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Question
Find the mean deviation about median for the following data:
| Marks | Number of girls |
| 0-10 | 6 |
| 10-20 | 8 |
| 20-30 | 14 |
| 30-40 | 16 |
| 40-50 | 4 |
| 50-60 | 2 |
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Solution
| Marks | Mid-point | fi | c.f. | |xi − M| | fi |xi − M| |
| 0 - 10 | 5 | 6 | 6 | 22.86 | 137.16 |
| 10 - 20 | 15 | 8 | 14 | 12.86 | 102.88 |
| 20 - 30 | 25 | 14 | 28 | 2.86 | 40.04 |
| 30 - 40 | 35 | 16 | 44 | 7.14 | 114.24 |
| 40 - 50 | 45 | 4 | 48 | 17.14 | 68.56 |
| 50 - 60 | 55 | 2 | 50 | 27.14 | 54.28 |
| Sum | - | - | - | - | 517.16 |
Median = `"l" + ("N"/2 - "c")/"f" xx "h"`
= `20 + (25 - 14)/14 xx 10`
= `20 + 110/14`
= 20 + 7.86
= 27.86
Mean Deviation (M) = `(sum"f"_"i" |"x"_"i" - "M"|)/(sum"f"_"i")`
= `517.16/50`
= 10.34
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