Question

Find the interquartile range (IQR) and list any outliers: 60, 74, 70, 70, 50, 62, 54, 89, 67, 88, 82, 74 A. IQR = 39: 89 is an outlier B. IQR = 17: no outliers C. IQR = 39: no outliers D. IQR = 17: 50 is an outlie

Answer 1

Given:

The data set is 60, 74, 70, 70, 50, 62, 54, 89, 67, 88, 82, 74.

To find:

The IQR and outliers.

Solution:

The given data set is

60, 74, 70, 70, 50, 62, 54, 89, 67, 88, 82, 74

Arrange the data values in ascending order.

50, 54, 60, 62, 67, 70, 70, 74, 74, 82, 88, 89

Divide the data set in two equal parts.

(50, 54, 60, 62, 67, 70), (70, 74, 74, 82, 88, 89)

Divide each parentheses in two equal parts.

(50, 54, 60), (62, 67, 70), (70, 74, 74), (82, 88, 89)

Now,

`Q_1=(60+62)/(2)`

`Q_1=(122)/(2)`

`Q_1=61`

And,

`Q_3=(74+82)/(2)`

`Q_3=(156)/(2)`

`Q_3=78`

We know that, the inter quartile range is

`IQR=Q_3-Q_1`

`IQR=78-61`

`IQR=17`

The IQR is 17.

If the data values lie outside the interval
`[Q_1-1.5IQR,Q_3+1.5IQR]`, then those values are known as outliers.

`[Q_1-1.5IQR,Q_3+1.5IQR]=[61-1.5(17),78+1.5(17)]`

`[Q_1-1.5IQR,Q_3+1.5IQR]=[35.5,103.5]`

All data values lie in the interval [35.5,103.5]. So, there are no outliers.

Therefore, the correct option is B.