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 company has cars that are more consistent in highway fuel efficiency, we can calculate the standard deviation for each data set. A smaller standard deviation indicates that the data points are closer to the mean, meaning the cars have more consistent fuel efficiency.
Standard deviation for Car Company A:
First, calculate the mean:
(35 + 28 + 35 + 30 + 31 + 36 + 35 + 30) / 8 = 32
Next, calculate the squared difference for each data point from the mean:
(35-32)^2 = 9
(28-32)^2 = 16
(35-32)^2 = 9
(30-32)^2 = 4
(31-32)^2 = 1
(36-32)^2 = 16
(35-32)^2 = 9
(30-32)^2 = 4
Then, calculate the variance by summing these squared differences and dividing by the number of data points:
(9+16+9+4+1+16+9+4) / 8 = 68/8 = 8.5
Finally, calculate the standard deviation by taking the square root of the variance:
√8.5 ≈ 2.92
Standard deviation for Car Company B:
First, calculate the mean:
(29 + 33 + 40 + 27 + 34 + 34 + 34 + 25) / 8 = 31.375
Next, calculate the squared difference for each data point from the mean:
(29-31.375)^2 = 6.14
(33-31.375)^2 = 2.72
(40-31.375)^2 = 74.27
(27-31.375)^2 = 19.97
(34-31.375)^2 = 6.88
(34-31.375)^2 = 6.88
(34-31.375)^2 = 6.88
(25-31.375)^2 = 40.27
Then, calculate the variance by summing these squared differences and dividing by the number of data points:
(6.14+2.72+74.27+19.97+6.88+6.88+6.88+40.27) / 8 = 163.71 / 8 = 20.46
Finally, calculate the standard deviation by taking the square root of the variance:
√20.46 ≈ 4.52
Comparing the standard deviations, we see that Car Company A has a standard deviation of approximately 2.92 mpg, while Car Company B has a standard deviation of approximately 4.52 mpg. Therefore, Car Company A has cars that are more consistent in highway fuel efficiency than Car Company B.