if the mean of the following frequency distribution is 91, find the missing frequency x and y :
classes frequency
0 - 30 12
30-60 21
60 - 90 x
90 -120 52
120 - 150 y
150 - 180 11
total 150
| class | frequency (fi) | mid-point (xi) | xi × fi |
| 0-30 | 12 | 15 | 180 |
| 30-60 | 21 | 45 | 945 |
| 60-90 | x | 75 | 75x |
| 90-120 | 52 | 105 | 5460 |
| 120-150 | y | 135 | 135y |
| 150-180 | 11 | 165 | 1815 |
Total 150
mean = ∑(xi × fi)/150 = 91
⇒8400+75x+135y = 13650
⇒5x+9y = 350
Also, 96+x+y = 150
⇒ x+y = 54
solving both equations we get x = 34 and y =20