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.
