Class interval | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 | 80-85 | 85-90 |
Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |
Solution:
(i) Class mark (xi) = (upper limit + lower limit)/2
Let assumed mean (A) = 67.5
Class size (h) = 5
Class Interval | Frequency (fi) | Class mark (xi) | di = xi – A | ui = di/h | fiui |
50-55 | 5 | 52.5 | -15 | -3 | -15 |
55-60 | 20 | 57.5 | -10 | -2 | -40 |
60-65 | 10 | 62.5 | 5 | -1 | -10 |
65-70 | 10 | 67.5 | 10 | 0 | 0 |
70-75 | 9 | 72.5 | 15 | 1 | 9 |
75-80 | 6 | 77.5 | 20 | 2 | 12 |
80-85 | 12 | 82.5 | 25 | 3 | 36 |
85-90 | 8 | 87.5 | 30 | 4 | 32 |
Total | ∑fi = 80 | ∑fiui = 24 |
By step deviation method, Mean = x̄ = A+h∑fiui /∑fi
= 67.5+5(24/80)
= 67.5+5×0.3
= 67.5+1.5
= 69
Hence the mean of the distribution is 69.
(ii) Modal class is the class with highest frequency.
Here the modal class is 55-60.