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Question
Calculate the mean deviation about median age for the age distribution of 100 persons given below:
| Age | Number |
| 16 - 20 | 5 |
| 21 - 25 | 6 |
| 26 - 30 | 12 |
| 31 - 35 | 14 |
| 36 - 40 | 26 |
| 41 - 45 | 12 |
| 46 - 50 | 16 |
| 51 - 55 | 9 |
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Solution
Converting the given data into continuous frequency distribution:
| Modified Class | Mid-point | fi | c.f. | |xi − M| | fi |xi − M| |
| 15.5 - 20.5 | 5 | 5 | 18 | 20 | 100 |
| 20.5 - 25.5 | 6 | 11 | 23 | 15 | 30 |
| 25.5 - 30.5 | 12 | 23 | 28 | 10 | 120 |
| 30.5 - 35.5 | 14 | 37 | 33 | 5 | 70 |
| 35.5 - 40.5 | 26 | 63 | 38 | 0 | 0 |
| 40.5 - 45.5 | 12 | 75 | 43 | 5 | 60 |
| 45.5 - 50.5 | 16 | 91 | 48 | 10 | 160 |
| 50.5 - 55.5 | 9 | 100 | 53 | 15 | 135 |
| Sum | - | 100 | - | - | 735 |
Median Age: 35.5 − 40.5, l = 35.5, h = 5, C = 37, f = 26
∴ Median = `"l" + ("N"/2 -"c")/"f" xx "h"`
= `35.5 + ((0 - 37)/26) xx 5`
= `35.5 + 13/26 xx 5`
= 35.5 + 2.5
= 38
Mean Deviation (M) = `(sum"f"_"i" |"x"_"i" - "M"|)/"N"`
= `735/100`
= 7.35
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