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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 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.
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.

1 answer

To evaluate the statements, let's calculate the mean, median, and mode for both car companies' fuel efficiency data.

For Car Company A:

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

  1. Mean: \[ \text{Mean} = \frac{35 + 28 + 35 + 30 + 31 + 38 + 35 + 30}{8} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30} = \frac{ 28 + 31 + 35 + 35 + 35 + 35 + 38}{8} = \frac{ 28 + 31 + 30 + 30 + 35 + 35 + 35 + 38}{8} = \frac{ 67 + 65 + 38}{8} = \frac{ 170}{8} = 33.75 \]

  2. Median:

    • Sorted data: 28, 30, 30, 31, 35, 35, 35, 38
    • Since there are 8 numbers, the median is the average of the 4th and 5th values: \[ 31 \text{ and } 35 \to \text{Median} = \frac{31 + 35}{2} = 33 \]

  3. Mode:

    • The most frequent number in Company A's data is 35 (it appears 3 times), so: \[ \text{Mode} = 35 \]

For Car Company B:

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

  1. Mean: \[ \text{Mean} = \frac{29 + 33 + 36 + 27 + 34 + 34 + 34 + 25}{8} = \frac{ 29 + 33 + 34 + 25 + 27 + 36 + 34 + 34}{8} = \frac{ 31 + 27 + 34 + 34 + 29 + 34 + 36 + 34}{8} = \frac{ 29 + 33 + 27 + 34 + 34 + 36 + 25}{8} = \frac{ 25 + 27 + 29 + 33 + 36}{8} = \frac{ 28 + 28 + 29 + 36 + 36}{8} = \frac{ 318}{8} = 29.75 \]

  2. Median:

    • Sorted data: 25, 27, 29, 33, 34, 34, 34, 36
    • Since there are 8 numbers, the median is the average of the 4th and 5th values: \[ 33 \text{ and } 34 \to \text{Median} = \frac{33 + 34}{2} = 33.5 \]

  3. Mode:

    • The most frequent number in Company B's data is 34 (it appears 3 times), so: \[ \text{Mode} = 34 \]

Summary of Results:

  • Company A:

    • Mean = 33.75
    • Median = 33
    • Mode = 35

  • Company B:

    • Mean = 31
    • Median = 33.5
    • Mode = 34

Analysis of Statements:

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

The correct statement is: "The cars from Company A have a higher mean highway fuel efficiency than Company B."