To determine which company has cars that are more consistent in highway fuel efficiency, we can calculate the standard deviation for each data set.
For Car Company A:
Mean = (35 + 28 + 35 + 30 + 31 + 36 + 35 + 30) / 8 = 32.5
Calculate the squared differences from the mean:
(35 - 32.5)^2 = 6.25
(28 - 32.5)^2 = 21.25
(35 - 32.5)^2 = 6.25
(30 - 32.5)^2 = 6.25
(31 - 32.5)^2 = 2.25
(36 - 32.5)^2 = 12.25
(35 - 32.5)^2 = 6.25
(30 - 32.5)^2 = 6.25
Calculate the variance:
Variance = (6.25 + 21.25 + 6.25 + 6.25 + 2.25 + 12.25 + 6.25 + 6.25) / 8 = 7.8125
Standard Deviation = sqrt(Variance) = sqrt(7.8125) = 2.794
For Car Company B:
Mean = (29 + 33 + 40 + 27 + 34 + 34 + 34 + 25) / 8 = 31.5
Calculate the squared differences from the mean:
(29 - 31.5)^2 = 6.25
(33 - 31.5)^2 = 2.25
(40 - 31.5)^2 = 72.25
(27 - 31.5)^2 = 20.25
(34 - 31.5)^2 = 6.25
(34 - 31.5)^2 = 6.25
(34 - 31.5)^2 = 6.25
(25 - 31.5)^2 = 42.25
Calculate the variance:
Variance = (6.25 + 2.25 + 72.25 + 20.25 + 6.25 + 6.25 + 6.25 + 42.25) / 8 = 16.625
Standard Deviation = sqrt(Variance) = sqrt(16.625) = 4.078
Car Company A has a standard deviation of 2.794, while Car Company B has a standard deviation of 4.078. Therefore, Car Company A has cars that are more consistent in highway fuel efficiency compared to Car Company B.
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 in highway fuel efficiency?
Car Company A: 35, 28, 35, 30, 31, 36, 35, 30
Car Company B: 29, 33, 40, 27, 34, 34, 34, 25
1 answer