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Home > Statistical Methods calculators > Quartile, Decile, Percentile, Octile, Quintile for grouped data example
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Quartile, Decile, Percentile, Octile, Quintile for grouped data Formula & Example
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- Formula & Example
- Quartile Example
- Decile Example
- Percentile Example
- Octile Example
- Quintile 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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1. Formula & Example
Formula
1. Quartile
`Q_i` class = `((i n)/4)^(th)` value of the observation
`Q_i = L + ((i n)/4 - cf)/f * c`, where i=1,2,3
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2. Deciles
`D_i` class = `((i n)/10)^(th)` value of the observation
`D_i = L + ((i n)/10 - cf)/f * c`, where i=1,2,3, ..., 9
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3. Percentiles
`P_i` class = `((i n)/100)^(th)` value of the observation
`P_i = L + ((i n)/100 - cf)/f * c`, where i=1,2,3, ..., 99
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Examples
1. Calculate Quartile-3, Deciles-7, Percentiles-20 from the following grouped data
| Class | Frequency | | 2 - 4 | 3 | | 4 - 6 | 4 | | 6 - 8 | 2 | | 8 - 10 | 1 |
Solution:
| 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_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`
`D_7` class :
Class with `((7n)/10)^(th)` value of the observation in `cf` column
`=((7*10)/10)^(th)` value of the observation in `cf` column
`=(7)^(th)` value of the observation in `cf` column
and it lies in the class `4 - 6`.
`:. D_7` class : `4 - 6`
The lower boundary point of `4 - 6` is `4`.
`:. L = 4`
`D_7 = L + ((7 n)/10 - cf)/f * c`
`=4 + (7 - 3)/4 * 2`
`=4 + (4)/4 * 2`
`=4 + 2`
`=6`
`P_20` class :
Class with `((20n)/100)^(th)` value of the observation in `cf` column
`=((20*10)/100)^(th)` value of the observation in `cf` column
`=(2)^(th)` value of the observation in `cf` column
and it lies in the class `2 - 4`.
`:. P_20` class : `2 - 4`
The lower boundary point of `2 - 4` is `2`.
`:. L = 2`
`P_20 = L + ((20 n)/100 - cf)/f * c`
`=2 + (2 - 0)/3 * 2`
`=2 + (2)/3 * 2`
`=2 + 1.3333`
`=3.3333`
2. Calculate Quartile-3, Deciles-7, Percentiles-20 from the following grouped data
Solution:
| `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_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`
`D_7 = ((7(n+1))/10)^(th)` value of the observation
`=((7*26)/10)^(th)` value of the observation
`=(18.2)^(th)` value of the observation
`=3`
`P_20 = ((20(n+1))/100)^(th)` value of the observation
`=((20*26)/100)^(th)` value of the observation
`=(5.2)^(th)` value of the observation
`=1`
This material is intended as a summary. Use your textbook for detail explanation.
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