During a soccer tournament, Tara and Emek wondered whether their team played better before or after halftime. They recorded successful passes from six recent games. The first-half totals were 34, 38, 41, 43, 45, and 45, while the second-half totals were 39, 42, 46, 48, 50, and 51. They plotted both data sets on the same number line and compared their centers and spreads. The first-half data had a mean of 41 passes and a range of 11. The second-half data had a mean of 46 passes and a range of 12. Although the ranges were almost the same, the second-half values were generally higher. Tara noted that even the lowest second-half total was greater than several first-half totals. Their analysis suggested that the team became more effective after halftime rather than simply having one unusually strong game. For the next match, the coach decided to use the team's successful second-half passing strategy from the opening whistle.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
Compare both the centers and the spreads of the two data sets.
Which statement best supports Tara and Emek's conclusion that the team generally played better in the second half?
The second-half range was larger, so every second-half game had more successful passes.The second-half mean was 5 passes higher, while the two ranges were nearly the same.The first-half range was smaller, so the first-half passing totals were usually higher.The highest second-half total was 51, so one strong game alone proves the second half was better.
Correct. The higher second-half mean with a similar range supports a general shift toward more successful passes.
Not quite. Look for evidence that compares both typical performance and variation, rather than focusing on only one game.
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Hint
Add the six first-half totals and the six second-half totals, then find the difference.
Emek checks the stated means by finding the total number of successful passes in each half across all six games. How many more successful passes were made in the second halves than in the first halves altogether?
Correct. Across the six games, the team made 30 more successful passes in the second halves.
Check the total for each set of six games, then subtract the first-half total from the second-half total.
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Hint
Look for evidence that many second-half games, not just the highest one, had strong totals.
A student says, "The team's second-half mean was higher only because of the game with 51 successful passes." Which observation from the data best shows that this claim is not reasonable?
The second-half range was 12, which was 1 more than the first-half range.The first-half mean was 41 and the second-half mean was 46.Five of the six second-half totals were greater than the first-half mean of 41.The highest first-half total was 45 and the highest second-half total was 51.
Correct. Five second-half totals exceeded the first-half mean, so the higher second-half performance was not caused by only one game.
Not quite. Choose the evidence showing that several second-half results were high, not just the maximum value.
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Daha Güçlü Devreyi Bulmak
TR
ARC_G07_DP_02_STORY_03
Daha Güçlü Devreyi Bulmak
Finding the Stronger Half
EN
ARC_G07_DP_02_STORY_03
Finding the Stronger Half