Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.
x: | 10 | 30 | 50 | 70 | 90 | |
f : | 17 | f1 | 32 | f2 | 19 | Total 120. |
x | f | fx |
10 | 17 | 170 |
30 | f1 | 30f1 |
50 | 32 | 1600 |
70 | f2 | 70f2 |
90 | 19 | 1710 |
N = 120 | ∑fx = 3480 + 30f1 + 70f2 |
It is given that, mean = 50
= 50
= 50
3480 + 30f1 + 70f2 = 50 (120)
30f1 + 70f2 = 6000 – 3480
10 (3f1 + 7f2) = 10 (252)
3f1 + 7f2 = 252 (i) [Dividing by 10]
And N = 120
17 + f1 + 32 + f2 + 19 = 120
68 + f1 + f2 = 120
f1 + f2 = 52
Multiplying by ‘3’ on both sides, we get
3f1 + 3f2 = 156 (ii)
Subtracting (ii) from (i), we get
3f1 + 7f2 – 3f1 – 3f2 = 252 – 156
4f2 = 96
f2 =
= 24
Put value of f2 in (i), we get
3f1 + 7 * 24 = 252
3f1 = 252 – 168
3f1 = 84
f1 =
= 28