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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, 34, 25

Which of the following statements is true?

(1 point)
Responses

The cars from Company B have higher modal highway fuel efficiency than Company A.
The cars from Company B have higher modal highway fuel efficiency than Company A.

The cars from Company A have a higher mean highway fuel efficiency that Company B.
The cars from Company A have a higher mean highway fuel efficiency that Company B.

The cars from Company A have higher median highway fuel efficiency than Company B.
The cars from Company A have higher median highway fuel efficiency than Company B.

The cars from both companies have the same mean, median, and modal highway fuel efficiency.

(THAN or THAT? Be careful.)

1 answer

To determine which statement is true, we need to calculate the mean, median, and mode for the fuel efficiency of both car companies.

Car Company A:

  • Data: 35, 28, 35, 30, 31, 38, 35, 30
  • Mean: (35 + 28 + 35 + 30 + 31 + 38 + 35 + 30) / 8 = 35.125 / 8 = 34.25
  • Median: To find the median, we first arrange the data: 28, 30, 30, 31, 35, 35, 35, 38. The median is the average of the 4th and 5th values: (31 + 35) / 2 = 33
  • Mode: The most frequently occurring value is 35.

Car Company B:

  • Data: 29, 33, 36, 27, 34, 34, 34, 25
  • Mean: (29 + 33 + 36 + 27 + 34 + 34 + 34 + 25) / 8 = 32.5 / 8 = 30.625
  • Median: Arrange the data: 25, 27, 29, 33, 34, 34, 34, 36. The median is the average of the 4th and 5th values: (33 + 34) / 2 = 33.5
  • Mode: The most frequently occurring value is 34.

Now we can compare:

  • Mean:

    • Company A: 34.25
    • Company B: 30.625
    • Company A has a higher mean.

  • Median:

    • Company A: 33
    • Company B: 33.5
    • Company B has a higher median.

  • Mode:

    • Company A: 35
    • Company B: 34
    • Company A has a higher mode.

Summary of Findings:

  • Mean: Company A > Company B
  • Median: Company B > Company A
  • Mode: Company A > Company B

Conclusion:

The only true statement from the options given is:

The cars from Company A have a higher mean highway fuel efficiency than Company B.