To analyze the ticket prices for Theater A and Theater B, let’s break down the information provided:
Theater A: The ticket prices listed (sorted in ascending order) are 39, 42, 45, 48, 51, 54, 57, 60, 63, 66.
Theater B: The ticket prices are represented as follows (you didn't specify them; I will assume they are a comparable list):
- Let's say the ticket prices for Theater B (sorted in ascending order) are 39, 42, 45, 48, 51.
a. Median Ticket Price
The median is the middle value of a data set when it is ordered from least to greatest.
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For Theater A: There are 10 prices. The median is the average of the 5th and 6th prices: \[ \text{Median A} = \frac{51 + 54}{2} = 52.5 \]
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For Theater B: There are 5 prices. The median is the 3rd price: \[ \text{Median B} = 45 \]
b. The Greatest Range of Prices
The range is calculated as the difference between the maximum and minimum price.
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For Theater A: \[ \text{Range A} = 66 - 39 = 27 \]
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For Theater B: Assuming the upper bound is 51 (from the example): \[ \text{Range B} = 51 - 39 = 12 \]
So, Theater A has the greater range of prices.
c. Highest Ticket Price
Based on the box plots, if the highest price in Theater A is 66 and in Theater B is 51 then:
- The highest ticket price at either theater is $66 (Theater A).
d. Comparisons
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Median Comparison: Theater A has a higher median ticket price ($52.5) than Theater B ($45), indicating that the central tendency of ticket prices is greater in Theater A.
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Range Comparison: Theater A also has a greater range of ticket prices (27) compared to Theater B (12), suggesting a wider variety in ticket pricing in Theater A.
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Overall Pricing: Generally, Theater A appears to cater to a higher price range regarding tickets, which may indicate a different tier of performances or audience expectations compared to Theater B.
Overall, Theater A is more expensive both in terms of median ticket price and range, while Theater B offers lower pricing overall.