Marks | 10 | 11 | 12 | 13 | 14 | 16 | 19 | 20 |
Number of students | 3 | 5 | 4 | 5 | 2 | 3 | 2 | 1 |
We can draw the table in the given format
Marks (x) | Number of students (f) | Cumulative frequency | Fx |
10 | 3 | 3 | 30 |
11 | 5 | 8 | 55 |
12 | 4 | 12 | 48 |
13 | 5 | 17 | 65 |
14 | 2 | 19 | 38 |
16 | 3 | 22 | 48 |
19 | 2 | 24 | 38 |
20 | 1 | 25 | 20 |
N = 25 | ∑fx = 332 |
We have;
N = 25 (odd number)
Median =
= value of 13th term
= 13
Now,
∑fx = 332 and ∑f = N = 25
Mean =
Hence,
Mode = 3(median) – 2 (mean)
= 3×13 - 2×13.28
= 39 – 26.56
= 12.44