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Question
Find the mean deviation about the median for the data.
| xi | 5 | 7 | 9 | 10 | 12 | 15 |
| fi | 8 | 6 | 2 | 2 | 2 | 6 |
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Solution
| xi | fi | c.f | |xi − M| | fi |xi − M| |
| 5 | 8 | 8 | 2 | 16 |
| 7 | 6 | 14 | 0 | 0 |
| 9 | 2 | 16 | 2 | 4 |
| 10 | 2 | 18 | 3 | 6 |
| 12 | 2 | 20 | 5 | 10 |
| 15 | 6 | 26 | 8 | 48 |
| Sum | 26 | - | - | 84 |
Sum of frequencies = 26
`26/2` = 13th term = 7 and 14th term = 7
∴ Median = `(7 + 7)/2 = 7`
∴ Deviation about mean (M) = `(sum"f"_"i" |"x"_"i" - "M"|)/"N"`
= `84/26`
= 3.23
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