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Question
Find the mean of each of the following frequency distributions
| Class interval | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 |
| Frequency | 6 | 10 | 8 | 12 | 4 |
Solution
Let the assume mean A = 50
| Class interval | Mid value(x1) | d1 = x1 - 50 | `"u"_1=(x_1 - 50)/10` | f1 | f1u1 |
| 25 - 35 | 30 | -20 | -2 | 6 | -12 |
| 35 - 45 | 40 | -10 | -1 | 10 | -10 |
| 45 - 55 | 50 | 0 | 0 | 8 | 0 |
| 55 - 65 | 60 | 10 | 1 | 12 | 12 |
| 65 - 75 | 70 | 20 | 2 | 4 | 8 |
| N = 40 | `sumf_1"u"_1=-2` |
We have
A = 50, h = 10
Mean `=A+hxx(sumf_1"u"_1)/N`
`=50+10(-2)/40`
`=50+(-20)/40`
`= 50-20/40
= 50 - 0.5
= 49.5
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