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Question
Find the mean deviation from the mean for the data:
| Size | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 |
| Frequency | 3 | 3 | 4 | 14 | 7 | 4 | 3 | 4 |
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Solution
| Size(xi) | Frequency (fi) | fixi | \[\left| x_i - \bar{x} \right|\] \[ = \left| x_i - 8 \right|\] |
\[f_i \left| x_i - x \right|\] \[ = f_i \left| x_i - 8 \right|\] |
| 1 | 3 | 3 | 7 | 21 |
| 3 | 3 | 9 | 5 | 15 |
| 5 | 4 | 20 | 3 | 12 |
| 7 | 14 | 98 | 1 | 14 |
| 9 | 7 | 63 | 1 | 7 |
| 11 | 4 | 44 | 3 | 12 |
| 13 | 3 | 39 | 5 | 15 |
| 15 | 4 | 60 | 7 | 28 |
|
\[N = 42\]
|
\[\sum^n_{i = 1} f_i x_i = 336\]
|
\[\sum^n_{i = 1} f_i \left| x_i - x \right| = 124\]
|
\[\bar{x} = \frac{\sum ^n_{i = 1} f_ix_i}{N} = \frac{336}{42} = 8\]
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