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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
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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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