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Problem: coefficient of percentile deviation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} [ Calculator, Method and examples ]

Solution:
Your problem `->` coefficient of percentile deviation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}}


Percentile deviation :
ClassFrequency
`f`
`cf`
10 - 201515
20 - 302540
30 - 402060
40 - 501272
50 - 60880
---------
n = 80--


Here, `n = 80`


`P_10` class :

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

`=((10*80)/100)^(th)` value of the observation in `cf` column

`=(8)^(th)` value of the observation in `cf` column

and it lies in the class `10 - 20`.

`:. P_10` class : `10 - 20`

The lower boundary point of `10 - 20` is `10`.

`:. L = 10`

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

`=10 + (8 - 0)/15 * 10`

`=10 + (8)/15 * 10`

`=10 + 5.3333`

`=15.3333`




`P_90` class :

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

`=((90*80)/100)^(th)` value of the observation in `cf` column

`=(72)^(th)` value of the observation in `cf` column

and it lies in the class `50 - 60`.

`:. P_90` class : `50 - 60`

The lower boundary point of `50 - 60` is `50`.

`:. L = 50`

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

`=50 + (72 - 72)/8 * 10`

`=50 + (0)/8 * 10`

`=50 + 0`

`=50`



Percentile deviation `=(P_90 - P_10)/2=(50-15.3333)/2=34.6667/2=17.3333`

Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(50-15.3333)/(50+15.3333)=34.6667/65.3333=0.5306`








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