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Question
Calculate the mean deviation about the median of the observation:
38, 70, 48, 34, 42, 55, 63, 46, 54, 44
Solution
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
ii) Arranging the data in ascending order:
34, 38, 42, 44, 46, 48, 54, 55, 63, 70
Here, n is equal to 10.
Median is the arithmetic mean of the fifth and the sixth observation.
\[Median, M = \frac{46 + 48}{2} = 47\]
| xi | \[\left| d_i \right| = \left| x_i - M \right|\] |
| 38 | 9 |
| 70 | 23 |
| 48 | 1 |
| 34 | 13 |
| 42 | 5 |
| 55 | 8 |
| 63 | 16 |
| 46 | 1 |
| 54 | 7 |
| 44 | 3 |
| Total | 86 |
\[MD = \frac{1}{10} \times 86 = 8 . 6\]
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