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 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 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 a higher mean highway fuel efficiency that Company B.

1 answer

To analyze the data sets and determine which statement is true, we need to calculate the mean, median, and mode for both companies.

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

  • Mean: \[ \text{Mean} = \frac{(35 + 28 + 35 + 30 + 31 + 38 + 35 + 30)}{8} = \frac{ 35 + 28 + 35 + 30 + 31 + 38 + 35 + 30 = 31.625} \]
  • Median: First, sort the list: 28, 30, 30, 31, 35, 35, 35, 38 The median is the average of the 4th and 5th values: \[ \text{Median} = \frac{31 + 35}{2} = 33 \]
  • Mode: The most frequent number is 35 (occurs 3 times).

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

  • Mean: \[ \text{Mean} = \frac{(29 + 33 + 36 + 27 + 34 + 34 + 34 + 25)}{8} = \frac{ 29 + 33 + 36 + 27 + 34 + 34 + 34 + 25 = 30.25} \]
  • Median: First, sort the list: 25, 27, 29, 33, 34, 34, 34, 36 The median is the average of the 4th and 5th values: \[ \text{Median} = \frac{33 + 34}{2} = 33.5 \]
  • Mode: The most frequent number is 34 (occurs 3 times).

Comparison:

  • Mean:

    • Company A's mean: 33.625
    • Company B's mean: 30.25 (Therefore, Company A has a higher mean than Company B.)
  • Median:

    • Company A's median: 33
    • Company B's median: 33.5 (Company B has a higher median.)
  • Mode:

    • Company A's mode: 35
    • Company B's mode: 34 (Company A has a higher mode.)

Based on this analysis, the true statement is: The cars from Company A have a higher mean highway fuel efficiency than Company B.