Find the missing frequency p for the following frequency distribution whose mean is 28.25.
X | 15 | 20 | 25 | 30 | 35 | 40 |
F | 8 | 7 | P | 14 | 15 | 6 |
Let’s draw the table and calculate the relative value of variables ∑xi×fi
(xi) | (fi) | (xi×fi) |
15 | 8 | 120 |
20 | 7 | 140 |
25 | P | 25P |
30 | 14 | 420 |
35 | 15 | 525 |
40 | 6 | 240 |
∑fi = 50 + P | ∑xi×fi = 1445 + 25P |
By putting the formula of mean we get;
Mean = = 28.25 (given)
28.25(50 + P) = 1445 + 25P
28.25×50 + 28.25×P = 1445 + 25P
1412.50 + 28.25P = 1445 + 25P =
28.25P – 25P = 1445 – 1412.50
3.25P = 32.5
= 10
Hence the value of P is 10.