2. Calculate Quartile deviation, Coefficient of Q.D., Interquartile range from the following grouped data

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

Solution:
Quartile 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`

`Q_1 = ((n+1)/4)^(th)` value of the observation

`=(49/4)^(th)` value of the observation

`=(12.25)^(th)` value of the observation

`=11`

---

`Q_3 = ((3(n+1))/4)^(th)` value of the observation

`=((3*49)/4)^(th)` value of the observation

`=(36.75)^(th)` value of the observation

`=13`

---

InterQuartile range `=Q_3 - Q_1=13-11=2`

Quartile deviation `=(Q_3 - Q_1)/2=(13-11)/2=2/2=1` (Semi-InterQuartile range)

Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(13-11)/(13+11)=2/24=0.0833`

---

---

---