Find the value of p for the following frequency distribution whose mean is 16.6.
X | 8 | 12 | 15 | P | 20 | 25 | 30 |
F | 12 | 16 | 20 | 24 | 16 | 8 | 4 |
xi | fi | xi×fi |
8 | 12 | 96 |
12 | 16 | 192 |
15 | 20 | 300 |
P | 24 | 24P |
20 | 16 | 320 |
25 | 8 | 200 |
30 | 4 | 120 |
∑fi = 100 | ∑xi×fi = 1228 + 24P |
By putting the formula of mean we get;
Mean = = 16.6 (given)
16.6×100 = 1228 + 24P
1660 = 1228 + 24P
24P = 1660-1228
24P = 432
So, the value of P is 18.