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4 Multiple Choice 1 point The data sets below show the ages of the starting members of two college football teams. Team \( 1: 21,25,20,18,24,21,21,20,24,23,22 \) Team \( 2: 19,18,22,20,21,20,23,23,23,25,19 \) Based on these sets of data, which of the following statements is correct? The mode of the ages on Team 1 is greater than the mode of the ages on Team 2 , and the median of the ages on Team 1 is less than the median of the ages on team 2 The mode of the ages on Team 1 is less than the mode of the ages on Team 2 , and the median of the ages on Team 1 is equal to the median of the ages on team 2 . The mode of the ages on Team 1 is less than the mode of the ages on Team 2 , and the median of the ages on Team 1 is greater than the median of the ages on team 2 . The mode of the ages on Team 1 is greater than the mode of the ages on Team 2 , and the median of the ages on Team 1 is greater than the median of the ages on team 2 .

Ask by Powell Brooks. in the United States
Jan 14,2025

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The mode of Team 1 is less than Team 2's mode, and both teams have the same median age.

Solución

Let's analyze the data for both teams to determine the correct statement. **Team 1 Data:** - Ages: 21, 25, 20, 18, 24, 21, 21, 20, 24, 23, 22 - **Sorted:** 18, 20, 20, 21, 21, 21, 22, 23, 24, 24, 25 - **Mode:** 21 (appears 3 times) - **Median:** 21 (the 6th value in the sorted list) **Team 2 Data:** - Ages: 19, 18, 22, 20, 21, 20, 23, 23, 23, 25, 19 - **Sorted:** 18, 19, 19, 20, 20, 21, 22, 23, 23, 23, 25 - **Mode:** 23 (appears 3 times) - **Median:** 21 (the 6th value in the sorted list) **Comparing Both Teams:** - **Mode:** Team 1's mode (21) is less than Team 2's mode (23). - **Median:** Both teams have the same median (21). **Correct Statement:** *The mode of the ages on Team 1 is less than the mode of the ages on Team 2, and the median of the ages on Team 1 is equal to the median of the ages on Team 2.* **Answer:** The mode of the ages on Team 1 is less than the mode of the ages on Team 2 , and the median of the ages on Team 1 is equal to the median of the ages on team 2.

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To find the modes and medians for both teams, we can start with Team 1. The ages are \(18, 20, 20, 21, 21, 21, 22, 23, 24, 24, 25\). The mode here is \(21\) (appearing three times), and the median (the middle value in a sorted list) is \(21\) as well. For Team 2, the ages are \(18, 19, 19, 20, 20, 21, 22, 23, 23, 23, 25\). The mode is \(23\) (appearing three times), and the median is also \(21\). Now, we compare the modes and medians: Team 1 has a mode of \(21\) which is less than Team 2's mode of \(23\), and both teams have the same median of \(21\). This means the correct statement is: "The mode of the ages on Team 1 is less than the mode of the ages on Team 2 , and the median of the ages on Team 1 is equal to the median of the ages on team 2."

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