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Question
Calculate the mean deviation about the median of the observation:
3011, 2780, 3020, 2354, 3541, 4150, 5000
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
Arranging the data in ascending order:
2354, 2780, 3011, 3020, 3541, 4150, 5000
Here, median \[(M) = 3020\] and n = 7.
| \[x_i\] |
\[\left| d_i \right|\]
\[\left| x_i - 3020 \right|\]
|
|---|---|
| 3011 | 9 |
| 2780 | 240 |
| 3020 | 0 |
| 2354 | 666 |
| 3541 | 521 |
| 4150 | 1130 |
| 5000 | 1980 |
| Total | 4546 |
\[\Rightarrow MD = \frac{1}{7} \times 4546 = 649 . 42\]
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