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Home > Statistical Methods calculators > Mean deviation, Quartile deviation, Decile deviation, Percentile deviation for ungrouped data example
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Percentile deviation, Coefficient of Percentile deviation Example for ungrouped 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
- 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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4. Percentile deviation, Coefficient of Percentile deviation Example
1. Calculate Percentile deviation from the following data
`10,50,30,20,10,20,70,30`
Solution:
Percentile deviation :
Arranging Observations in the ascending order, We get :
`10,10,20,20,30,30,50,70`
Here, `n = 8`
`P_10 = ((10(n+1))/100)^(th)` value of the observation
`=((10*9)/100)^(th)` value of the observation
`=(0.9)^(th)` value of the observation
`=0^(th)` observation ` + 0.9 [1^(st) - 0^(th)]`
`=0 + 0.9 [10 - 0]`
`=0 + 0.9 (10)`
`=0 + 9`
`=9`
`P_90 = ((90(n+1))/100)^(th)` value of the observation
`=((90*9)/100)^(th)` value of the observation
`=(8.1)^(th)` value of the observation
`=8^(th)` observation ` + 0.1 [9^(th) - 8^(th)]`
`=70 + 0.1 [0 - 70]`
`=70 + 0.1 (-70)`
`=70 + -7`
`=63`
Inter Percentile range `=P_90 - P_10=63-9=54`
Percentile deviation `=(P_90 - P_10)/2=(63-9)/2=54/2=27`
Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(63-9)/(63+9)=54/72=0.75`
2. Calculate Percentile deviation from the following data
`85,96,76,108,85,80,100,85,70,95`
Solution:
Percentile deviation :
Arranging Observations in the ascending order, We get :
`70,76,80,85,85,85,95,96,100,108`
Here, `n = 10`
`P_10 = ((10(n+1))/100)^(th)` value of the observation
`=((10*11)/100)^(th)` value of the observation
`=(1.1)^(th)` value of the observation
`=1^(st)` observation ` + 0.1 [2^(nd) - 1^(st)]`
`=70 + 0.1 [76 - 70]`
`=70 + 0.1 (6)`
`=70 + 0.6`
`=70.6`
`P_90 = ((90(n+1))/100)^(th)` value of the observation
`=((90*11)/100)^(th)` value of the observation
`=(9.9)^(th)` value of the observation
`=9^(th)` observation ` + 0.9 [10^(th) - 9^(th)]`
`=100 + 0.9 [108 - 100]`
`=100 + 0.9 (8)`
`=100 + 7.2`
`=107.2`
Inter Percentile range `=P_90 - P_10=107.2-70.6=36.6`
Percentile deviation `=(P_90 - P_10)/2=(107.2-70.6)/2=36.6/2=18.3`
Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(107.2-70.6)/(107.2+70.6)=36.6/177.8=0.2058`
3. Calculate Percentile deviation from the following data
`73,70,71,73,68,67,69,72,76,71`
Solution:
Percentile deviation :
Arranging Observations in the ascending order, We get :
`67,68,69,70,71,71,72,73,73,76`
Here, `n = 10`
`P_10 = ((10(n+1))/100)^(th)` value of the observation
`=((10*11)/100)^(th)` value of the observation
`=(1.1)^(th)` value of the observation
`=1^(st)` observation ` + 0.1 [2^(nd) - 1^(st)]`
`=67 + 0.1 [68 - 67]`
`=67 + 0.1 (1)`
`=67 + 0.1`
`=67.1`
`P_90 = ((90(n+1))/100)^(th)` value of the observation
`=((90*11)/100)^(th)` value of the observation
`=(9.9)^(th)` value of the observation
`=9^(th)` observation ` + 0.9 [10^(th) - 9^(th)]`
`=73 + 0.9 [76 - 73]`
`=73 + 0.9 (3)`
`=73 + 2.7`
`=75.7`
Inter Percentile range `=P_90 - P_10=75.7-67.1=8.6`
Percentile deviation `=(P_90 - P_10)/2=(75.7-67.1)/2=8.6/2=4.3`
Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(75.7-67.1)/(75.7+67.1)=8.6/142.8=0.0602`
This material is intended as a summary. Use your textbook for detail explanation.
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