Find the median of the following data. (Rounded off to 2 decimal places.)
| Class interval | 0 - 5 | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 |
| Frequency | 3 | 5 | 4 | 2 | 7 | 6 | 5 |
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 21.43.
| Class Interval | Frequency (f) | Cumulative Frequency (cf) |
| 0 - 5 | 3 | 3 |
| 5 - 10 | 5 | 3 + 5 = 8 |
| 10 - 15 | 4 | 8 + 4 = 12 |
| 15 - 20 | 2 | 12 + 2 = 14 |
| 20 - 25 | 7 | 14 + 7 = 21 |
| 25 - 30 | 6 | 21 + 6 = 27 |
| 30 - 35 | 5 | 27 + 5 = 32 |
The total frequency (N) = 32
The median position is N/2 = 32/2 = 16
The cumulative frequency of just greater than 16 is 21.
Thus, the median class = 20-25
Median = L + [(N/2 - cf)/f] × h
Where L = Lower limit of the median class = 20
N = Total frequency = 32
cf = Cumulative frequency of the class preceding the median class = 14
f = Frequency of the median class = 7
h = Class width = 5
Median = 20 + [(16 - 14)/7] × 5 = 20 + (2/7) × 5 = 21.4285... = 21.43 (approx)
Therefore, the median of the given data is 21.43.