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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
16
18
20
22
24
26
28
30
32
34

Question content area bottom
Part 1
a. The median ticket price for theater A is ​$
  
24.
Part 2
The median ticket price for theater B is ​$
  
20.
Part 3
b.
Theater A
has the greatest range of prices.
Part 4
c. The highest ticket price is ​$
  
30 at
theater A.
Part 5
d. Choose the correct answer below.
A.
There is more variation at theater​ B; also there are higher ticket prices at theater B.
B.
Theater A has higher ticket​ prices, but there is more variation in prices at theater B.
C.
There is more variation at theater​ A; also there are higher ticket prices at theater A.
D.
Theater B has higher ticket​ prices, but there is more variation in prices at theater A.

1 answer

Let's break down the answers according to the information you've provided:

Part 1

a. The median ticket price for Theater A is $24.
The median ticket price for Theater B is $20.

Part 2

b. Theater A has the greatest range of prices. (This would imply that the difference between the maximum and minimum ticket prices is larger for Theater A than for Theater B.)

Part 3

c. The highest ticket price is $30 at Theater A.

Part 4

d. Now let's analyze the options:

  • A. There is more variation at theater B; also there are higher ticket prices at theater B.
    (This option contradicts your findings, since Theater A has higher ticket prices.)

  • B. Theater A has higher ticket prices, but there is more variation in prices at theater B.
    (This might not hold true if Theater A indeed has greater variation.)

  • C. There is more variation at theater A; also there are higher ticket prices at theater A.
    (This option is likely correct based on your findings.)

  • D. Theater B has higher ticket prices, but there is more variation in prices at theater A.
    (This option is also incorrect; Theater B has lower ticket prices.)

Conclusion

Given your inputs, the correct conclusion is likely C. There is more variation at theater A; also there are higher ticket prices at theater A.

If there are still some specifics I need from the box plots (like exact values for the min and max) to confirm the variations correctly, please let me know!