Question

The following table shows monthly wages of 10 workers:

Calculate first third quartiles and quartile deviation.

Answer 1

Calculation of the Partition Values

`Q_(1)="Size of "((N+1)/(4))th "item"`
=`"Size of" ((10+1)/(4))"th item"`
=Size of 2.75th item
Size of 2nd item `+(3)/(4)("Size of" 3rd" item"-"Size of " 2nd" item")`
`=₹ 150+(3)/(4)(170-150)`
`Q_(1)=₹ 165`
`Q_(3)`=Size of `3((N+1)/(4))`th item =Size of 8.25th item
=Size of 8th item`+(1)/(4)("Size of" 9th" item"-"Size of" 8th "item")`
`Q_(3)=₹ 192+(1)/(4)(200-192)=₹ 194 `
`QD=(Q_(3)-Q_(1))/(2)=(194-165)/(2)=(29)/(2)=14.5`