Question

A random sample of 11 days were selected from last year's records maintained by the maternity ward in a local hospital, and the number of babies born each day of the days is given below: 3 7710 0 712 530 Find the five number summary (minimum, first quartile, second quartile, third quartile, maximum) of the data.

Answer 1

Answer: ( Min = 0 ,
`Q_1=1` ,
`Q_2=3` ,
`Q_3=7` , Max = 10 )

Explanation:

Given : A random sample of 11 days were selected from last year's records maintained by the maternity ward in a local hospital, and the number of babies born each day of the days is given below:

3 7 7 10 0 7 1 2 5 3 0

We first arrange them in increasing order , we get

0 0 1 2 3 3 5 7 7 7 10

Here , N= 11

Now , we can see that

Minimum value = 0

Maximum value = 10

First quartile
`Q_1`=
`((N+1)/(4))^(th)\ term=((12)/(4))^(th)\ term = 3^(rd) term =1`

Second quartile
`Q_2`= Median = Middlemost number = 3

Third quartile
`Q_3` =
`((3(N+1))/(4))^(th)\ term=((36)/(4))^(th)\ term`

`= 9^(th) term =7`

∴ The required five number summary : ( Min = 0 ,
`Q_1=1` ,
`Q_2=3` ,
`Q_3=7` , Max = 10 )