To determine which statement about highway fuel efficiency is true, we'll need to calculate the mean, median, and mode for both car companies.
Car Company A: 35, 28, 35, 30, 31, 38, 35, 30
-
Mean: \[ \text{Mean} = \frac{35 + 28 + 35 + 30 + 31 + 38 + 35 + 30}{8} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 = 28 + 30 + 30 + 31 + 35 + 35 + 35 + 38 = 8}{8} = \frac{ = 35 + 28 + 35 + 30 = 35 + 31 + 31 + 32 = 31 = 34.625}{8} \approx 33.625 \]
-
Median:
- Arrange in ascending order: 28, 30, 30, 31, 35, 35, 35, 38
- Median = (31 + 35) / 2 = 33
-
Mode:
- The mode is 35 (it appears most frequently).
Car Company B: 29, 33, 36, 27, 34, 34, 34, 25
-
Mean: \[ \text{Mean} = \frac{29 + 33 + 36 + 27 + 34 + 34 + 34 + 25}{8} = \frac{ 29 + 33 + 36 + 27 + 34 + 34 + 34 + 25 = 29 + 30 + 34 + 34 = 31 = 29 + 33 + 34 + 25 = 35 + 34 + 34 + 36 = 36}{8} \approx 31 \]
-
Median:
- Arrange in ascending order: 25, 27, 29, 33, 34, 34, 34, 36
- Median = (33 + 34) / 2 = 33.5
-
Mode:
- The mode is 34 (it appears most frequently).
Now we will compare the calculated values:
Car Company A:
- Mean ≈ 33.625
- Median = 33
- Mode = 35
Car Company B:
- Mean ≈ 31.25
- Median = 33.5
- Mode = 34
Now we can analyze the statements:
-
The cars from both companies have the same mean, median, and modal highway fuel efficiency.
- False: The means and modes differ.
-
The cars from Company B have higher modal highway fuel efficiency than Company A.
- False: Company A's mode is higher (35 vs. 34).
-
The cars from Company A have higher median highway fuel efficiency than Company B.
- False: Company B's median is higher (33.5 vs. 33).
-
The cars from Company A have a higher mean highway fuel efficiency than Company B.
- True: Company A's mean (33.625) is higher than Company B's mean (31.25).
The true statement is:
The cars from Company A have a higher mean highway fuel efficiency than Company B.