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Question
Calculate the mean deviation from the mean for the data:
38, 70, 48, 40, 42, 55, 63, 46, 54, 44a
Solution
Formula used for finding the mean deviation about the mean is given below:
\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right| , \text{ where } \left| d_i \right| = \left| x_i - x \right|\]
Let x be the mean of the given data.
\[x = \frac{38 + 70 + 48 + 40 + 42 + 55 + 63 + 46 + 54 + 44}{10} = 50\]
|
|
\[\left| d_i \right| = \left| x_i - \bar{x} \right|\]
|
| 38 | 12 |
| 70 | 20 |
| 48 | 2 |
| 40 | 10 |
| 42 | 8 |
| 55 | 5 |
| 63 | 13 |
| 46 | 4 |
| 54 | 4 |
| 44 | 6 |
| Total | 84 |
\[MD = \frac{1}{10} \times 84 = 8 . 4\]
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