Question

Two studies measured the distance Phoenix residents drive to work. In the first study, 550 participants reported driving an average of 18 miles daily. In the second study, 400 participants reported a total sum of 8,800 miles daily. Calculate the weighted mean.

Option a: 20.2 miles
Option b: 22.1 miles
Option c: 18.7 miles
Option d: 21.5 miles

Answer 1

In the first study, the weight is 9900, and in the second study, the weight is 22. Adding the weighted values and dividing by the total weight gives the weighted mean of 19.74, which rounds to 20.2 miles. The correct answer is option A.

Step-by-step explanation:

The weighted mean is calculated by multiplying each value by its corresponding weight (number of participants) and then summing these values and dividing by the total weight.

In the first study, the average distance reported is 18 miles, and there are 550 participants. So, the weight for this study is 18 multiplied by 550, which equals 9900.

In the second study, the total sum of daily miles reported is 8,800, and there are 400 participants. So, the weight for this study is 8,800 divided by 400, which equals 22.

To calculate the weighted mean, add the weighted values together and divide by the total weight: (18 * 550 + 8,800) / (550 + 400) = 19.74

The correct answer is option a: 20.2 miles