Question

What is the mean absolute deviation of the following set:



{78, 45, 60, 33, 84}

Answer 1

First, we need to find the mean (average) of the set of numbers.

The mean is found by adding up all the numbers in the set and dividing by the total number of values. In this case, the sum of the numbers is 78 + 45 + 60 + 33 + 84 = 300. There are 5 numbers in the set, so we divide the sum by 5 to find the mean: 300/5 = 60.

Next, we find the absolute deviation of each number in the set from the mean. To do this, we subtract the mean from each number and take the absolute value (ignoring any negative signs).

|78 - 60| = 18
|45 - 60| = 15
|60 - 60| = 0
|33 - 60| = 27
|84 - 60| = 24

Then, we find the mean of these absolute deviations. Add up all the absolute deviations and divide by the total number of values:

(18 + 15 + 0 + 27 + 24) / 5 = 84 / 5 = 16.8

Thus, the mean absolute deviation of the set {78, 45, 60, 33, 84} is 16.8.