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
To determine which car 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 = 31.75
Calculate the squared differences from the mean: (35-31.75)^2, (28-31.75)^2, (35-31.75)^2, (30-31.75)^2, (31-31.75)^2, (36-31.75)^2, (35-31.75)^2, (30-31.75)^2
Sum of squared differences = 28.5
Variance = 28.5/7 = 4.07
Standard Deviation = sqrt(4.07) = 2.02
For Car Company B:
Mean = (29+33+40+27+34+34+34+25) / 8 = 32.5
Calculate the squared differences from the mean: (29-32.5)^2, (33-32.5)^2, (40-32.5)^2, (27-32.5)^2, (34-32.5)^2, (34-32.5)^2, (34-32.5)^2, (25-32.5)^2
Sum of squared differences = 257
Variance = 257/7 = 36.71
Standard Deviation = sqrt(36.71) = 6.06
Since the standard deviation for Car Company A is 2.02 and for Car Company B is 6.06, we can conclude that Car Company A has cars that are more consistent in highway fuel efficiency.