To evaluate the true statements about the bowling scores of Bernie and Sarah, we first need to calculate the median and range for each of their scores.
Bernie's Scores:
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Scores: 90, 110, 115, 120, 118, 130, 124, 125
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Arranged: 90, 110, 115, 118, 120, 124, 125, 130
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Median: The median is the average of the 4th and 5th scores. \[ \text{Median} = \frac{118 + 120}{2} = 119 \]
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Range: The range is the difference between the maximum and minimum scores. \[ \text{Range} = 130 - 90 = 40 \]
Sarah's Scores:
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Scores: 100, 120, 110, 105, 95, 125, 170, 155
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Arranged: 95, 100, 105, 110, 120, 125, 155, 170
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Median: The median is the average of the 4th and 5th scores. \[ \text{Median} = \frac{110 + 120}{2} = 115 \]
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Range: The range is the difference between the maximum and minimum scores. \[ \text{Range} = 170 - 95 = 75 \]
Now we summarize the findings:
- Bernie's median score: 119
- Sarah's median score: 115
- Bernie's range: 40
- Sarah's range: 75
Now, we evaluate each statement:
A. Sarah has the same median score as Bernie.
False (119 ≠ 115)
B. Bernie has the same range of scores as Sarah.
False (40 ≠ 75)
C. Sarah has a greater median score than Bernie.
False (115 < 119)
D. Bernie has a greater median score than Sarah.
True (119 > 115)
E. Sarah has a greater range of scores than Bernie.
True (75 > 40)
Final Evaluation of Statements:
- D: True
- E: True
Thus, the true statements about the scores are D and E.
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