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?
a The cars from both companies have the same mean, median, and modal highway fuel efficiency.
b The cars from Company B have higher modal highway fuel efficiency than Company A.
c The cars from Company A have higher median highway fuel efficiency than Company B.
d The cars from Company A have a higher mean highway fuel efficiency that Company B.
d The cars from Company A have a higher mean highway fuel efficiency that Company B.
To determine which statement is true, we need to calculate the mean, median, and mode for both sets of data.
For Car Company A:
Data: 35, 28, 35, 30, 31, 38, 35, 30
Mean:
To find the mean, we add up all the values and divide by the total number of values.
Mean = (35 + 28 + 35 + 30 + 31 + 38 + 35 + 30) / 8
Mean = 264 / 8
Mean = 33
Median:
To find the median, we need to arrange the values in ascending order and find the middle value.
Arranged data: 28, 30, 30, 31, 35, 35, 35, 38
Median = (31 + 35) / 2
Median = 33
Mode:
The mode is the value(s) that appear most frequently in the data set.
In this case, we have multiple modes: 35 (appears 3 times)
Mode = 35
For Car Company B:
Data: 29, 33, 36, 27, 34, 34, 34, 25
Mean:
Mean = (29 + 33 + 36 + 27 + 34 + 34 + 34 + 25) / 8
Mean = 252 / 8
Mean = 31.5
Median:
Arranged data: 25, 27, 29, 33, 34, 34, 34, 36
Median = (29 + 33) / 2
Median = 31
Mode:
The mode is the value(s) that appear most frequently in the data set.
In this case, the mode is 34 (appears 3 times)
Mode = 34
Now, let's analyze each statement:
a) The cars from both companies have the same mean, median, and modal highway fuel efficiency.
Based on the calculations above, this statement is FALSE because both car companies differ in terms of mean highway fuel efficiency (Company A: 33 mpg, Company B: 31.5 mpg).
b) The cars from Company B have higher modal highway fuel efficiency than Company A.
Based on the calculations, this statement is FALSE because both car companies have the same mode highway fuel efficiency (both have a mode of 34).
c) The cars from Company A have higher median highway fuel efficiency than Company B.
Based on the calculations, this statement is TRUE because Company A has a higher median highway fuel efficiency (33 mpg) compared to Company B (31 mpg).
d) The cars from Company A have a higher mean highway fuel efficiency than Company B.
Based on the calculations, this statement is TRUE because Company A has a higher mean highway fuel efficiency (33 mpg) compared to Company B (31.5 mpg).
Therefore, the correct answer is:
Statement d) The cars from Company A have a higher mean highway fuel efficiency than Company B.