To determine which statements are true, we need to calculate the mean and median fuel efficiency for both car companies, as well as identify the mode for each company.
Data for Car Company A:
- Values: 35, 28, 35, 30, 31, 38, 35, 30
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Mean for Company A
- \( \text{Mean} = \frac{(35 + 28 + 35 + 30 + 31 + 38 + 35 + 30)}{8} \)
- \( = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 }{8} = \frac{ 28 + 30 + 30 + 31 + 35 + 35 + 35 + 38 }{8} = \frac{ 319 }{8} = 39.875 \)
- Mean = 33.875 mpg
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Median for Company A
- Sorted: 28, 30, 30, 31, 35, 35, 35, 38
- Median = (31 + 35) / 2 = 33 mpg.
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Mode for Company A
- Mode = 35 (appears most frequently)
Data for Car Company B:
- Values: 29, 33, 36, 27, 34, 34, 34, 25
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Mean for Company B
- \( \text{Mean} = \frac{(29 + 33 + 36 + 27 + 34 + 34 + 34 + 25)}{8} \)
- \( = \frac{ 29 + 33 + 34 + 36 + 34 + 34 + 25 + 27 }{8} = \frac{ 32 + 27 + 33 + 29 + 34 + 34 + 25 }{8} = \frac{ 20 + 32 + 29 + 33 + 34 + 34 + 25 }{8} = \frac{ 282 }{8} = 35.25 \)
- Mean = 30.25 mpg
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Median for Company B
- Sorted: 25, 27, 29, 33, 34, 34, 34, 36
- Median = (33 + 34) / 2 = 33.5 mpg.
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Mode for Company B
- Mode = 34 (appears most frequently)
Now we can draw conclusions based on the calculations:
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Mean:
- Company A: 33.875 mpg
- Company B: 30.25 mpg
- Conclusion: Company A has a higher mean than Company B.
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Median:
- Company A: 33.0 mpg
- Company B: 33.5 mpg
- Conclusion: Company B has a higher median than Company A.
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Mode:
- Company A: 35
- Company B: 34
- Conclusion: Company A has a higher mode than Company B.
Based on this analysis, the true statements are:
- The cars from Company A have higher mean highway fuel efficiency than Company B.
Thus, the correct responses from the options provided are:
The cars from Company A have a higher mean highway fuel efficiency than Company B.