Question

Bernie and Sarah go bowling together. The table shows their scores for the past eight weeks.
Bowling Scores:
• Bernie: 90, 110, 115, 120, 118, 130, 124, 125
• Sarah: 100, 120, 110, 105, 95, 125, 170, 155Choose all the true statements about the scores.
A. Sarah has the same median score as Bernie.
B. Bernie has the same range of scores as Sarah.
C. Sarah has a greater median score than Bernie.
D. Bernie has a greater median score than Sarah.
E. Sarah has a greater range of scores than Bernie.

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Answer 1

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:**
- Scores: 90, 110, 115, 120, 118, 130, 124, 125
- Arranged: 90, 110, 115, 118, 120, 124, 125, 130
- Median: The median is the average of the 4th and 5th scores.
\[
\text{Median} = \frac{118 + 120}{2} = 119
\]

- Range: The range is the difference between the maximum and minimum scores.
\[
\text{Range} = 130 - 90 = 40
\]

**Sarah's Scores:**
- Scores: 100, 120, 110, 105, 95, 125, 170, 155
- Arranged: 95, 100, 105, 110, 120, 125, 155, 170
- Median: The median is the average of the 4th and 5th scores.
\[
\text{Median} = \frac{110 + 120}{2} = 115
\]

- 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**.