Question

a sample of 33 broadway shows was examined. each show was categorized as being either a musical or a play, and the run time (or total length of the show, in minutes) was recorded. this data is summarized below with both a graphical display and a table of summary statistics. which one of the following is the most accurate conclusion to draw based on this information?
type of show
musical
play
run time

type|minimum|q1|median|q3|maximum
musical|80|142.5|150|157.5|175
play|90|96.5|115|152.5|210

at least one musical must have had a run time equal to 142.5 minutes.
the run times of plays are skewed to the right.
less than half of the musicals in the sample have run times above 150 minutes.
the majority of shows in this data set are plays.
the run times of plays are less variable than the run times of musicals.

Explanation:

Step1: Understand quartiles and median concepts

The median divides the data - set into two halves. Q1 is the first - quartile (25th percentile) and Q3 is the third - quartile (75th percentile).

Step2: Analyze the musical data

For musicals, the median is 150 minutes. This means that 50% of the musicals have run - times below 150 minutes and 50% have run - times above 150 minutes. So, less than half of the musicals in the sample have run - times above 150 minutes is a correct statement.

Step3: Analyze other statements

• Just because Q1 for musicals is 142.5 minutes, it doesn't mean at least one musical has a run - time of exactly 142.5 minutes.
• For plays, since the distance from Q3 to the maximum (210 - 152.5=57.5) is much larger than the distance from Q1 to the minimum (96.5 - 90 = 6.5), the run - times of plays are skewed to the right, but we need to find the most accurate conclusion.
• There's no information to suggest that the majority of shows are plays.
• The inter - quartile range (IQR) for musicals is \(IQR_{musical}=Q3 - Q1=157.5 - 142.5 = 15\) and for plays is \(IQR_{play}=Q3 - Q1=152.5 - 96.5 = 56\). So, the run - times of plays are more variable than those of musicals.

Answer:

Less than half of the musicals in the sample have run times above 150 minutes.