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Question
Find the mean of each of the following frequency distributions
| Class interval | 0 - 8 | 8 - 16 | 16 - 24 | 24 - 32 | 32 - 40 |
| Frequency | 5 | 9 | 10 | 8 | 8 |
Solution
Let the assumed mean be A = 20 and h = 8.
| Class interval | Mid value(x1) | d1 = x1 - 20 | `"u"_1=(x_1-20)/8` | f1 | f1u1 |
| 0 - 8 | 4 | -16 | -2 | 5 | -10 |
| 8 - 16 | 12 | -8 | -1 | 9 | -9 |
| 16 - 24 | 20 | 0 | 0 | 10 | 0 |
| 24 - 32 | 28 | 8 | 1 | 8 | 8 |
| 32 - 40 | 36 | 16 | 2 | 8 | 16 |
| N = 40 | `sumf_1"u"_1=5` |
We have
A = 20, h = 8
Mean `=A+hxx(sumf_1"u"_1)/N`
`=20+8xx5/40`
`= 20+40/40`
= 20 + 1
= 21
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