Mean Absolute Deviation: 26 Interpretation: The data, on average, are 26 units away from the mean of 139.
Practice makes perfect
The mean absolute deviation (MAD) is the average of the absolute values of the differences between the mean and each value in the data set. Let's see the given data set.
101, 115, 124, 125, 173, 165, 170
We will start by calculating the mean of the given set of numbers. We can see that there is 7 values in our data set. Let's calculate the mean!
We found that the mean of the given data set is 139. We are ready to calculate the MAD. As previously stated, the MAD of a set of data is the average of the absolute values of the differences between the mean and each value in the data set.
| x- x_1|+| x- x_2|+...+| x- x_n|/n
In this formula, x_1,...,x_n are the values in the set of data, x is the mean, and n is the number of values. We already know that x= 139 and n= 7. Let's use a table to find the sum of the absolute values of the differences.
x_i
x-x_i
|x-x_i|
101
139- 101=38
|38|=38
115
139- 115=24
|24|=24
124
139- 124=15
|15|=15
125
139- 125=14
|14|=14
173
139- 173=-34
|-34|=34
165
139- 165=-26
|-26|=26
170
139- 170=-31
|-31|=31
Sum of Values
182
Finally, we need to divide by 7.
Mean Absolute Deviation (MAD)
182/7=26
A MAD of 26 indicates that the data, on average, are 26 units away from the mean of 139.
