Question

The following data sets represent the highway fuel efficiency in miles per gallon mpg of randomly selected cars from two car companies. Which company has cars that are more consistent and Highway fuel efficiency?

Answer 1

To determine which company has cars that are more consistent in highway fuel efficiency, we can compare the variability of the mpg values within each data set. One way to measure variability is to calculate the standard deviation of the mpg values for each company.

Let's calculate the standard deviation for both data sets:

Company A:
{25, 28, 24, 27, 26}
mean = (25+28+24+27+26)/5 = 26
Standard deviation = sqrt[((25-26)^2 + (28-26)^2 + (24-26)^2 + (27-26)^2 + (26-26)^2)/4] = sqrt[(1 + 4 + 4 + 1 + 0)/4] = sqrt(2.5) ≈ 1.58

Company B:
{30, 20, 25, 28, 22}
mean = (30+20+25+28+22)/5 = 25
Standard deviation = sqrt[((30-25)^2 + (20-25)^2 + (25-25)^2 + (28-25)^2 + (22-25)^2)/4] = sqrt[(25 + 25 + 0 + 9 + 9)/4] = sqrt(67/4) ≈ 2.59

Since Company A has a smaller standard deviation (1.58) compared to Company B (2.59), we can conclude that Company A has cars that are more consistent in highway fuel efficiency.