Question

Caculate `Q_(1),Q_(3),D_(9)andP_(70)` from the following data :
`{:(120,187,170,180,192,150,190,181,200,210):}`

Answer 1

The data is first arranged in ascending order :

`Q_(1)` = Size of `((N+1)/(4))` th item = Size of `((10+4)/(4))` th item
= Size of 2.75 th item
= Size of 2nd item + 0.75 (Size of 3 rd item = Size of 2nd item)
`=150+(3)/(4)(170-150)`
`150+15=165`
`Q_(3)`= Size of `3((N+1)/(4))` th item = Size of `3((10+1)/(4))` th item
= Size of 8.25th item
= Size of 8th item + 0.25 (Size of 9th item - Size of 8 th item)
`=192+(1)/(4)(200-192)`
`=192+2=194`
`D_(9)` = Size of `9((N+1)/(10))` th item = Size of `9((10+1)/(10))`th item
=Size of 9.9 th item
Size of 9th +0.9( Size of 10 th item - Size of 9th item)
`=200+(9)/(10)(210-200)`
`200+9=209`
`P_(70)` = Size of `70((N+1)/(100))` th item
= Size of 70th item
= Size of 7.7 th item
= Size of 7th item +0.7 (Size of 8th item - Size of 7th item)
`=190+(7)/(10)(192-190)`
`=190+1.4=191.4`
Thus , `Q_(1)=165,Q_(3)=194,D_(9)=209,P_(70)191.4`.