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Home > Statistical Methods calculators > Mean deviation, Quartile deviation, Decile deviation, Percentile deviation for grouped data example
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Quartile deviation, Coefficient of Quartile 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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2. Quartile deviation, Coefficient of Quartile deviation Example
1. Calculate Quartile deviation from the following grouped data
Solution:
Quartile 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`
`Q_1 = ((n+1)/4)^(th)` value of the observation
`=(26/4)^(th)` value of the observation
`=(6.5)^(th)` value of the observation
`=2`
`Q_3 = ((3(n+1))/4)^(th)` value of the observation
`=((3*26)/4)^(th)` value of the observation
`=(19.5)^(th)` value of the observation
`=3`
Quartile deviation `=(Q_3 - Q_1)/2=(3-2)/2=1/2=0.5`
Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(3-2)/(3+2)=1/5=0.2`
2. Calculate Quartile deviation from the following grouped data
| X | Frequency | | 10 | 3 | | 11 | 12 | | 12 | 18 | | 13 | 12 | | 14 | 3 |
Solution:
Quartile 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`
`Q_1 = ((n+1)/4)^(th)` value of the observation
`=(49/4)^(th)` value of the observation
`=(12.25)^(th)` value of the observation
`=11`
`Q_3 = ((3(n+1))/4)^(th)` value of the observation
`=((3*49)/4)^(th)` value of the observation
`=(36.75)^(th)` value of the observation
`=13`
Quartile deviation `=(Q_3 - Q_1)/2=(13-11)/2=2/2=1`
Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(13-11)/(13+11)=2/24=0.0833`
3. Calculate Quartile deviation from the following grouped data
| Class | Frequency | | 2 - 4 | 3 | | 4 - 6 | 4 | | 6 - 8 | 2 | | 8 - 10 | 1 |
Solution:
Quartile 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`
`Q_1` class :
Class with `(n/4)^(th)` value of the observation in `cf` column
`=(10/4)^(th)` value of the observation in `cf` column
`=(2.5)^(th)` value of the observation in `cf` column
and it lies in the class `2 - 4`.
`:. Q_1` class : `2 - 4`
The lower boundary point of `2 - 4` is `2`.
`:. L = 2`
`Q_1 = L + (( n)/4 - cf)/f * c`
`=2 + (2.5 - 0)/3 * 2`
`=2 + (2.5)/3 * 2`
`=2 + 1.6667`
`=3.6667`
`Q_3` class :
Class with `((3n)/4)^(th)` value of the observation in `cf` column
`=((3*10)/4)^(th)` value of the observation in `cf` column
`=(7.5)^(th)` value of the observation in `cf` column
and it lies in the class `6 - 8`.
`:. Q_3` class : `6 - 8`
The lower boundary point of `6 - 8` is `6`.
`:. L = 6`
`Q_3 = L + ((3 n)/4 - cf)/f * c`
`=6 + (7.5 - 7)/2 * 2`
`=6 + (0.5)/2 * 2`
`=6 + 0.5`
`=6.5`
Quartile deviation `=(Q_3 - Q_1)/2=(6.5-3.6667)/2=2.8333/2=1.4166`
Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(6.5-3.6667)/(6.5+3.6667)=2.8333/10.1667=0.2787`
4. Calculate Quartile 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:
Quartile 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`
`Q_1` class :
Class with `(n/4)^(th)` value of the observation in `cf` column
`=(50/4)^(th)` value of the observation in `cf` column
`=(12.5)^(th)` value of the observation in `cf` column
and it lies in the class `2 - 4`.
`:. Q_1` class : `2 - 4`
The lower boundary point of `2 - 4` is `2`.
`:. L = 2`
`Q_1 = L + (( n)/4 - cf)/f * c`
`=2 + (12.5 - 5)/16 * 2`
`=2 + (7.5)/16 * 2`
`=2 + 0.9375`
`=2.9375`
`Q_3` class :
Class with `((3n)/4)^(th)` value of the observation in `cf` column
`=((3*50)/4)^(th)` value of the observation in `cf` column
`=(37.5)^(th)` value of the observation in `cf` column
and it lies in the class `6 - 8`.
`:. Q_3` class : `6 - 8`
The lower boundary point of `6 - 8` is `6`.
`:. L = 6`
`Q_3 = L + ((3 n)/4 - cf)/f * c`
`=6 + (37.5 - 34)/7 * 2`
`=6 + (3.5)/7 * 2`
`=6 + 1`
`=7`
Quartile deviation `=(Q_3 - Q_1)/2=(7-2.9375)/2=4.0625/2=2.0312`
Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(7-2.9375)/(7+2.9375)=4.0625/9.9375=0.4088`
This material is intended as a summary. Use your textbook for detail explanation.
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