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प्रश्न
Calculate the mean deviation about the median of the observation:
22, 24, 30, 27, 29, 31, 25, 28, 41, 42
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उत्तर
Formula used for mean deviation:
\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|\]
\[Here, \]
\[ d_i = x_i - M\]
M = Median
iv) Arranging the data in ascending order.
22, 24, 25, 27, 28, 29, 30, 31, 41, 42
\[\text{ Here } , n = 10 .\]
Also, median is the AM of the fifth and the sixth observation.
\[Median, M = \frac{28 + 29}{2} = 28 . 5\]
| xi |
\[\left| d_i \right| = \left| x_i - M \right|\]
|
| 22 | 6.5 |
| 24 | 4.5 |
| 30 | 1.5 |
| 27 | 1.5 |
| 29 | 0.5 |
| 31 | 2.5 |
| 25 | 3.5 |
| 28 | 0.5 |
| 41 | 12.5 |
| 41 | 13.5 |
| Total | 47 |
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