Question

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

Answer 1

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.