| Marks | 5 | 6 | 7 | 8 | 9 |
| No. of students | 6 | a | 16 | 13 | b |
If the mean of the distribution is 7.2, find a and b.
Solution:
| Marks (x) | No. of students (f) | fx |
| 5 | 6 | 30 |
| 6 | a | 6a |
| 7 | 16 | 112 |
| 8 | 13 | 104 |
| 9 | b | 9b |
| Total | Ʃf = 35+a+b | Ʃfx = 246+6a+9b |
Given number of students = 40
Ʃf = 35+a+b = 40
a+b = 40-35 = 5
a = 5-b ……(i)
Mean = Ʃfx/Ʃf
Given mean = 7.2
( 246+6a+9b) /40 = 7.2
( 246+6a+9b) = 40×7.2
( 246+6a+9b) = 288
6a+9b = 288-246
6a+9b = 288-246
6a+9b = 42
2a+3b = 14 …..(ii)
Substitute (i) in (ii)
2(5-b)+3b = 14
10-2b+3b = 14
10+b = 14
b = 14-10 = 4
a = 5-4 = 1
Hence the value of a and b is 1 and 4 respectively.