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प्रश्न
Calculate the mean deviation about the median of the observation:
38, 70, 48, 34, 63, 42, 55, 44, 53, 47
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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
v) Arranging the data in ascending order:
34, 38, 42, 44, 47, 48, 53, 55, 63, 70
Here,
\[n = 10\].
Also, median is the AM of the fifth and the sixth observation.
\[Median, M = \frac{47 + 48}{2} = 47 . 5\]
| xi |
|
| 38 | 9.5 |
| 70 | 22.5 |
| 48 | 0.5 |
| 34 | 13.5 |
| 63 | 15.5 |
| 42 | 5.5 |
| 55 | 7.5 |
| 44 | 3.5 |
| 53 | 5.5 |
| 47 | 0.5 |
| Total | 84 |
\[MD = \frac{1}{10} \times 84 = 8 . 4\]
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