Question

The following data shows daily wages of 199 workers of a factory. Find out quartile deviation and the coefficient of quartile deviation.

Answer 1

The above series is first converted into a cumulative frequency distribution series.

`Q_(1)="Size of "((N+1)/(4))th" item"`
`="Size of" ((199+1)/(4))th" item "`=Size of 150th item
50th item lies falls in 65th cumulative frequency of the series. Wage corresponding to 65th cumulative frequancy is `₹ 40` which therefore is first quartile of the distribution. Likewise,

`Q_(3)="Size of "3((N+1)/(4))th" item"`
=Size of `3((199+1)/(4))th` item =Size of 150th item
150th item falls in 155th cumulative frequency of the series. Wage corresponding to 155th cumulative frequency is `₹ 70` which therefore is the third quartile of the series.
Quartile Deviation (QD)`=(Q_(3)-Q_(1))/(2)`
`=(70-40)/(2)=(30)/(2)=15`
Coefficient of QD`=(Q_(3)-Q_(1))/(Q_(3)+Q_(1))=(70-40)/(70+40)=(30)/(110)=0.27`