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Home > Statistical Methods calculators > Mean deviation, Quartile deviation, Decile deviation, Percentile deviation for grouped data example
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Decile deviation, Coefficient of Decile deviation Example for grouped data
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- Mean deviation, Coefficient of Mean deviation Example
- Quartile deviation, Coefficient of Quartile deviation Example
- Decile deviation, Coefficient of Decile deviation Example
- Percentile deviation, Coefficient of Percentile deviation Example
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Other related methods
- Mean, Median and Mode
- Quartile, Decile, Percentile, Octile, Quintile
- Population Variance, Standard deviation and coefficient of variation
- Sample Variance, Standard deviation and coefficient of variation
- Population Skewness, Kurtosis
- Sample Skewness, Kurtosis
- Geometric mean, Harmonic mean
- Mean deviation, Quartile deviation, Decile deviation, Percentile deviation
- Five number summary
- Box and Whisker Plots
- Mode using Grouping Method
- Less than type Cumulative frequency table
- More than type Cumulative frequency table
- Class and their frequency table
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3. Decile deviation, Coefficient of Decile deviation Example
1. Calculate Decile deviation from the following grouped data
Solution:
Decile deviation :
| `x` | Frequency
`f` | `cf` | | 0 | 1 | 1 | | 1 | 5 | 6 | | 2 | 10 | 16 | | 3 | 6 | 22 | | 4 | 3 | 25 | | --- | --- | --- | | n = 25 | -- |
Here, `n = 25`
`D_1 = ((n+1)/10)^(th)` value of the observation
`=(26/10)^(th)` value of the observation
`=(2.6)^(th)` value of the observation
`=1`
`D_9 = ((9(n+1))/10)^(th)` value of the observation
`=((9*26)/10)^(th)` value of the observation
`=(23.4)^(th)` value of the observation
`=4`
Decile deviation `=(D_9 - D_1)/2=(4-1)/2=3/2=1.5`
Coefficient of Decile deviation `=(D_9 - D_1)/(D_9 + D_1)=(4-1)/(4+1)=3/5=0.6`
2. Calculate Decile deviation from the following grouped data
| X | Frequency | | 10 | 3 | | 11 | 12 | | 12 | 18 | | 13 | 12 | | 14 | 3 |
Solution:
Decile deviation :
| `x` | Frequency
`f` | `cf` | | 10 | 3 | 3 | | 11 | 12 | 15 | | 12 | 18 | 33 | | 13 | 12 | 45 | | 14 | 3 | 48 | | --- | --- | --- | | n = 48 | -- |
Here, `n = 48`
`D_1 = ((n+1)/10)^(th)` value of the observation
`=(49/10)^(th)` value of the observation
`=(4.9)^(th)` value of the observation
`=11`
`D_9 = ((9(n+1))/10)^(th)` value of the observation
`=((9*49)/10)^(th)` value of the observation
`=(44.1)^(th)` value of the observation
`=13`
Decile deviation `=(D_9 - D_1)/2=(13-11)/2=2/2=1`
Coefficient of Decile deviation `=(D_9 - D_1)/(D_9 + D_1)=(13-11)/(13+11)=2/24=0.0833`
3. Calculate Decile deviation from the following grouped data
| Class | Frequency | | 2 - 4 | 3 | | 4 - 6 | 4 | | 6 - 8 | 2 | | 8 - 10 | 1 |
Solution:
Decile deviation :
| Class | Frequency
`f` | `cf` | | 2 - 4 | 3 | 3 | | 4 - 6 | 4 | 7 | | 6 - 8 | 2 | 9 | | 8 - 10 | 1 | 10 | | --- | --- | --- | | n = 10 | -- |
Here, `n = 10`
`D_1` class :
Class with `(n/10)^(th)` value of the observation in `cf` column
`=(10/10)^(th)` value of the observation in `cf` column
`=(1)^(th)` value of the observation in `cf` column
and it lies in the class `2 - 4`.
`:. D_1` class : `2 - 4`
The lower boundary point of `2 - 4` is `2`.
`:. L = 2`
`D_1 = L + (( n)/10 - cf)/f * c`
`=2 + (1 - 0)/3 * 2`
`=2 + (1)/3 * 2`
`=2 + 0.6667`
`=2.6667`
`D_9` class :
Class with `((9n)/10)^(th)` value of the observation in `cf` column
`=((9*10)/10)^(th)` value of the observation in `cf` column
`=(9)^(th)` value of the observation in `cf` column
and it lies in the class `6 - 8`.
`:. D_9` class : `6 - 8`
The lower boundary point of `6 - 8` is `6`.
`:. L = 6`
`D_9 = L + ((9 n)/10 - cf)/f * c`
`=6 + (9 - 7)/2 * 2`
`=6 + (2)/2 * 2`
`=6 + 2`
`=8`
Decile deviation `=(D_9 - D_1)/2=(8-2.6667)/2=5.3333/2=2.6666`
Coefficient of Decile deviation `=(D_9 - D_1)/(D_9 + D_1)=(8-2.6667)/(8+2.6667)=5.3333/10.6667=0.5`
4. Calculate Decile deviation from the following grouped data
| Class | Frequency | | 0 - 2 | 5 | | 2 - 4 | 16 | | 4 - 6 | 13 | | 6 - 8 | 7 | | 8 - 10 | 5 | | 10 - 12 | 4 |
Solution:
Decile deviation :
| Class | Frequency
`f` | `cf` | | 0 - 2 | 5 | 5 | | 2 - 4 | 16 | 21 | | 4 - 6 | 13 | 34 | | 6 - 8 | 7 | 41 | | 8 - 10 | 5 | 46 | | 10 - 12 | 4 | 50 | | --- | --- | --- | | n = 50 | -- |
Here, `n = 50`
`D_1` class :
Class with `(n/10)^(th)` value of the observation in `cf` column
`=(50/10)^(th)` value of the observation in `cf` column
`=(5)^(th)` value of the observation in `cf` column
and it lies in the class `0 - 2`.
`:. D_1` class : `0 - 2`
The lower boundary point of `0 - 2` is `0`.
`:. L = 0`
`D_1 = L + (( n)/10 - cf)/f * c`
`=0 + (5 - 0)/5 * 2`
`=0 + (5)/5 * 2`
`=0 + 2`
`=2`
`D_9` class :
Class with `((9n)/10)^(th)` value of the observation in `cf` column
`=((9*50)/10)^(th)` value of the observation in `cf` column
`=(45)^(th)` value of the observation in `cf` column
and it lies in the class `8 - 10`.
`:. D_9` class : `8 - 10`
The lower boundary point of `8 - 10` is `8`.
`:. L = 8`
`D_9 = L + ((9 n)/10 - cf)/f * c`
`=8 + (45 - 41)/5 * 2`
`=8 + (4)/5 * 2`
`=8 + 1.6`
`=9.6`
Decile deviation `=(D_9 - D_1)/2=(9.6-2)/2=7.6/2=3.8`
Coefficient of Decile deviation `=(D_9 - D_1)/(D_9 + D_1)=(9.6-2)/(9.6+2)=7.6/11.6=0.6552`
This material is intended as a summary. Use your textbook for detail explanation.
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