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Home > Statistical Methods calculators > Mean deviation, Quartile deviation, Decile deviation, Percentile deviation for grouped data example
Percentile deviation, Coefficient of Percentile deviation Example for grouped data ( Enter your problem )
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  1. Mean deviation, Coefficient of Mean deviation Example
  2. Quartile deviation, Coefficient of Quartile deviation Example
  3. Decile deviation, Coefficient of Decile deviation Example
  4. Percentile deviation, Coefficient of Percentile deviation Example
 		Other related methods
  1. Mean, Median and Mode
  2. Quartile, Decile, Percentile, Octile, Quintile
  3. Population Variance, Standard deviation and coefficient of variation
  4. Sample Variance, Standard deviation and coefficient of variation
  5. Population Skewness, Kurtosis
  6. Sample Skewness, Kurtosis
  7. Geometric mean, Harmonic mean
  8. Mean deviation, Quartile deviation, Decile deviation, Percentile deviation
  9. Five number summary
  10. Box and Whisker Plots
  11. Mode using Grouping Method
  12. Less than type Cumulative frequency table
  13. More than type Cumulative frequency table
  14. Class and their frequency table
3. Decile deviation, Coefficient of Decile deviation Example
(Previous example)		9. Five number summary
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4. Percentile deviation, Coefficient of Percentile deviation Example


1. Calculate Percentile deviation from the following grouped data
XFrequency
01
15
210
36
43


Solution:
Percentile deviation :
`x`Frequency
`f`		`cf`
011
156
21016
3622
4325
---------
n = 25--


Here, `n = 25`

`P_10 = ((10(n+1))/100)^(th)` value of the observation

`=((10*26)/100)^(th)` value of the observation

`=(2.6)^(th)` value of the observation

`=1`


`P_90 = ((90(n+1))/100)^(th)` value of the observation

`=((90*26)/100)^(th)` value of the observation

`=(23.4)^(th)` value of the observation

`=4`


Percentile deviation `=(P_90 - P_10)/2=(4-1)/2=3/2=1.5`

Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(4-1)/(4+1)=3/5=0.6`

2. Calculate Percentile deviation from the following grouped data
XFrequency
103
1112
1218
1312
143


Solution:
Percentile deviation :
`x`Frequency
`f`		`cf`
1033
111215
121833
131245
14348
---------
n = 48--


Here, `n = 48`

`P_10 = ((10(n+1))/100)^(th)` value of the observation

`=((10*49)/100)^(th)` value of the observation

`=(4.9)^(th)` value of the observation

`=11`


`P_90 = ((90(n+1))/100)^(th)` value of the observation

`=((90*49)/100)^(th)` value of the observation

`=(44.1)^(th)` value of the observation

`=13`


Percentile deviation `=(P_90 - P_10)/2=(13-11)/2=2/2=1`

Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(13-11)/(13+11)=2/24=0.0833`

3. Calculate Percentile deviation from the following grouped data
ClassFrequency
2 - 43
4 - 64
6 - 82
8 - 101


Solution:
Percentile deviation :
ClassFrequency
`f`		`cf`
2 - 433
4 - 647
6 - 829
8 - 10110
---------
n = 10--


Here, `n = 10`


`P_10` class :

Class with `((10n)/100)^(th)` value of the observation in `cf` column

`=((10*10)/100)^(th)` value of the observation in `cf` column

`=(1)^(th)` value of the observation in `cf` column

and it lies in the class `2 - 4`.

`:. P_10` class : `2 - 4`

The lower boundary point of `2 - 4` is `2`.

`:. L = 2`

`P_10 = L + ((10 n)/100 - cf)/f * c`

`=2 + (1 - 0)/3 * 2`

`=2 + (1)/3 * 2`

`=2 + 0.6667`

`=2.6667`



`P_90` class :

Class with `((90n)/100)^(th)` value of the observation in `cf` column

`=((90*10)/100)^(th)` value of the observation in `cf` column

`=(9)^(th)` value of the observation in `cf` column

and it lies in the class `6 - 8`.

`:. P_90` class : `6 - 8`

The lower boundary point of `6 - 8` is `6`.

`:. L = 6`

`P_90 = L + ((90 n)/100 - cf)/f * c`

`=6 + (9 - 7)/2 * 2`

`=6 + (2)/2 * 2`

`=6 + 2`

`=8`


Percentile deviation `=(P_90 - P_10)/2=(8-2.6667)/2=5.3333/2=2.6666`

Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(8-2.6667)/(8+2.6667)=5.3333/10.6667=0.5`

4. Calculate Percentile deviation from the following grouped data
ClassFrequency
0 - 25
2 - 416
4 - 613
6 - 87
8 - 105
10 - 124


Solution:
Percentile deviation :
ClassFrequency
`f`		`cf`
0 - 255
2 - 41621
4 - 61334
6 - 8741
8 - 10546
10 - 12450
---------
n = 50--


Here, `n = 50`


`P_10` class :

Class with `((10n)/100)^(th)` value of the observation in `cf` column

`=((10*50)/100)^(th)` value of the observation in `cf` column

`=(5)^(th)` value of the observation in `cf` column

and it lies in the class `0 - 2`.

`:. P_10` class : `0 - 2`

The lower boundary point of `0 - 2` is `0`.

`:. L = 0`

`P_10 = L + ((10 n)/100 - cf)/f * c`

`=0 + (5 - 0)/5 * 2`

`=0 + (5)/5 * 2`

`=0 + 2`

`=2`



`P_90` class :

Class with `((90n)/100)^(th)` value of the observation in `cf` column

`=((90*50)/100)^(th)` value of the observation in `cf` column

`=(45)^(th)` value of the observation in `cf` column

and it lies in the class `8 - 10`.

`:. P_90` class : `8 - 10`

The lower boundary point of `8 - 10` is `8`.

`:. L = 8`

`P_90 = L + ((90 n)/100 - cf)/f * c`

`=8 + (45 - 41)/5 * 2`

`=8 + (4)/5 * 2`

`=8 + 1.6`

`=9.6`


Percentile deviation `=(P_90 - P_10)/2=(9.6-2)/2=7.6/2=3.8`

Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(9.6-2)/(9.6+2)=7.6/11.6=0.6552`

This material is intended as a summary. Use your textbook for detail explanation.
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3. Decile deviation, Coefficient of Decile deviation Example
(Previous example)		9. Five number summary
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