2. Calculate Percentile deviation, Coefficient of P.D., Interpercentile range from the following grouped data

X	Frequency
10	3
11	12
12	18
13	12
14	3

Solution:
Percentile deviation :

`x`	Frequency `f`	`cf`
10	3	3
11	12	15
12	18	33
13	12	45
14	3	48
---	---	---
	`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`

---

InterPercentile range `=P_90 - P_10=13-11=2`

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

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

---

---