he 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 point)
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
Variance = ((35-32.5)^2 + (28-32.5)^2 + (35-32.5)^2 + (30-32.5)^2 + (31-32.5)^2 + (36-32.5)^2 + (35-32.5)^2 + (30-32.5)^2) / 8
= (6.25 + 22.25 + 6.25 + 6.25 + 2.25 + 12.25 + 6.25 + 6.25) / 8
= 6.375
Standard deviation = sqrt(6.375) = 2.52
For Car Company B:
Mean = (29 + 33 + 40 + 27 + 34 + 34 + 34 + 25) / 8 = 31.75
Variance = ((29-31.75)^2 + (33-31.75)^2 + (40-31.75)^2 + (27-31.75)^2 + (34-31.75)^2 + (34-31.75)^2 + (34-31.75)^2 + (25-31.75)^2) / 8
= (7.5625 + 2.0625 + 70.5625 + 24.5625 + 7.5625 + 7.5625 + 7.5625 + 41.5625) / 8
= 17.875
Standard deviation = sqrt(17.875) = 4.23
Based on the standard deviation calculations, Car Company A has cars that are more consistent in highway fuel efficiency compared to Car Company B. The standard deviation for Car Company A is 2.52 mpg, while the standard deviation for Company B is 4.23 mpg. A lower standard deviation indicates less variation or more consistency in the data set.