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Question
Calculate the mean deviation from the mean for the data:
13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
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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.
\[x = \frac{13 + 17 + 16 + 14 + 11 + 13 + 10 + 16 + 11 + 18 + 12 + 17}{12} = 14\]
|
|
|
| 13 | 1 |
| 17 | 3 |
| 16 | 2 |
| 14 | 0 |
| 11 | 3 |
| 13 | 1 |
| 10 | 4 |
| 16 | 2 |
| 11 | 3 |
| 18 | 4 |
| 12 | 2 |
| 17 | 3 |
| Total | 28 |
\[MD = \frac{1}{12} \times 28 = 2.33\]
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