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Question
For the following distribution, calculate mean using all suitable methods:
| Size of item | 1 - 4 | 4 - 9 | 9 - 16 | 16 - 27 |
| Frequency | 6 | 12 | 26 | 20 |
Solution
By direct method
| Class interval | Mid value(x1) | Frequency(f1) | f1x1 |
| 1 - 4 | 2.5 | 6 | 15 |
| 4 - 9 | 6.5 | 12 | 78 |
| 9 - 16 | 12.5 | 26 | 325 |
| 16 - 27 | 21.5 | 20 | 430 |
| N = 64 | `sumf_1"u"_1=848` |
Mean `=(sumf_1"u"_1)/N`
`=848/64=13.25`
By assuming mean method
Let the assumed mean A = 6.5
| Class interval | Mid value(x1) |
u1 = x1 - A = x1 - 6.5 |
Frequency(f1) | f1u1 |
| 1 - 4 | 2.5 | -4 | 6 | -24 |
| 4 - 9 | 6.5 | 0 | 12 | 0 |
| 9 - 16 | 12.5 | 6 | 26 | 156 |
| 16 - 27 | 21.5 | 15 | 20 | 300 |
| N = 64 | `sumf_1"u"_1=432` |
Mean `=A + (sumf_1"u"_1)/N`
`=6.5+432/64`
= 6.5 + 6.75
= 13.25
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