Before a basketball tournament, Tara, Emek, and Luna studied the team's statistics screen to help choose a starting lineup. One player had scored 12, 13, 14, 15, and 16 points in five recent games, giving a mean and median of 14. Another had scored 9, 10, 11, 12, and 28 points. Her mean was also 14, but her median was only 11. Emek noticed that the unusually high 28-point game raised her mean. The friends checked the other players' records in the same way, comparing both mean and median instead of relying on one number. They selected players whose scores were strong and steady across several games. With a balanced starting lineup chosen from the data, the team entered the tournament confident and prepared.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Compare the mean and median given for each player's five games.
Which statement best compares the two players described in the story?
The second player has both a greater mean and a greater median.The players have the same mean, but the first player has the greater median.The first player has the greater mean, but the players have the same median.The players have the same mean and the same median.Correct. Both players have a mean of 14, but their medians are 14 and 11.
Check the mean and median for each player separately before comparing them.
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Hint
Add the new set of five scores, then divide the total by 5.
The second player's five scores were 9, 10, 11, 12, and 28. If the 28-point game were replaced by a 13-point game, what would the new mean score be?
Correct. Replacing 28 with 13 lowers the mean to 11.
Use the scores 9, 10, 11, 12, and 13, find their total, and divide by 5.
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Hint
Think about how the 28-point game affected the second player's mean compared with her median.
Why was it useful for Tara, Emek, and Luna to compare both mean and median when choosing steady players?
Because the mean always equals the highest score, while the median equals the lowest score.Because the median uses every score, while the mean uses only the middle score.Because a very high or low score can affect the mean more than the median, so the two measures can give different information.Because mean and median must always be different for a set of scores.Correct. An unusually high score can pull the mean upward while leaving the median much less affected.
Use the second player's 28-point game as a clue and compare its effect on the mean and median.
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