We found that the mean of the given data set is 8. We are ready to calculate the MAD. We noted before that 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= 8 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|
6
8- 6=2
|2|=2
8.5
8- 8.5=- 0.5
|- 0.5|=0.5
6
8- 6=2
|2|=2
9
8- 9=-1
|-1|=1
10
8- 10=- 2
|- 2|=2
7
8- 7=1
|1|=1
8
8- 8=0
|0|=0
9.5
8- 9.5=- 1.5
|- 1.5|=1.5
Sum of Values
10
Finally, we need to divide by 8. This will give us the average.
Mean Absolute Deviation (MAD)
10/8=1.25
A MAD of 1.25 indicates that the data, on average, are 1.25 units away from the mean. In the context of the problem, this means that the shoe sizes, on average, are 1.25 units away from the mean 8.
