Before a soccer tournament, Emek and Luna helped the coach compare two goalkeepers using graphs of saves from seven recent matches. Goalkeeper A had 3, 4, 5, 4, 5, 4, and 10 saves. Goalkeeper B had 5, 6, 5, 4, 6, 5, and 5 saves. At first, A's graph looked impressive because of the 10-save match. Emek calculated that both goalkeepers had a median of 4 saves for A and 5 saves for B, while Luna compared their ranges: A's was 7, but B's was only 2. They also noticed that six of A's seven results were between 3 and 5, whereas all of B's results were between 4 and 6. The single high result made A seem stronger than the overall distribution suggested. Since the coach wanted dependable performance throughout the tournament, Emek and Luna recommended Goalkeeper B, whose results had a higher center and much smaller spread.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Think about whether one unusually high result represents the consistency of all seven matches.
A student says Goalkeeper A must be more dependable because A had the highest single-match result of 10 saves. Which response best explains the problem with this reasoning?
The highest result alone does not describe the whole data set, and A's range of 7 shows much more variation than B's range of 2.A range of 7 means Goalkeeper A made exactly 7 saves in most matches.Goalkeeper B is more dependable only because B never made 10 saves.The highest value should always be ignored when comparing two data sets.
Correct. One high value does not show overall consistency, and A's much larger range indicates greater spread.
Not quite. Compare the full distributions, especially their spreads, rather than focusing only on the largest value.
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Hint
Add all seven numbers of saves, then divide the total by 7.
Goalkeeper A had 3, 4, 5, 4, 5, 4, and 10 saves in seven matches. What was the mean number of saves per match?
Correct. Goalkeeper A averaged 5 saves per match.
Check the sum of all seven match results, including the 10-save match, and divide by 7.
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Hint
Use both a measure of center and a measure of spread to compare the goalkeepers.
The coach wants to judge dependable typical performance rather than being influenced by one unusually high match. Which comparison best supports choosing Goalkeeper B?
A has a median of 4 and a range of 7, while B has a median of 5 and a range of 2, so B has both a higher center and a smaller spread.A has a higher maximum, so A must also have the higher median and smaller range.B has a median of 5 and a range of 7, so B's results are more spread out.The two goalkeepers should be considered equally dependable because each played seven matches.
Correct. Goalkeeper B has the higher median and the smaller range, which supports more dependable typical performance.
Not quite. Compare both the medians and the ranges instead of focusing on the number of matches or one extreme result.
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İki Kalecinin Hikâyesi
TR
ARC_G08_DP_02_STORY_03
İki Kalecinin Hikâyesi
A Tale of Two Goalkeepers
EN
ARC_G08_DP_02_STORY_03
A Tale of Two Goalkeepers