The box plots below show attendance at a local movie theater and high school basketball games: Two box plots are shown. The top one is labeled Movies. Minimum at 100, Q1 at 130, median at 165, Q3 at 185, maximum at 200. The bottom box plot is labeled Basketball games. Minimum at 135, Q1 at 225, median at 248, Q3 at 275, maximum at 300.

Which of the following best describes how to measure the spread of the data?

The IQR is a better measure of spread for movies than it is for basketball games.
The standard deviation is a better measure of spread for movies than it is for basketball games.
The IQR is the best measurement of spread for games and movies.
The standard deviation is the best measurement of spread for games and movies.

Option B: The standard deviation is a better measure of spread for movies than it is for basketball games.

Step-by-step explanation:

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

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.

step-by-step explanation:

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