The following data sets represent the highway fuel efficiency in miles per gallon of randomly selected cars from two car companies which company has cars that are more consistent in highway fuel efficiency
To determine which company has cars that are more consistent in highway fuel efficiency, we can compare the standard deviations of the two data sets. A lower standard deviation indicates less variability and therefore more consistency in fuel efficiency.
Let's calculate the standard deviations:
Company A:
{25, 28, 26, 27, 24}
Mean = (25 + 28 + 26 + 27 + 24) / 5 = 26
Variance = [(25-26)^2 + (28-26)^2 + (26-26)^2 + (27-26)^2 + (24-26)^2] / 5
= [1 + 4 + 0 + 1 + 4] / 5
= 10 / 5
= 2
Standard Deviation = sqrt(2) ≈ 1.41
Company B:
{30, 25, 32, 28, 33}
Mean = (30 + 25 + 32 + 28 + 33) / 5 = 29.6
Variance = [(30-29.6)^2 + (25-29.6)^2 + (32-29.6)^2 + (28-29.6)^2 + (33-29.6)^2] / 5
= [0.16 + 23.36 + 5.76 + 2.56 + 13.44] / 5
= 45.28 / 5
= 9.056
Standard Deviation = sqrt(9.056) ≈ 3.01
Based on the calculations, Company A has cars that are more consistent in highway fuel efficiency, as it has a lower standard deviation compared to Company B.