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:
1. Calculate the mean:
(35 + 28 + 35 + 30 + 31 + 36 + 35 + 30) / 8 = 32.5
2. Subtract the mean from each data point and square the result:
(35 - 32.5)^2 = 6.25
(28 - 32.5)^2 = 18.25
(35 - 32.5)^2 = 6.25
(30 - 32.5)^2 = 6.25
(31 - 32.5)^2 = 2.25
(36 - 32.5)^2 = 12.25
(35 - 32.5)^2 = 6.25
(30 - 32.5)^2 = 6.25
3. Find the sum of the squared differences:
6.25 + 18.25 + 6.25 + 6.25 + 2.25 + 12.25 + 6.25 + 6.25 = 54.75
4. Divide by the number of data points minus one (n-1):
54.75 / 7 = 7.82
5. Take the square root of the result to get the standard deviation:
√7.82 = 2.79
For Car Company B:
1. Calculate the mean:
(29 + 33 + 40 + 27 + 34 + 34 + 34 + 25) / 8 = 31.5
2. Subtract the mean from each data point and square the result:
(29 - 31.5)^2 = 6.25
(33 - 31.5)^2 = 2.25
(40 - 31.5)^2 = 72.25
(27 - 31.5)^2 = 18.25
(34 - 31.5)^2 = 6.25
(34 - 31.5)^2 = 6.25
(34 - 31.5)^2 = 6.25
(25 - 31.5)^2 = 42.25
3. Find the sum of the squared differences:
6.25 + 2.25 + 72.25 + 18.25 + 6.25 + 6.25 + 6.25 + 42.25 = 159.75
4. Divide by the number of data points minus one (n-1):
159.75 / 7 = 22.82
5. Take the square root of the result to get the standard deviation:
√22.82 = 4.78
Based on these calculations, Car Company A has a standard deviation of 2.79 mpg, while Car Company B has a standard deviation of 4.78 mpg. This means that Car Company A's cars are more consistent in highway fuel efficiency, as their data points are closer together and have less variability.