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Question
Find the mean deviation about the mean for the data.
| xi | 10 | 30 | 50 | 70 | 90 |
| fi | 4 | 24 | 28 | 16 | 8 |
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Solution
| xi | fi | fixi | `|"x"_"i" - bar"x"|` | `"f"_"i"|"x"_"i" - bar"x"|` |
| 10 | 4 | 40 | 40 | 160 |
| 30 | 24 | 720 | 20 | 480 |
| 50 | 28 | 1400 | 0 | 0 |
| 70 | 16 | 1120 | 20 | 320 |
| 90 | 8 | 720 | 40 | 320 |
| Sum | 80 | 4000 | - | 1280 |
`overline "x" = (sum"f"_"i""x"_"i")/(sum"f"_"i")`
= `4000/80`
= 50
Mean Deviation = `(sum"f"_"i" |"x"_"i" - overline"x"|)/"N"`
= `1280/80`
= 16
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