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 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 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.

1 answer

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

Car Company A:

  • Data: 35, 28, 35, 30, 31, 38, 35, 30

Mean for Company A: \[ \text{Mean} = \frac{35 + 28 + 35 + 30 + 31 + 38 + 35 + 30}{8} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 = 326 }{8} = 40.75 \text{ mpg} \]

Median for Company A:

  • Ordered Data: 28, 30, 30, 31, 35, 35, 35, 38
  • Median (average of the 4th and 5th values) = (31 + 35) / 2 = 33 mpg

Mode for Company A:

  • The mode (most frequent value) is 35 mpg (appears three times).

Car Company B:

  • Data: 29, 33, 36, 27, 34, 34, 34, 25

Mean for Company B: \[ \text{Mean} = \frac{29 + 33 + 36 + 27 + 34 + 34 + 34 + 25}{8} = \frac{ 29 + 33 + 36 + 27 + 34 + 34 + 34 + 25 = 312 }{8} = 39 \text{ mpg} \]

Median for Company B:

  • Ordered Data: 25, 27, 29, 33, 34, 34, 34, 36
  • Median = (33 + 34) / 2 = 33.5 mpg

Mode for Company B:

  • The mode is 34 mpg (appears three times).

Now, let's compare the values:

  • Mean:

    • Company A: 32.75 mpg
    • Company B: 39 mpg
  • Median:

    • Company A: 33 mpg
    • Company B: 33.5 mpg
  • Mode:

    • Company A: 35 mpg
    • Company B: 34 mpg

Based on this analysis, the true statements are:

  1. The cars from Company B have higher modal highway fuel efficiency than Company A (False).
  2. The cars from both companies have the same mean, median, and modal highway fuel efficiency (False).
  3. The cars from Company A have a higher mean highway fuel efficiency than Company B (True).
  4. The cars from Company A have higher median highway fuel efficiency than Company B (False).

Therefore, the true statement is: "The cars from Company A have a higher mean highway fuel efficiency than Company B."