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?

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, [tex]Q_1=34[/tex] and [tex]Q_3=38[/tex].

[tex]IQR=Q_3-Q_1[/tex]

[tex]IQR=38-34[/tex]

[tex]IQR=4[/tex]

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

Now,

[tex]Q_3+1.5\times IQR=38+1.5(4)[/tex]

[tex]Q_3+1.5\times IQR=38+6[/tex]

[tex]Q_3+1.5\times IQR=44[/tex]

We know that, 43<44.

Since, 43 is not greater than [tex]Q_3+1.5\times IQR[/tex], therefore, 43 is not an outlier and there is no evidence to support the claim.

Therefore, the correct option is D.

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