Ask a New Question
Menu

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 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 B have higher modal highway fuel efficiency than Company A.

1 answer

Let's calculate the mean, median, and mode for both car companies:

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

  1. Mean: \[ \text{Mean} = \frac{35 + 28 + 35 + 30 + 31 + 38 + 35 + 30}{8} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 = 28 + 30 + 30 + 31 + 35 + 35 + 35 + 38 }{8}
    \] \[ \text{Mean} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 = 35 + 28 + 30 + 31 + 35 + 38 + 30 }{8} = \frac{28 + 30 + 30 + 31 + 35 + 35 + 35 + 38 = 35 + 31 + 38 + 30 + 35 }{8} = 34.5\text{Mean} = \frac{ 35 + 28 + 30 + 38 + 31 + 30 = 30 + 31 + 28 + 31 + 30 + 35 + 35 }{8}
    \] \[ = \frac{168}{8} = 33 \]

  2. Median:

    • Arranging the data: 28, 30, 30, 31, 35, 35, 35, 38
    • Median = (31 + 35)/2 = 33

  3. Mode:

    • The mode is 35 (appears three times).

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

  1. Mean: \[ \text{Mean} = \frac{29 + 33 + 36 + 27 + 34 + 34 + 34 + 25}{8} = \frac{ 29 + 33 + 36 + 27 + 34 + 34 + 34 + 25 }{8} \] \[ = \frac{ 29 + 33 + 36 + 34 + 27 + 34 + 34 + 25 = 36 + 34 + 33 + 29 + 27 + 34 + 34 + 25 }{8} = \frac{ 29 + 33 + 36 + 34 + 34 + 34 + 34 + 25 = 36 + 34 + 33 + 29 + 27 + 34 + 34 + 25 }{8} \] \[ = \frac{ 29 + 33 + 36 + 34 + 34 + 34 + 34 + 25 = 36 + 34 + 33 + 29 + 27+ 33 + 29 }{8} = 35.25 \]

  2. Median:

    • Arranging the data: 25, 27, 29, 33, 34, 34, 34, 36
    • Median = (33 + 34)/2 = 33.5

  3. Mode:

    • The mode is 34 (appears three times).

Now we can summarize the results:

  • Company A:

    • Mean = 33
    • Median = 33
    • Mode = 35

  • Company B:

    • Mean = 33.75
    • Median = 33.5
    • Mode = 34

Now we can evaluate the statements:

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

    • False (Means, medians do not match)

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

    • False (A = 33, B = 33.5)

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

    • False (B's mean is 33.75; A's is less)

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

    • False (A = 35, B = 34)

The true statement is:

  • The cars from Company A have a higher mode of highway fuel efficiency than Company B.

Therefore, the answer to the question is:

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