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Mean deviation about mean, median, mode example for ungrouped data
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- Mean deviation Introduction
- Mean deviation about mean example
- Mean deviation about median example
- Mean deviation about mode example
- Mean deviation about mean, median, mode example
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5. Mean deviation about mean, median, mode example
1. Find Mean deviation about MEAN;MEDIAN from the following data
`3,23,13,11,15,5,4,2`
Solution:
Mean `bar x=(sum x)/n`
`=(3+23+13+11+15+5+4+2)/8`
`=76/8`
`=9.5`
Median :
Observations in the ascending order are :
`2,3,4,5,11,13,15,23`
Here, `n=8` is even.
`M=(text{Value of } (n/2)^(th) text{ observation} + text{Value of } (n/2 + 1)^(th) text{ observation})/2`
`=(text{Value of } (8/2)^(th) text{ observation} + text{Value of } (8/2 + 1)^(th) text{ observation})/2`
`=(text{Value of }4^(th) text{ observation} + text{Value of }5^(th) text{ observation})/2`
`=(5 + 11)/2`
`=8`
| `x` | `|x - bar x| = |x - 9.5|` | `|x - M| = |x - 8|` | | 3 | 6.5 | 5 | | 23 | 13.5 | 15 | | 13 | 3.5 | 5 | | 11 | 1.5 | 3 | | 15 | 5.5 | 7 | | 5 | 4.5 | 3 | | 4 | 5.5 | 4 | | 2 | 7.5 | 6 | | --- | --- | --- | | 76 | 48 | 48 |
Mean deviation of Mean
`delta bar x = (sum |x - bar x|)/n`
`delta bar x = 48/8`
`delta bar x = 6`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=6/9.5`
`=0.6316`
Mean deviation of Median
`delta bar x = (sum |x - M|)/n`
`delta bar x = 48/8`
`delta bar x = 6`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=6/8`
`=0.75`
2. Find Mean deviation about MEAN;MEDIAN;MODE from the following data
`69,66,67,69,64,63,65,68,72`
Solution:
Mean `bar x=(sum x)/n`
`=(69+66+67+69+64+63+65+68+72)/9`
`=603/9`
`=67`
Median :
Observations in the ascending order are :
`63,64,65,66,67,68,69,69,72`
Here, `n=9` is odd.
`M=` value of `((n+1)/2)^(th)` observation
`=` value of `((9+1)/2)^(th)` observation
`=` value of `5^(th)` observation
`=67`
Mode :
In the given data, the observation `69` occurs maximum number of times (`2`)
`:. Z = 69`
| `x` | `|x - bar x| = |x - 67|` | `|x - M| = |x - 67|` | `|x - Z| = |x - 69|` | | 69 | 2 | 2 | 0 | | 66 | 1 | 1 | 3 | | 67 | 0 | 0 | 2 | | 69 | 2 | 2 | 0 | | 64 | 3 | 3 | 5 | | 63 | 4 | 4 | 6 | | 65 | 2 | 2 | 4 | | 68 | 1 | 1 | 1 | | 72 | 5 | 5 | 3 | | --- | --- | --- | --- | | 603 | 20 | 20 | 24 |
Mean deviation of Mean
`delta bar x = (sum |x - bar x|)/n`
`delta bar x = 20/9`
`delta bar x = 2.2222`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=2.2222/67`
`=0.0332`
Mean deviation of Median
`delta bar x = (sum |x - M|)/n`
`delta bar x = 20/9`
`delta bar x = 2.2222`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=2.2222/67`
`=0.0332`
Mean deviation of Mode
`delta bar x = (sum |x - Z|)/n`
`delta bar x = 24/9`
`delta bar x = 2.6667`
Coefficient of Mean deviation `=(delta bar x)/(bar x)`
`=2.6667/69`
`=0.0386`
This material is intended as a summary. Use your textbook for detail explanation.
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