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
29,33,40,27,33,34,34,25
To determine which company has cars that are most consistent in highway fuel efficiency, we can calculate the standard deviation of the highway fuel efficiency for each company.
For car company A:
Mean = (35+28+35+30+31+36+35+30) / 8 = 32.5
Standard Deviation = sqrt[ ( (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 ]
= sqrt[ (8.25 + 22.25 + 8.25 + 6.25 + 2.25 + 14.25 + 8.25 + 6.25) / 8 ]
= sqrt[75.0 / 8] = sqrt(9.375) = 3.06
For car company B:
Mean = (29+33+40+27+33+34+34+25) / 8 = 31.625
Standard Deviation = sqrt[ ( (29-31.625)^2 + (33-31.625)^2 + (40-31.625)^2 + (27-31.625)^2 + (33-31.625)^2 + (34-31.625)^2 + (34-31.625)^2 + (25-31.625)^2 ) / 8 ]
= sqrt[ (6.25 + 1.93 + 68.06 + 23.20 + 1.93 + 4.65 + 4.65 + 39.05) / 8 ]
= sqrt[ 149.32 / 8] = sqrt(18.665) = 4.32
Therefore, car company A has cars that are more consistent in highway fuel efficiency since it has a smaller standard deviation of 3.06 compared to car company B's standard deviation of 4.32.