Question

The list shows the number of miles to major cities from El Paso:

14, 20, 25, 17, 44.
What is the mean absolute deviation for these numbers?

a) 6
b) 8
c) 10
d) 12

Answer 1

The correct answer is option b) 8. The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the data set.

Step-by-step explanation:

To find the MAD for the given numbers, we calculate the mean, find the deviations, take the absolute value of each deviation, and finally calculate the average of the absolute deviations.

The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the data set. To find the MAD, we need to follow these steps:

1. Calculate the mean (average) of the given numbers. In this case, the mean is (14 + 20 + 25 + 17 + 44) / 5 = 20.
2. Subtract the mean from each individual data point to find the deviation. The deviations are: 14 - 20 = -6, 20 - 20 = 0, 25 - 20 = 5, 17 - 20 = -3, 44 - 20 = 24.
3. Take the absolute value of each deviation to eliminate negative values. The absolute deviations are: |-6| = 6, |0| = 0, |5| = 5, |-3| = 3, |24| = 24.
4. Calculate the average of the absolute deviations. (6 + 0 + 5 + 3 + 24) / 5 = 8.So, the mean absolute deviation for these numbers is 8.