Statistical Measures

Method

Finding the Mean Absolute Deviation

The mean absolute deviation is a measure that describes the average absolute difference between the data points in a data set and the mean of the data set. It is calculated by finding the absolute difference between each data point and the mean, then taking the average of those absolute differences. Consider for example the following data set. 82, 85, 90, 75, 95, 85, 90, 70 The values are the scores of 8 students on a math test. The mean absolute deviation of the data set can be found by following these three steps.

1
Calculate the Mean
expand_more
The mean of a data set is the sum of all values in the set divided by the number of values.

Mean = Sum of Values/Number of Values
Mean = 82+85+90+75+95+85+90+70/8
Mean =672/8
Mean = 84

The mean of the data is 84.

2
Calculate the Distance Between Each Data Point and the Mean
expand_more
Next, calculate the absolute value of the differences between each data value and the mean.

Data Value Absolute Value of Difference
82 |82- 84| = 2
85 |85- 84| = 1
90 |90- 84| = 6
75 |75- 84| = 9
95 |95- 84| = 11
85 |85- 84| = 1
90 |90- 84| = 6
70 |70- 84| = 14
3
Calculate the Average of the Distances Found in Step 2
expand_more
Find the average of the absolute values of the differences between each data value and the mean.

2+1+6+9+11+1+6+14/8
50/8
6.25

The mean absolute deviation for the given data set is 6.25. This means that the average distance each data value is from the mean is 6.25 points. In other words, on average, the students' test scores deviate from the mean of 84 by 6.25 points.

Exercises
Edit Lesson