Item (x) | 5 | 7 | 9 | 12 | 14 | 17 | 19 | 21 |
Frequency (f) | 6 | 5 | 3 | 6 | 5 | 3 | 2 | 4 |
Draw the table as below,
Items (x) | Frequency (f) | Cumulative frequency | Fx |
5 | 6 | 6 | 30 |
7 | 5 | 11 | 35 |
9 | 3 | 14 | 27 |
12 | 6 | 20 | 72 |
14 | 5 | 25 | 70 |
17 | 3 | 28 | 51 |
19 | 2 | 30 | 38 |
21 | 4 | 34 | 84 |
N = 34 | ∑fx = 407 |
We have;
N = 34 (even number)
Median =
Now,
∑fx = 407 and ∑f = N = 34
Mean =
Hence,
Mode = 3(median) – 2 (mean)
= 3×12 - 2×11.97
= 36 – 23.94
= 12.06