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Question
Calculate the mean deviation from the mean for the data:
4, 7, 8, 9, 10, 12, 13, 17
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.
\[x = \frac{4 + 7 + 8 + 9 + 10 + 12 + 13 + 17}{8} = 10\]
|
|
|
| 4 | 6 |
| 7 | 3 |
| 8 | 2 |
| 9 | 1 |
| 10 | 0 |
| 12 | 2 |
| 13 | 3 |
| 17 | 7 |
| Total | 24 |
\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|\]
\[MD = \frac{1}{8} \times 24 = 3\]
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