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Home > Statistical Methods calculators > Mean deviation, Quartile deviation, Decile deviation, Percentile deviation for ungrouped data example
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Quartile deviation, Coefficient of Quartile 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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2. Quartile deviation, Coefficient of Quartile deviation Example
1. Calculate Quartile deviation from the following data
`10,50,30,20,10,20,70,30`
Solution:
Quartile deviation :
Arranging Observations in the ascending order, We get :
`10,10,20,20,30,30,50,70`
Here, `n = 8`
`Q_1 = ((n+1)/4)^(th)` value of the observation
`=(9/4)^(th)` value of the observation
`=(2.25)^(th)` value of the observation
`=2^(nd)` observation ` + 0.25 [3^(rd) - 2^(nd)]`
`=10 + 0.25 [20 - 10]`
`=10 + 0.25 (10)`
`=10 + 2.5`
`=12.5`
`Q_3 = ((3(n+1))/4)^(th)` value of the observation
`=((3*9)/4)^(th)` value of the observation
`=(6.75)^(th)` value of the observation
`=6^(th)` observation ` + 0.75 [7^(th) - 6^(th)]`
`=30 + 0.75 [50 - 30]`
`=30 + 0.75 (20)`
`=30 + 15`
`=45`
Inter Quartile range `=Q_3 - Q_1=45-12.5=32.5`
Quartile deviation `=(Q_3 - Q_1)/2=(45-12.5)/2=32.5/2=16.25`
Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(45-12.5)/(45+12.5)=32.5/57.5=0.5652`
2. Calculate Quartile deviation from the following data
`85,96,76,108,85,80,100,85,70,95`
Solution:
Quartile deviation :
Arranging Observations in the ascending order, We get :
`70,76,80,85,85,85,95,96,100,108`
Here, `n = 10`
`Q_1 = ((n+1)/4)^(th)` value of the observation
`=(11/4)^(th)` value of the observation
`=(2.75)^(th)` value of the observation
`=2^(nd)` observation ` + 0.75 [3^(rd) - 2^(nd)]`
`=76 + 0.75 [80 - 76]`
`=76 + 0.75 (4)`
`=76 + 3`
`=79`
`Q_3 = ((3(n+1))/4)^(th)` value of the observation
`=((3*11)/4)^(th)` value of the observation
`=(8.25)^(th)` value of the observation
`=8^(th)` observation ` + 0.25 [9^(th) - 8^(th)]`
`=96 + 0.25 [100 - 96]`
`=96 + 0.25 (4)`
`=96 + 1`
`=97`
Inter Quartile range `=Q_3 - Q_1=97-79=18`
Quartile deviation `=(Q_3 - Q_1)/2=(97-79)/2=18/2=9`
Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(97-79)/(97+79)=18/176=0.1023`
3. Calculate Quartile deviation from the following data
`73,70,71,73,68,67,69,72,76,71`
Solution:
Quartile deviation :
Arranging Observations in the ascending order, We get :
`67,68,69,70,71,71,72,73,73,76`
Here, `n = 10`
`Q_1 = ((n+1)/4)^(th)` value of the observation
`=(11/4)^(th)` value of the observation
`=(2.75)^(th)` value of the observation
`=2^(nd)` observation ` + 0.75 [3^(rd) - 2^(nd)]`
`=68 + 0.75 [69 - 68]`
`=68 + 0.75 (1)`
`=68 + 0.75`
`=68.75`
`Q_3 = ((3(n+1))/4)^(th)` value of the observation
`=((3*11)/4)^(th)` value of the observation
`=(8.25)^(th)` value of the observation
`=8^(th)` observation ` + 0.25 [9^(th) - 8^(th)]`
`=73 + 0.25 [73 - 73]`
`=73 + 0.25 (0)`
`=73 + 0`
`=73`
Inter Quartile range `=Q_3 - Q_1=73-68.75=4.25`
Quartile deviation `=(Q_3 - Q_1)/2=(73-68.75)/2=4.25/2=2.125`
Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(73-68.75)/(73+68.75)=4.25/141.75=0.03`
This material is intended as a summary. Use your textbook for detail explanation.
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