Question

Find the mean and the MAD of the following data set. Do not round your answers. 10, 15, 20, 25, 30, 35.

A. Mean = 22.5, MAD = 7.5
B. Mean = 25, MAD = 10
C. Mean = 30, MAD = 5
D. Mean = 20, MAD = 15

Answer 1

The mean of the data set is 22.5 and the mean absolute deviation (MAD) is 7.5.

Step-by-step explanation:

To find the mean of a data set, you add up all the numbers and divide the sum by the total number of values. In this case, the sum of the data set 10, 15, 20, 25, 30, 35 is 135. Since there are 6 values, the mean is 135 divided by 6, which is 22.5.

To find the MAD (Mean Absolute Deviation), you subtract the mean from each value, take the absolute value of the difference, and then find the average of those differences. The differences from the mean for this data set are 10-22.5 = 12.5, 15-22.5 = 7.5, 20-22.5 = 2.5, 25-22.5 = 2.5, 30-22.5 = 7.5, 35-22.5 = 12.5. The average of these differences is (12.5 + 7.5 + 2.5 + 2.5 + 7.5 + 12.5) / 6 = 45 / 6 = 7.5. Therefore, the mean is 22.5 and the MAD is 7.5.