Question

What is the interquartile range of the data set?

{18, 17, 10, 25, 20, 20, 30, 18, 18, 30, 25}



Enter the answer in the box.

Answer 1

`IQR=7`

Explanation:

The given data set is:

18, 17, 10, 25, 20, 20, 30, 18, 18, 30, 25

In order to find the Interquartile range, firstly arrange the given data set in ascending order,

10, 17, 18, 18, 18, 20, 20, 25, 25, 30, 30

The Upper quartile is:

20, 25, 25, 30, 30, thus

`UQ=25`

And, the lower quartile is:

10, 17, 18, 18, 18, thus

`LQ=18`

Now, the Interquatile range is given as:

`IQR=UQ-LQ`

`IQR=25-18`

`IQR=7`

Thus, the Interquartile range of the given data set is 7.

Answer 2

The interquartile range of the data set is 7.

Explanation:

The given set of data is

{18, 17, 10, 25, 20, 20, 30, 18, 18, 30, 25}

Arrange the data in ascending order.

10, 17, 18, 18, 18, 20, 20, 25, 25, 30, 30

Divide the data in two equal parts.

(10, 17, 18, 18, 18), 20, (20, 25, 25, 30, 30)

Divide each parenthesis in 2 equal parts.

(10, 17), 18, (18, 18), 20, (20, 25), 25, (30, 30)

Now we can say that,

`Q_1=18, Median=20, Q_3=25`

Interquartile rage of a data is

`I.Q.R.=Q_3-Q_1`

`I.Q.R.=25-18=7`

Therefore the interquartile range of the data set is 7.