Let's calculate the mean, median, and mode for both car companies.
Car Company A:
- Data: 35, 28, 35, 30, 31, 38, 35, 30
Mean for Company A: \[ \text{Mean} = \frac{35 + 28 + 35 + 30 + 31 + 38 + 35 + 30}{8} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 = 326 }{8} = 40.75 \text{ mpg} \]
Median for Company A:
- Ordered Data: 28, 30, 30, 31, 35, 35, 35, 38
- Median (average of the 4th and 5th values) = (31 + 35) / 2 = 33 mpg
Mode for Company A:
- The mode (most frequent value) is 35 mpg (appears three times).
Car Company B:
- Data: 29, 33, 36, 27, 34, 34, 34, 25
Mean for Company B: \[ \text{Mean} = \frac{29 + 33 + 36 + 27 + 34 + 34 + 34 + 25}{8} = \frac{ 29 + 33 + 36 + 27 + 34 + 34 + 34 + 25 = 312 }{8} = 39 \text{ mpg} \]
Median for Company B:
- Ordered Data: 25, 27, 29, 33, 34, 34, 34, 36
- Median = (33 + 34) / 2 = 33.5 mpg
Mode for Company B:
- The mode is 34 mpg (appears three times).
Now, let's compare the values:
-
Mean:
- Company A: 32.75 mpg
- Company B: 39 mpg
-
Median:
- Company A: 33 mpg
- Company B: 33.5 mpg
-
Mode:
- Company A: 35 mpg
- Company B: 34 mpg
Based on this analysis, the true statements are:
- The cars from Company B have higher modal highway fuel efficiency than Company A (False).
- The cars from both companies have the same mean, median, and modal highway fuel efficiency (False).
- The cars from Company A have a higher mean highway fuel efficiency than Company B (True).
- The cars from Company A have higher median highway fuel efficiency than Company B (False).
Therefore, the true statement is: "The cars from Company A have a higher mean highway fuel efficiency than Company B."