Question

question 2 of 10
this box plot shows the heights (in feet) of a sample of pine trees.
pine tree heights
25 45 55 65 75
20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120
height (ft)
a pine tree that is 140 feet tall is added to the sample. how
will this outlier affect the shape of the box plot?
a. the new box plot will be positively skewed.
b. the new box plot will look the same.
c. the new box plot will be negatively skewed.
d. the new box plot will be symmetric.

Explanation:

Step1: Recall Box Plot Skewness

A box plot's skewness is determined by the position of the median within the box and the length of the whiskers. A positive skew (right skew) occurs when there are outliers or a long tail on the right (higher values) side. A negative skew (left skew) has a long tail on the left (lower values) side. A symmetric box plot has the median in the middle of the box and equal - looking whiskers.

Step2: Analyze the Outlier's Effect

The original box plot has data up to around 75 feet (from the whisker). We add a data point of 140 feet, which is a high - value outlier. This outlier will create a long tail on the right - hand side of the box plot. When there is a long tail on the right, the box plot is positively skewed. The original box plot was likely symmetric (since the box is centered and whiskers look balanced), but adding a large outlier on the right will make it positively skewed. Option B is wrong because adding an outlier will change the plot. Option C is wrong because the outlier is on the right, not the left. Option D is wrong because the outlier disrupts symmetry.

Answer:

A. The new box plot will be positively skewed.