0-4 2 4-8 4 8-12 7 12 - 16 5 16-20 8 20 -24 3 24 - 28 2 28 -32 1 32 - 36 13 36 - 40 5 40 -44 3 44 - 48 3 find the median . also use ogives
Class Interval | Frequency (f) | Cumulative Frequency (CF) |
0-4 | 2 | 2 |
4-8 | 4 | 6 |
8-12 | 7 | 13 |
12-16 | 5 | 18 |
16-20 | 8 | 26 |
20-24 | 3 | 29 |
24-28 | 2 | 31 |
28-32 | 1 | 32 |
32-36 | 13 | 45 |
36-40 | 5 | 50 |
40-44 | 3 | 53 |
44-48 | 3 | 56 |
Median = Size of th item
N = 56
Þ Median = Size of th item
= Size of 28^{th} item
This corresponds to 26^{th} cumulative frequency and the median class is (20-24)
l = 20, CF = 26, f = 3
Ogive Method
Converting the series into Less than cumulative frequency.
| Commutative Frequency (CF) | Coordinates of Less than Ogive |
Less than 4 | 2 | (4, 2) |
Less than 8 | 6 | (8, 6) |
Less than 12 | 13 | (12, 13) |
Less than 16 | 18 | (16, 18) |
Less than 20 | 26 | (20, 26) |
Less than 24 | 29 | (24, 29) |
Less than 28 | 31 | (28, 31) |
Less than 32 | 32 | (32, 32) |
Less than 36 | 45 | (36, 45) |
Less than 40 | 50 | (40, 50) |
Less than 44 | 53 | (44, 53) |
Less than 48 | 56 | (48, 56) |
Converting the series into More than cumulative frequency
| Commutative Frequency (CF) | Coordinates of More than Ogive |
More than 0 | 56 | (4, 2) |
More than 4 | 54 | (8, 6) |
More than 8 | 50 | (12, 13) |
More than 12 | 43 | (16, 18) |
More than 16 | 38 | (20, 26) |
More than 20 | 30 | (24, 29) |
More than 24 | 27 | (28, 31) |
More than 28 | 25 | (32, 32) |
More than 32 | 24 | (36, 45) |
More than 36 | 11 | (40, 50) |
More than 40 | 6 | (44, 53) |
More than 44 | 3 | (48, 56) |
So, graphically Median is determined where both Less than Ogive and More than Ogive curves intersect each other.