Find the range which contains the middle 50% of the items and coefficient of quartile deviation from the following data:

Explanation

Since , we are given inclusive series, we first convert it into exclusive one:

`Q_(1)`=Size of `((N)/(4))`th item
=Size of `((50)/(4))`th item
= Size of 12.5th item
`:. Q_(1)` lies in the class 30.5-40.5.
`Q_(1)=l_(1)+(((N)/(4))-c.f.)/(f)xxi`
`=30.5+((50)/(4)-12)/(20)xx10`
`=30.5+(12.5-12)/(20)xx10`
`=30.5+(0.5)/(20)xx10`
=30.5+0.25
=30.75
`Q_(3)`=Size of `3((N)/(4))`th" item"
=Size of `3((50)/(4))`th" item"
=Size of 37.5th item
`:. Q_(3)` lies in the class 40.5-50.5.
`Q_(3)=l_(1)+(3((N)/(4))-c.f.)/(f)xxi`
`=40.5+(3((50)/(4))-32)/(12)xx10`
`=40.5+(37.5-32)/(12)xx10`
`=40.5+(5.5)/(12)xx10`
=40.5+4.58
=45.08
To find the middle 50% if the items, compute `Q_(3)-Q_(1)`,i.e., inter quartile range.
Inter Quartile Range=`Q_(3)-Q_(1)=45.08-30.75=14.33`
Coefficient of Quartile Deviation `=(Q_(3)-Q_(1))/(Q_(3)+Q_(1))`
`=(45.08-30.75)/(45.08+30.75)=(14.33)/(75.83)`
=0.19