Question

The following data set represents the highway fuel efficiency in miles per gallon (mpg) of randomly selected cars from two car companies.
Car Company A: 35, 28, 35, 30, 31, 38, 35, 30
Car Company B: 29, 33, 36, 27, 34, 34, 25
Which of the following statements is true?
Remember to put each set of numbers in order from LEAST to GREATEST before starting the problem.
A. The cars from Company A have higher MEDIAN highway fuel efficiency than Company B.
B. The cars from Company A have higher MEAN highway fuel efficiency than Company B.
C. The cars from Company B have a higher MODE of highway fuel efficiency than Company A.
D. The cars from both companies have the same mean, median, and mode for highway fuel efficiency.

Answer 1

To determine which statement is true, let's first organize the data sets in order from least to greatest:

Car Company A: 28, 30, 30, 31, 35, 35, 35, 38
Car Company B: 25, 27, 29, 33, 34, 34, 36

A. Median:
For Company A, the median is the middle value when the data is in order, in this case it is 32.5. For Company B, the median is 33.
Therefore, the cars from Company B have a higher median highway fuel efficiency.

B. Mean:
To find the mean, we sum up all the values and divide by the total number of values.
For Company A, the mean is (28 + 30 + 30 + 31 + 35 + 35 + 35 + 38) / 8 = 32.5
For Company B, the mean is (25 + 27 + 29 + 33 + 34 + 34 + 36) / 7 ≈ 30.71
Therefore, the cars from Company A have a higher mean highway fuel efficiency.

C. Mode:
The mode is the value that appears most frequently.
For Company A, the mode is 35.
For Company B, the mode is 34.
Therefore, the cars from Company A have a higher mode of highway fuel efficiency.

D. The statement that the cars from both companies have the same mean, median, and mode for highway fuel efficiency is not true.

Therefore, the correct statement is:
B. The cars from Company A have higher MEAN highway fuel efficiency than Company B.