Mean Absolute Deviation: 8.75 Interpretation: The data, on average, are 8.75 units away from the mean of 54.
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.
46, 54, 43, 57, 50, 62, 78, 42
We will start by calculating the mean of the given set of numbers. We can see that there is 8 values in our data set. Let's calculate the mean!
We found that the mean of the given data set is 54. 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= 54 and n= 8. Let's use a table to find the sum of the absolute values of the differences.
x_i
x-x_i
|x-x_i|
46
54- 46=8
|8|=8
54
54- 54=0
|0|=0
43
54- 43=11
|11|=11
57
54- 57=-3
|-3|=3
50
54- 50=4
|4|=4
62
54- 62=-8
|-8|=8
78
54- 78=-24
|-24|=24
42
54- 42=12
|12|=12
Sum of Values
70
Finally, we need to divide by 8.
Mean Absolute Deviation (MAD)
70/8=8.75
A MAD of 8.75 indicates that the data, on average, are 8.75 units away from the mean of 54.
