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 |
171.5 - 174.5 |
18 |
420 |
172 - 174 |
171.5 - 174.5 |
18 |
420 |
|
|
N = 420 |
|
We have,
N = 420
\(\frac{N}{2}=\frac{420}{2}=210\)
The cumulative frequency just greater than \(\frac{N}{2}\) is 275 then 165.5-168.5 is the median class such that,
I = 165.5, f = 142, F = 133 and h = 168.5-165.5 = 3
Median = I + \(\frac{\frac{N}{2}-F}{f}\times h\)
\(=165.5+\frac{210-133}{142}\times 3\)
\(=165.5+\frac{77}{142}\times 3\)
\(=165.5+1.63\)
\(=167.13\)