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Question
Find the mean deviation from the mean for the data:
| Size | 20 | 21 | 22 | 23 | 24 |
| Frequency | 6 | 4 | 5 | 1 | 4 |
Solution
| Size(xi) | Frequency (fi) | fixi | \[\left| x_i - \bar{x} \right|\] \[ = \left| x_i - 21 . 65 \right|\] |
\[f_i \left| x_i - x \right|\]
\[ = f_i \left| x_i - 21 . 65 \right|\] |
| 20 | 6 | 120 | 1.65 | 9.9 |
| 21 | 4 | 84 | 0.65 | 2.6 |
| 22 | 5 | 110 | 0.35 | 1.75 |
| 23 | 1 | 23 | 1.35 | 1.35 |
| 24 | 4 | 96 | 2.35 | 9.4 |
|
\[N = 20\]
|
\[\sum^n_{i = 1} f_i x_i = 433\]
|
\[\sum^n_{i = 1} f_i \left| x_i - x \right| = 25\]
|
\[\bar{x} = \frac{\sum^{n}_{i = 1} f_ix_i}{N} = \frac{433}{20} = 21 . 65\]
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