During a soccer strategy meeting, Tara, Emek, and Luna studied the statistics of two goalkeepers. In five recent games, Kai made 5, 6, 6, 7, and 11 saves. Mira made 6, 7, 7, 7, and 8 saves. Tara calculated that both players had a mean of 7 saves. Their medians were different, though: Kai's was 6, while Mira's was 7. Emek noticed that Kai's 11-save game raised his mean, even though he usually made fewer saves. Mira's results were grouped more closely around 7, showing steadier performance. Since the upcoming match called for a goalkeeper who could perform consistently, they recommended Mira. The coach agreed that looking beyond the mean gave a clearer picture and chose Mira to start the important match.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Compare how closely each goalkeeper's five results are grouped.
A student says Kai and Mira performed equally steadily because they both had a mean of 7 saves. Which statement best explains the mistake?
The mean alone does not show how spread out the saves are from game to game.Players with the same mean must also have the same median.The median is always greater than the mean for a steady player.The highest number of saves should be used instead of both the mean and median.Correct. The same mean can come from data sets with very different amounts of variation.
Think about what the mean tells you and what it does not tell you about consistency.
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Hint
For each goalkeeper, subtract the smallest number of saves from the largest number of saves, then compare the ranges.
How many saves greater is Kai's range than Mira's range over the five games?
Correct. Kai's range is 4 saves greater than Mira's range.
Find each goalkeeper's range first, then subtract the smaller range from the larger range.
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Hint
Replace 11 with 6, then find the new mean and identify the middle value after ordering the scores.
Suppose Kai's 11-save game had instead been a 6-save game. Which statement about his new five-game data would be correct?
His mean would stay 7 and his median would become 7.His mean would become 6 and his median would remain 6.His mean would become 6 and his median would become 5.His mean would become 7 and his median would remain 6.Correct. The new scores have a mean of 6 and a median of 6.
Use the new scores 5, 6, 6, 6, and 7. Check both their total and their middle value.
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