Question

Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1.5x IQR rule for outliers, is there evidence to support the claim?

Answer 1

Given:

Emily claims that a tree height of 43 inches is an outlier for the distribution.

To find:

Evidence to support the claim if any.

Solution:

The starting and the end of the box in box plot are first and third quartile respectively.

From the given box plot it is clear that,
`Q_1=34` and
`Q_3=38`.

`IQR=Q_3-Q_1`

`IQR=38-34`

`IQR=4`

According to 1.5x IQR rule for outliers, all the data values lies outside the interval
`[Q_1-1.5* IQR,Q_3+1.5* IQR]` are outliers.

Now,

`Q_3+1.5* IQR=38+1.5(4)`

`Q_3+1.5* IQR=38+6`

`Q_3+1.5* IQR=44`

We know that, 43<44.

Since, 43 is not greater than
`Q_3+1.5* IQR`, therefore, 43 is not an outlier and there is no evidence to support the claim.

Therefore, the correct option is D.