Question

What is the third quartile of 14,18,20,21,25,32,40,44,48

Answer 1

The data from lowest to highest is,

`14,18,20,21,25,32,40,44,48`

There are 9 number of observations in the data. So median value of the data is, (n+1)/2, which is equal to

`\begin{gathered} (9+1)/(2)=(10)/(2) \\ =5 \end{gathered}`

The 5th term from starting is 25. So median value is 25.

The upper Quartile (or third quartile) is median value of upper half of the data. The upper half of data is, 32,40,44,48.

There are 4 observations in upper half. So median value of upper half is average value of (n/2)th term and (n/2 + 1)th term.

The value of n/2 and n/2 + 1is,

`(4)/(2)=2`
`\begin{gathered} (4)/(2)+1=2+1 \\ =3 \end{gathered}`

The second and third term of upper half of data is 40 and 44.

Determine the average value of 40 and 44.

`\begin{gathered} Q_3=(40+44)/(2) \\ =(84)/(2) \\ =42 \end{gathered}`