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प्रश्न
Calculate the mean deviation about the median of the observation:
34, 66, 30, 38, 44, 50, 40, 60, 42, 51
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
iii) Arranging the data in ascending order:
30, 34, 38, 40, 42, 44, 50, 51, 60, 66
Here,
\[n = 10\]
Also, median is the AM of the fifth and the sixth observation.
\[Median, M = \frac{42 + 44}{2} = 43\]
| xi |
\[\left| d_i \right| = \left| x_i - M \right|\]
|
| 34 | 9 |
| 66 | 23 |
| 30 | 13 |
| 38 | 5 |
| 44 | 1 |
| 50 | 7 |
| 40 | 3 |
| 60 | 17 |
| 42 | 1 |
| 51 | 8 |
| Total | 87 |
\[MD = \frac{1}{10} \times 87 = 8 . 7\]
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