Question : The mean of the following frequency distribution is 25. Find the value of f.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 5 | 18 | 15 | f |
6 |
Doubt by CBSE
Solution :
Mean (x̄) = 25
| Class Interval (CI) | Frequency (fi) | xi | di=xi-a | fidi |
| 0-10 | 5 | 5 | -20 | -100 |
| 10-20 | 18 | 15 | -10 | -180 |
| 20-30 | 15 | 25 = a | 0 | 0 |
| 30-40 | f | 35 | 10 | 10f |
| 40-50 | 6 | 45 | 20 | 120 |
| Σfi = 44+f |
Σfidi = -160+10f |
Using Assumed Mean Method
x̄ = a + Σfidi/Σfi
25 = 25 + (-160+10f)/(44+f)
25-25 = (-160+10f)/(44+f)
0 = (-160+10f)/(44+f)
0×(44+f) = -160+10f
0 = -160+10f
-10f = -160
f = -160/-10
f = 16
Hence, the required value of f is 16.