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

X	Frequency
0	1
1	5
2	10
3	6
4	3

Solution:
Quartile deviation :

`x`	Frequency `f`	`cf`
0	1	1
1	5	6
2	10	16
3	6	22
4	3	25
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	`n = 25`	--

Here, `n = 25`

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

`=(26/4)^(th)` value of the observation

`=(6.5)^(th)` value of the observation

`=2`

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

`=((3*26)/4)^(th)` value of the observation

`=(19.5)^(th)` value of the observation

`=3`

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InterQuartile range `=Q_3 - Q_1=3-2=1`

Quartile deviation `=(Q_3 - Q_1)/2=(3-2)/2=1/2=0.5` (Semi-InterQuartile range)

Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(3-2)/(3+2)=1/5=0.2`

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