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To the right are box plots comparing the ticket prices of two performing arts theaters.

a. What is the median ticket price for each​ theater?
b. Which theater has the greatest range of​ prices?
c. What is the highest ticket price at either​ theater?
d. Make some statements comparing the ticket prices at the two theaters.
Theater A
Theater B
39
42
45
48
51
54
57
60
63
66

Question content area bottom
Part 1
a. The median ticket price for theater A is ​$
  
51.
Part 2
The median ticket price for theater B is ​$
  
45.
Part 3
b.
Theater A
has the greatest range of prices.
Part 4
c. The highest ticket price is ​$
  
60 at
theater A.
Part 5
d. Choose the correct answer below.
A.
There is more variation at theater​ A; also there are higher ticket prices at theater A.
B.
Theater A has higher ticket​ prices, but there is more variation in prices at theater B.
C.
Theater B has higher ticket​ prices, but there is more variation in prices at theater A.
D.
There is more variation at theater​ B; also there are higher ticket prices at theater B.

1 answer

Let's analyze the data provided to answer each part of your question.

Part 1:

a. Median ticket price for each theater:

  • For Theater A, the median ticket price is $51.
  • For Theater B, the median ticket price is $45.

Part 2:

b. The theater with the greatest range of prices:

  • First, we calculate the range for each theater.
    • Range = Maximum price - Minimum price.

For the data provided, we'll assume the minimum and maximum ticket prices in the box plot are:

  • Theater A: Min is 39, Max is 66.
  • Theater B: Min is 42, Max is 60.

Calculating the ranges:

  • Theater A: Range = 66 - 39 = 27.
  • Theater B: Range = 60 - 42 = 18.

Thus, Theater A has the greatest range of prices.

Part 3:

c. Highest ticket price at either theater: The highest ticket price is from Theater A, which is $66.

Part 4:

d. Choose the correct answer comparing ticket prices: Comparison: Theater A has higher median ticket prices and greater variation (greater range) compared to Theater B.

Thus, the correct answer is: A. There is more variation at theater A; also, there are higher ticket prices at theater A.

Summary of Answers:

  • a: Median price for A: $51, for B: $45.
  • b: Theater A has the greatest range of prices.
  • c: Highest ticket price: $66 at Theater A.
  • d: Correct answer: A. There is more variation at theater A; also, there are higher ticket prices at theater A.