To analyze the data sets and determine which statement is true, we need to calculate the mean, median, and mode for both companies.
Car Company A: 35, 28, 35, 30, 31, 38, 35, 30
- Mean: \[ \text{Mean} = \frac{(35 + 28 + 35 + 30 + 31 + 38 + 35 + 30)}{8} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 = 31.625} \]
- Median: First, sort the list: 28, 30, 30, 31, 35, 35, 35, 38 The median is the average of the 4th and 5th values: \[ \text{Median} = \frac{31 + 35}{2} = 33 \]
- Mode: The most frequent number is 35 (occurs 3 times).
Car Company B: 29, 33, 36, 27, 34, 34, 34, 25
- Mean: \[ \text{Mean} = \frac{(29 + 33 + 36 + 27 + 34 + 34 + 34 + 25)}{8} = \frac{ 29 + 33 + 36 + 27 + 34 + 34 + 34 + 25 = 30.25} \]
- Median: First, sort the list: 25, 27, 29, 33, 34, 34, 34, 36 The median is the average of the 4th and 5th values: \[ \text{Median} = \frac{33 + 34}{2} = 33.5 \]
- Mode: The most frequent number is 34 (occurs 3 times).
Comparison:
-
Mean:
- Company A's mean: 33.625
- Company B's mean: 30.25 (Therefore, Company A has a higher mean than Company B.)
-
Median:
- Company A's median: 33
- Company B's median: 33.5 (Company B has a higher median.)
-
Mode:
- Company A's mode: 35
- Company B's mode: 34 (Company A has a higher mode.)
Based on this analysis, the true statement is: The cars from Company A have a higher mean highway fuel efficiency than Company B.