Question

What is the third quartile, Q3, of the following distribution?

4,5, 33, 10, 12, 14, 34, 43, 21, 22, 21, 22, 44, 29, 16, 18, 20, 24, 26, 29

Answer 1

29

Explanation:

Answer 2

The third quartile is:

`Q_3=29`

Explanation:

First organize the data from lowest to highest

4, 5, 10, 12, 14, 16, 18, 20, 21, 21, 22, 22, 24, 26, 29, 29, 33, 34, 43, 44

Notice that we have a quantity of n = 20 data

Use the following formula to calculate the third quartile
`Q_3`

For a set of n data organized in the form:

`x_1, x_2, x_3, ..., x_n`

The third quartile is
`Q_3`:

`Q_3=x_{(3)/(4)(n+1)}`

With n=20

`Q_3=x_{(3)/(4)(20+1)}`

`Q_3=x_(15.75)`

The third quartile is between
`x_(15)=29` and
`x_(16)=29`

Then

`Q_3 =x_(15) + 0.75*(x_(16)- x_(15))`

`Q_3 =29 + 0.75*(29- 29)\\\\Q_3 =29`