The average deviation is the sum of the difference between each value and the median, divided by the number of observations. The average deviation should be used when the median is the only measure of central tendency used.
The average deviation is a useful measure when your data distribution does not look like a normal curve -- when the data is skewed. In this situation, the median is the best measure of central tendency, and the average deviation is the best measure of dispersion.
The average deviation is the sum of the difference between each value and the median, divided by the number of observations. In mathematical notation, it looks like this:
Translated to English:
|
AvgDev |
The Average Deviation. |
|
|
This is the summation sign, and indicates that you should add (sum) all the values from 1 to n for the equation that follows. This means you will calculate the difference between each value in your data set and the median, and add all those values together. |
|
|
The bars on either side of this equation indicate you are supposed to take the absolute value of your calculation. Calculate the difference between each value (xi) and the median. If the result of a calculation is negative, remove the 'minus' sign. You aren't interested in whether the number is positive or negative. Rather, you are interested in how each value in the data set is from the median. |
|
'n' |
This represents the total count of values in your data set. |
Suppose we have a sampling of weight in pounds of 11 high school students from two different communities. The table below provides both data and statistics about the students' weights. The data provided is the weight for each student. The statistics provided include the mean, median, and range (listed under the weight column for each high school). We've also calculated the sum of the differences from the median as well as calculating the average deviation statistic. Note that the difference from the median are provided in absolute values, or non-negative numbers.
Based on the values listed in the table below, the average deviation is calculated as follows:
|
Average Deviation = |
Sum of differences from median number of observations |
|
High School 1 Average Deviation: |
266 / 11 = 24.9 |
|
High School 2 Average Deviation: |
425 / 11 = 38.64 |
|
|
High School 1 |
High School 2 | ||
|
Weight |
Absolute Value of |
Weight |
Absolute Value of | |
|
78 |
|78 - 138| = 60 |
113 |
25 | |
|
80 |
|80 - 138| = 58 |
115 |
23 | |
|
85 |
|85 - 138| = 53 |
120 |
18 | |
|
95 |
|95 - 138| = 43 |
135 |
3 | |
|
130 |
|130 - 138| = 8 |
137 |
1 | |
|
138 |
|138 - 138| = 0 |
138 |
0 | |
|
140 |
140 - 138 = 2 |
185 |
47 | |
|
145 |
145 - 138 = 7 |
190 |
52 | |
|
148 |
148 - 138 = 10 |
200 |
62 | |
|
150 |
150 - 138 = 12 |
220 |
82 | |
|
151 |
151 - 138 = 13 |
250 |
112 | |
|
Mean |
121.8 |
|
163.9 |
|
|
Median |
138 |
|
138 |
|
|
Range |
73 |
|
137 |
|
|
Sum of Differences |
|
266 |
|
425 |
|
Average Deviation |
|
24.2 |
|
38.6 |
Weight in Pounds of High School Students
The median suggests that the two sets of data provided above are very similar. However, the average deviation tells us that the weights of students in High School 2 have a greater variation than the weights of students in High School 1.
