| Marks | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of students | 1 | 3 | 6 | 10 | 5 | 5 |
Calculate the mean, median and mode of the above distribution.
Solution:
We write the data in cumulative frequency table.
| Marks x | Frequency (f) | Cumulative frequency | fx |
| 0 | 1 | 1 | 0 |
| 1 | 3 | 4 | 3 |
| 2 | 6 | 10 | 12 |
| 3 | 10 | 20 | 30 |
| 4 | 5 | 25 | 20 |
| 5 | 5 | 30 | 25 |
| Total | Ʃf = 30 | Ʃfx = 90 |
Mean = Ʃfx/Ʃf
= 90/30
= 3
Hence the mean is 3.
Here number of observations, n = 30 which is even.
So median = ½ ( n/2 th term + ((n/2)+1)th term)
= ½ (30/2 th term + ((30/2)+1)th term)
= ½ (15 th term + (15+1)th term)
= ½ (15 th term + 16th term)
= ½ (3+3)
= 6/2
= 3
Hence the median is 3.
Here the mark 3 occurs maximum number of times.
Hence the mode is 3.