f1 + f2 |
50-60 | 3 | 29 + f1 + f2 |
60-70 | 2 | 31 + f1 + f2 |
N = 40 |
Given, Median = 32.5
Then median class = 30-40
l = 30, h = 10, f = 12, F = 14 + f1
Median = l +
32.5 = 30 + * 10
2.5 = * 5
15 = (6 – f1) 5
3 = 6 – f1
f1 = 3
Given, sum of frequencies = 40
= 3 + 5 + 9 + 12 + f2 + 3 + 2 = 40
= 34 + f2 = 40
= f2 = 6
Therefore, f1 = 3 and f2 = 6