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 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 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 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.
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1 answer

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

  1. Mean: \[ \text{Mean} = \frac{35 + 28 + 35 + 30 + 31 + 38 + 35 + 30}{8} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 = 28 + 30 + 30 + 31 + 35 + 35 + 35 + 38 = 8}{8} = \frac{ = 35 + 28 + 35 + 30 = 35 + 31 + 31 + 32 = 31 = 34.625}{8} \approx 33.625 \]

  2. Median:

    • Arrange in ascending order: 28, 30, 30, 31, 35, 35, 35, 38
    • Median = (31 + 35) / 2 = 33
  3. Mode:

    • The mode is 35 (it appears most frequently).

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

  1. Mean: \[ \text{Mean} = \frac{29 + 33 + 36 + 27 + 34 + 34 + 34 + 25}{8} = \frac{ 29 + 33 + 36 + 27 + 34 + 34 + 34 + 25 = 29 + 30 + 34 + 34 = 31 = 29 + 33 + 34 + 25 = 35 + 34 + 34 + 36 = 36}{8} \approx 31 \]

  2. Median:

    • Arrange in ascending order: 25, 27, 29, 33, 34, 34, 34, 36
    • Median = (33 + 34) / 2 = 33.5
  3. 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:

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

    • False: The means and modes differ.
  2. The cars from Company B have higher modal highway fuel efficiency than Company A.

    • False: Company A's mode is higher (35 vs. 34).
  3. 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).
  4. 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.