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Question
Find the mean deviation about the median for the data.
36, 72, 46, 42, 60, 45, 53, 46, 51, 49
Solution
Writing the given data in ascending order
36, 42, 45, 46, 46, 49, 51, 53, 60, 72
n = 10
∴ `10/2` = 5th term = 46, and 5 + 1 = 6th term = 49
∴ Median = `(46 + 49)/2`
= `95/2`
= 47.5
| xi | |xi - 47.5| |
| 36 | 11.5 |
| 42 | 5.5 |
| 45 | 2.5 |
| 46 | 1.5 |
| 46 | 1.5 |
| 49 | 1.5 |
| 51 | 3.5 |
| 53 | 5.5 |
| 60 | 12.5 |
| 72 | 24.5 |
| Total | 70 |
Mean deviation (M) = `(sum|x_i - "M"|)/n`
= `70/70`
= 7
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