Question

comparing the means of two data sets
robin and evelyn are playing a target game. the object of the game is to get an object as close to the center as possible. each player’s score is the number of centimeters away from the center. robin’s mean is 107, and evelyn’s mean is 138. compare the means. explain what this comparison indicates in the context of the data. who is winning the game? why?

Explanation:

1. First, compare the two mean values: Robin's mean (107) is less than Evelyn's mean (138), so $107 < 138$.
2. In this game, a lower score (distance from center) means better performance, as the goal is to be as close to the center as possible. A smaller mean distance indicates Robin's throws are, on average, closer to the center than Evelyn's.
3. Since Robin has a lower average distance from the center, Robin is winning the game.

Answer:

Robin's mean score (107) is less than Evelyn's mean score (138). In this game, a lower score means the object is closer to the center. Robin's lower average distance from the center indicates their throws are, on average, closer to the target center than Evelyn's. Robin is winning the game because their mean distance from the center is smaller, meaning they are closer to the target on average.