Question

1. at a football game, 40 fans were randomly surveyed. of the sampled fans, named darren as the best player. given this sample, if there are 12,000 fans altogether at the game, how many would likely name darren as the best player? a. 720 b. 1,800 c. 4,800 d. 80,000 30. the ages of the starting players of two soccer teams are shown below. knights: 18, 16, 15, 14, 17, 17, 18, 16, 15, 14, 17, 18 trojans: 18, 14, 17, 15, 16, 18, 16, 14, 17, 16 based on this data, select all the true statements below. a. the median of ages on the knights team is greater than the median of ages on the trojans team. b. the mean of ages on the knights team is greater than the range of ages on the trojans team. c. the median of ages on the knights team is one greater than the median of ages on the trojans team. d. the mean of ages on the knights team is less than the mean of ages on the trojans team. e. the mean of ages on the knights team is greater than the mean of ages on the trojans team.

Explanation:

Step1: Calculate the median for Knights

First, arrange Knights' ages in ascending - order: 14, 14, 15, 16, 17, 17, 18, 18. There are 8 values. The median is the average of the 4th and 5th values. So, median$_{Knights}=\frac{16 + 17}{2}=16.5$.

Step2: Calculate the median for Trojans

Arrange Trojans' ages in ascending - order: 14, 15, 15, 16, 16, 17, 18, 18. There are 8 values. The median is the average of the 4th and 5th values. So, median$_{Trojans}=\frac{16+16}{2}=16$.

Step3: Calculate the mean for Knights

Mean$_{Knights}=\frac{14 + 14+15+16+17+17+18+18}{8}=\frac{129}{8}=16.125$.

Step4: Calculate the mean for Trojans

Mean$_{Trojans}=\frac{14 + 15+15+16+16+17+18+18}{8}=\frac{130}{8}=16.25$.

Step5: Analyze each statement

• A: median$_{Knights}=16.5$ and median$_{Trojans}=16$, so the median of ages on the Knights team is greater than the median of ages on the Trojans team. This statement is true.
• B: The mean of ages on the Knights team ($16.125$) is less than the mean of ages on the Trojans team ($16.25$), so this statement is false.
• C: The range of ages on the Knights team: $18 - 14=4$, and on the Trojans team: $18 - 14 = 4$. So this statement is false.
• D: The mean of ages on the Knights team ($16.125$) is less than the mean of ages on the Trojans team ($16.25$), so this statement is false.
• E: The mean of ages on the Knights team ($16.125$) is less than the mean of ages on the Trojans team ($16.25$), so this statement is false.

Answer:

A. The median of ages on the Knights team is greater than the median of ages on the Trojans team.