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Home > Statistical Methods calculators > Quartile, Decile, Percentile, Octile, Quintile for ungrouped data example
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Quartile, Decile, Percentile, Octile, Quintile for ungrouped 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
- Construct an ungrouped frequency distribution table
- Construct a grouped frequency distribution table
- Maximum, Minimum
- Sum, Length
- Range, Mid Range
- Stem and leaf plot
- Ascending order, Descending order
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1. Formula & Example
Formula
Arrange the data in ascending order, then
1. Quartile
`Q_i = ((i * (n+1))/4)^(th)` value of the observation, where i=1,2,3
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2. Deciles
`D_i = ((i * (n+1))/10)^(th)` value of the observation, where i=1,2,3, ..., 9
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3. Percentiles
`P_i = ((i * (n+1))/100)^(th)` value of the observation, where i=1,2,3, ..., 99
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Examples
1. Calculate Quartile-1, Deciles-3, Percentiles-20 from the following data
3,13,11,11,5,4,2
Solution:
Arranging Observations in the ascending order, We get :
`2, 3, 4, 5, 11, 11, 13`
Here, `n = 7`
`Q_1 = ((n+1)/4)^(th)` value of the observation
`=(8/4)^(th)` value of the observation
`=2^(nd)` value of the observation
`=3`
`D_3 = ((3(n+1))/10)^(th)` value of the observation
`=(3(8/10))^(th)` value of the observation
`=(2.4)^(th)` value of the observation
`=2^(nd)` observation ` + 0.4 [3^(rd) - 2^(nd)]`
`=3 + 0.4 [4 - 3]`
`=3 + 0.4 (1)`
`=3 + 0.4`
`=3.4`
`P_20 = ((20(n+1))/100)^(th)` value of the observation
`=(20(8/100))^(th)` value of the observation
`=(1.6)^(th)` value of the observation
`=1^(st)` observation ` + 0.6 [2^(nd) - 1^(st)]`
`=2 + 0.6 [3 - 2]`
`=2 + 0.6 (1)`
`=2 + 0.6`
`=2.6`
2. Calculate Quartile-2, Deciles-6, Percentiles-45 from the following data
85,96,76,108,85,80,100,85,70,95
Solution:
Arranging Observations in the ascending order, We get :
`70, 76, 80, 85, 85, 85, 95, 96, 100, 108`
Here, `n = 10`
`Q_2 = ((2(n+1))/4)^(th)` value of the observation
`=(2(11/4))^(th)` value of the observation
`=(5.5)^(th)` value of the observation
`=5^(th)` observation ` + 0.5 [6^(th) - 5^(th)]`
`=85 + 0.5 [85 - 85]`
`=85 + 0.5 (0)`
`=85 + 0`
`=85`
`D_6 = ((6(n+1))/10)^(th)` value of the observation
`=(6(11/10))^(th)` value of the observation
`=(6.6)^(th)` value of the observation
`=6^(th)` observation ` + 0.6 [7^(th) - 6^(th)]`
`=85 + 0.6 [95 - 85]`
`=85 + 0.6 (10)`
`=85 + 6`
`=91`
`P_45 = ((45(n+1))/100)^(th)` value of the observation
`=(45(11/100))^(th)` value of the observation
`=(4.95)^(th)` value of the observation
`=4^(th)` observation ` + 0.95 [5^(th) - 4^(th)]`
`=85 + 0.95 [85 - 85]`
`=85 + 0.95 (0)`
`=85 + 0`
`=85`
This material is intended as a summary. Use your textbook for detail explanation.
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