Find out quartile deviation of the following series:

Explanation

`Q_(1)="Size of "((N)/(4))th" item"="Size of "((60)/(4))th "item"`
=Size of 15th item
15th item lies in group 40-60 and falls within 29th cumulative frequency of the series.
`Q_(1)=l_(1)+((N)/(4)-c.f)/(f)xxi`
(Here, `l_(1)`=Lower limit of the class interval, N=Sum total of the frequencies, c.f.=Cumumlative frequency of the class preceding the first quartile class preceding the first quartile class, f=Frequency of the quartile class, i=Class interval.)
Thus,
`Q_(1)=40+((60)/(4)-14)/(15)xx20`
`=40+(15-14)/(15)xx20`
`=40+(1)/(15)xx20`
=40+1.33=41.33
Likewise,
`Q_(3)=" Size of "3((N)/(4))th" item"`
`="Size of "3((60)/(4))"th item"`
=Size of 45th item
45th item falls within 49th cumulative frequency of the series. Thus,
`Q_(3)=l_(1)+(3((N)/(4))-c.f)/(f)xxi`
`=60+(3((60)/(4))-29)/(20)xx20`
`=60+(45-29)/(20)xx20`
`=60+(16)/(20)xx20`
=60+16=76
Having known the values of `Q_(1)` and `Q_(2)`, quartile deviation (QD) is found as,
`QD=(Q_(3)-Q_(1))/(2)`
`=(76-41.33)/(2)=(34.67)/(2)=17.34`
and,
Coefficient of QD`=(Q_(3)-Q_(1))/(Q_(3)-Q_(1))`
`=(76-41.33)/(76+41.33)=(34.67)/(117.33)`
=0.30
Thus,
QD=17.34, and
Coefficient of QD=0.30.