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Question
Find the mean of each of the following frequency distributions
| Class interval | 50 - 70 | 70 - 90 | 90 - 110 | 110 - 130 | 130 - 150 | 150 - 170 |
| Frequency | 18 | 12 | 13 | 27 | 8 | 22 |
Solution
Let the a assumed mean be 100
| Class interval | Mid-value (x1) | d1 = x1 - 100 | `"u"_1 = (x_1 - 100)/20` | f1 | f1u1 |
| 50 - 70 | 60 | -40 | -2 | 18 | -36 |
| 70 - 90 | 80 | -20 | -1 | 12 | -12 |
| 90 - 110 | 100 | 0 | 0 | 13 | 0 |
| 110 - 130 | 120 | 20 | 1 | 27 | 27 |
| 130 - 150 | 140 | 40 | 2 | 8 | 16 |
| 150 - 170 | 160 | 60 | 3 | 22 | 66 |
| N = 100 | `sumf_1"u"_1=61` |
A = 100, h = 20
Mean `A+hxx(sumf_1"u"_1)/N`
`=100+20xx61/100`
`=100+1220/100`
= 100 + 12.20
= 112.20
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