2. Calculate Decile deviation, Coefficient of D.D., Interdecile range from the following grouped data

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

Solution:
Decile 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`

`D_1 = ((n+1)/10)^(th)` value of the observation

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

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

`=11`

---

`D_9 = ((9(n+1))/10)^(th)` value of the observation

`=((9*49)/10)^(th)` value of the observation

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

`=13`

---

InterDecile range `=D_9 - D_1=13-11=2`

Decile deviation `=(D_9 - D_1)/2=(13-11)/2=2/2=1` (Semi-InterDecile range)

Coefficient of Decile deviation `=(D_9 - D_1)/(D_9 + D_1)=(13-11)/(13+11)=2/24=0.0833`

---

---