The marks obtained by 100 students of a school are given below.
`{:("Marks",0-5,5-10,10-15,15-20,20-25,25-30,30-35,35-40),("No . of Students"," "4," "6," "10," "10," "25," "22," "18," "5):}`
Find out `Q_(1),Q_(3),D_(6)and P_(95)`.

Explanation

`Q_(1)` = Size of `((N)/(4))` th item
= Size of `((100)/(4))` th item
= Size of 25th item
25th item lies in the calss intervals 15-20.
`Q_(1)=l_(1)(N/(4)-c.f.)/(f)xxi`
`=15+(100/(4)-20)/(10)xx5`
`=15+(25-20)/(10)xx5=15+(5)/(10)xx5`
`=15+2.5`
`=17.5`
`Q_(3)` = Size of `3((N)/(4))`th item
= Size of `3((100)/(4))` th item = Size of 75th item
75th item lies in the class interval 25-30.
`Q_(3)=l_(1)+(3((N)/(4))-c.f.)/(f)xxi`
`=25+(3((100)/(4))-c.f.)/(22)xx55`
`=25+(75-55)/(22)xx5=25+(20)/(22)xx5`
`=25+4.55=29.55`
`D_(6)` Size of `6((N)/(10))` th item = Size of `6((100)/(10))`th item = Size of 60th item
60 th item lies in the class interval 25-30.
`D_(6)=l_(1)+(6((N)/(10))-c.f.)/(f)xxi`
`=25+(6((100)/(10))-55)/(22)xx5`
`=25+(60=55)/(22)xx5=25+(5)/(22)xx5`
`=25+1.14=26.14`
`P_(95)` = Size of 95 `((N)/(100))` th item
= Size of `((100)/(100))`th item
= Size of 95 th item
95th item lies in the class interval 30-35.
`P_(95)=l_(1)+(95((N)/(100))-c.f.)/(f)xxi`
`=30+(95((100)/(100))-77)/(18)xx5`
`=30+(95-77)/(18)xx5=30+(18)/(18)xx5`
`=30+5=35`
`Q_(1)=17.5,Q_(3)=29.55,D_(6)=26.14,P_(95)=35`.