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 most 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 company has cars that are most 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 = 32.625
Variance = ((35-32.625)^2 + (28-32.625)^2 + (35-32.625)^2 + (30-32.625)^2 + (31-32.625)^2 + (36-32.625)^2 + (35-32.625)^2 + (30-32.625)^2) / 8
= (5.75^2 + -4.625^2 + 5.75^2 + -2.625^2 + -1.625^2 + 3.375^2 + 5.75^2 + -2.625^2) / 8
= (33.0625 + 21.3906 + 33.0625 + 6.8906 + 2.6406 + 11.3906 + 33.0625 + 6.8906) / 8
= 148.3812 / 8
= 18.5476
Standard Deviation = sqrt(18.5476) = 4.31
For Car Company B:
Mean = (29 + 33 + 40 + 27 + 34 + 34 + 34 + 25) / 8 = 31.5
Variance = ((29-31.5)^2 + (33-31.5)^2 + (40-31.5)^2 + (27-31.5)^2 + (34-31.5)^2 + (34-31.5)^2 + (34-31.5)^2 + (25-31.5)^2) / 8
= (6.25^2 + 1.5^2 + 8.75^2 + 16.25^2 + 2.5^2 + 2.5^2 + 2.5^2 + 36.25^2) / 8
= (39.0625 + 2.25 + 76.5625 + 210.625 + 6.25 + 6.25 + 6.25 + 131.0625) / 8
= 478.3125 / 8
= 59.79
Standard Deviation = sqrt(59.79) = 7.74
Therefore, Car Company A has cars that are most consistent in highway fuel efficiency with a standard deviation of 4.31, compared to Car Company B with a standard deviation of 7.74.