Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
No. of students | 10 | 9 | 25 | 30 | 16 | 10 |
Solution:
Class mark (xi) = (upper limit + lower limit)/2
Let assumed mean (A) = 25
Class size (h) = 10
Class Interval | No. of students (fi) | Class mark (xi) | di = xi – A | ui = di/h | fiui |
0-10 | 10 | 5 | -20 | -2 | -20 |
10-20 | 9 | 15 | -10 | -1 | -9 |
20-30 | 25 | 25 | 0 | 0 | 0 |
30-40 | 30 | 35 | 10 | 1 | 30 |
40-50 | 16 | 45 | 20 | 2 | 32 |
50-60 | 10 | 55 | 30 | 3 | 30 |
Total | ∑fi = 100 | ∑fiui =63 |
By step deviation method, Mean = x̄ = A+h∑fiui /∑fi
= 25+10(63/100)
= 25+10×0.63
= 25+6.3
=31.3
Hence the mean of the distribution is 31.3.