Find the mean from the following frequency distribution of marks at a test in statistics:
Marks (x): | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
No. of students (f): | 15 | 50 | 80 | 76 | 72 | 45 | 39 | 9 | 8 | 6 |
Let the assumed mean (A) = 25
Marks (xi) | No. of students (fi) | ui = xi – A = xi - 25 | fiui |
5 | 15 | -20 | -300 |
10 | 50 | -15 | -750 |
15 | 80 | -10 | -800 |
20 | 76 | -5 | -380 |
25 | 72 | 0 | 0 |
30 | 45 | 5 | 225 |
35 | 39 | 10 | 390 |
40 | 9 | 15 | 135 |
45 | 8 | 20 | 160 |
50 | 6 | 25 | 150 |
N = 400 | ∑fiui = -1170 |
Mean = A +
= 25 + =
= 22.075