Question

question 4 (2 points)
the box plots below show attendance at a local movie theater and high school basketball games.
which of the following best describes how to measure the spread of the data? (2 points)
o a
the iqr is a better measure of spread for movies than it is for basketball games.
o b
the standard deviation is a better measure of spread for movies than it is for basketball games.
o c
the iqr is the best measurement of spread for games and movies.
o d
the standard deviation is the best measurement of spread for games and movies.

Explanation:

Step1: Recall the properties of IQR and standard deviation

IQR (Inter - Quartile Range) is robust to outliers. Standard deviation is sensitive to outliers.

Step2: Analyze the box - plots

Looking at the box - plots, we can assume (from the nature of box - plots which are based on quartiles) that for skewed data (which box - plots can represent), IQR is a better measure. Since we don't have information about the symmetry (to use standard deviation which is good for symmetric data), and box - plots are related to quartiles (from which IQR is calculated: \(IQR = Q_3 - Q_1\)).

Answer:

a. The IQR is a better measure of spread for movies than it is for basketball games.