Question

The box plots below show attendance at a local movie theater and high school basketball games:

Answer 1

Answer:

D. The standard deviation is the best measurement of spread for games and movies.

Step-by-step explanation:

Measures of spread are stats that describes how separated are the group of data between each other.

The measures are range, quartiles, variance and standard deviation. Among these measures, the standard deviation is the one that best expresses the variation, dispersion or spread of a set of values, because is based on the difference between each data and the mean, it takes in count each separation.

That's why the correct answer is D.

Answer 2

Assume that the data for both movies and basketball games are normally distributed.
Therefore, the median and the mean are assumed equal.
The standard deviation, σ, is related to the interquartile range by
IQR = 1.35

From the data, we can say the following:

Movies:
Range = 150 - 60 = 90 (approx)
Q1 = 62 (approx), first quartile
Q3 = 120 (approx), third quartlie
Q2 (median) = 90 (approx)
IQR = Q3 - Q1 = 58
σ = IQR/1.35 = 58/1.35 = 43

Basketball:
Range = 150 - 90 = 60 approx
Q1 = 95 (approx)
Q3 = 145 (approx)
Q2 = 125 (approx)
IQR = 145 - 95 = 50
σ = 50/1.35 = 37

Test the given answers.
A. The IQRs are approximately equal, so they are not good measures of spread. This is not a good answer.
B. The std. deviation is a better measure of spread for basketball. This is not a good answer.
C. IQR is not a better measure of spread for basketball games. This is not a good answer.
D. The standard deviation is a good measure of spread for both movies and basketball. This is the best answer.

Answer: D