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

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 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.

:)

1 answer

To determine the accuracy of the statements regarding the highway fuel efficiency of cars from Company A and Company B, let's first calculate the mean, median, and mode for both data sets.

Car Company A: 35, 28, 35, 30, 31, 38, 35, 30

  • Mean: \[ \text{Mean} = \frac{35 + 28 + 35 + 30 + 31 + 38 + 35 + 30}{8} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 }{ 8 } = \frac{ 28 + 30 + 30 + 31 + 35 + 35 + 35 + 38 } { 8 } = \frac{ 28 + 30 + 30 + 31 + 105 }{8} = \frac{ 224 }{8} = 32 \]

  • Median: (Ordered List: 28, 30, 30, 31, 35, 35, 35, 38)

    • Median = (31 + 35) / 2 = 33

  • Mode: 35 (appears 3 times)

Car Company B: 29, 33, 36, 27, 34, 34, 34, 25

  • Mean: \[ \text{Mean} = \frac{29 + 33 + 36 + 27 + 34 + 34 + 34 + 25}{8} = \frac{ 28 + 30 + 33 + 34 + 34 + 36}{8} = \frac{ 34 + 34 + 36 + 33 }{ 8 } = \frac{ 185}{8} = 23.125 \]

  • Median: (Ordered List: 25, 27, 29, 33, 34, 34, 34, 36)

    • Median = (29 + 33) / 2 = 31

  • Mode: 34 (appears 3 times)

Summary of Calculations:

  • Mean:
    • Company A: 32
    • Company B: 31
  • Median:
    • Company A: 33
    • Company B: 31
  • Mode:
    • Company A: 35
    • Company B: 34

Evaluating Statements:

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

    • False: Means and medians are different.

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

    • True: Median for Company A (33) is higher than for Company B (31).

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

    • False: Mode for Company A (35) is higher than for Company B (34).

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

    • True: Mean for Company A (32) is higher than for Company B (31).

Correct Conclusion:

The statements that are true are:

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

However, if you want to choose just one, the stronger statement is: The cars from Company A have higher median highway fuel efficiency than Company B.