The following is the distribution of height of students of a certain class in a certain city.
Height (in cms): | 160-162 | 163-165 | 166-168 | 169-171 | 172-174 |
No. of students: | 15 | 118 | 142 | 127 | 18 |
Find the median height.
Class interval (exclusive) | Class interval (inclusive) | Class interval (Frequency) | Cumulative frequency |
160-162 | 159.5-162.5 | 15 | 15 |
163-164 | 162.5-165.5 | 118 | 133 (F) |
166-168 | 165.5-168.5 | 142 (f) | 275 |
169-171 | 168.5-171.5 | 127 | 402 |
172-174 | 171.5-174.5 | 18 | 420 |
N = 420 |
We have, N = 420
= 
= 210
The cumulative frequency just greater than 
is 275 then 165.5-168.5 is the median class such that,
l = 165.5, f = 142, F = 133 and h = 168.5-165.5 = 3
Median = l + 
* h
= 165.5 + 
* 3
= 165.5 + 
* 3
= 165.5 + 1.63
= 167.13
2