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

Class	Frequency
2 - 4	3
4 - 6	4
6 - 8	2
8 - 10	1

Solution:
Quartile deviation :

Class	Frequency `f`	`cf`
2 - 4	3	3
4 - 6	4	7
6 - 8	2	9
8 - 10	1	10
---	---	---
	`n = 10`	--

Here, `n = 10`


`Q_1` class :

Class with `(n/4)^(th)` value of the observation in `cf` column

`=(10/4)^(th)` value of the observation in `cf` column

`=(2.5)^(th)` value of the observation in `cf` column

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

`:. Q_1` class : `2 - 4`

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

`:. L=2`

`Q_1=L+(( n)/4 - cf)/f * c`

`=2+(2.5-0)/3*2`

`=2+(2.5)/3*2`

`=2+1.6667`

`=3.6667`

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`Q_3` class :

Class with `((3n)/4)^(th)` value of the observation in `cf` column

`=((3*10)/4)^(th)` value of the observation in `cf` column

`=(7.5)^(th)` value of the observation in `cf` column

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

`:. Q_3` class : `6 - 8`

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

`:. L=6`

`Q_3=L+((3 n)/4 - cf)/f * c`

`=6+(7.5-7)/2*2`

`=6+(0.5)/2*2`

`=6+0.5`

`=6.5`

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InterQuartile range `=Q_3 - Q_1=6.5-3.6667=2.8333`

Quartile deviation `=(Q_3 - Q_1)/2=(6.5-3.6667)/2=2.8333/2=1.4166` (Semi-InterQuartile range)

Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(6.5-3.6667)/(6.5+3.6667)=2.8333/10.1667=0.2787`

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