| Variate | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Frequency | 20 | 17 | f | 10 | 8 | 6 | 7 | 6 |
Solution:
| Variate (x) | Frequency (f) | fx |
| 5 | 20 | 100 |
| 6 | 17 | 102 |
| 7 | f | 7f |
| 8 | 10 | 80 |
| 9 | 8 | 72 |
| 10 | 6 | 60 |
| 11 | 7 | 77 |
| 12 | 6 | 72 |
| Total | Ʃf = 74+f | Ʃfx = 563+7f |
Given mean = 7.5
Mean = Ʃfx/Ʃf
7.5= (563+f)/(74+7f)
7.5×(74+f) = 563+7f
555+7.5f = 563+7f
7.5f-7f = 563-555
0.5f = 8
f = 8/0.5 = 16
Hence the value of missing frequency f is 16.