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. Start by calculating the mean of the given set of numbers.
Mean: 2.25 MAD: 0.67
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. We will start by calculating the mean of the given set of numbers.
Mean
First we will find the sum of the given values.
1.25 + 2.5 + 3 = 6.75
Since there are 3 values in our set, to calculate the mean we have to divide the sum by 3.
Mean: 6.75/3 = 2.25
Mean Absolute Deviation
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=2.25 and n=3. Let's use a table to find the sum of the absolute values of the differences.
x_n
x-x_n
|x-x_n|
1.25
2.25- 1.25=1
|1|=1
2.5
2.25- 2.5=- 0.25
|- 0.25|=0.25
3
2.25- 3=- 0.75
|- 0.75|=0.75
Sum of Values
2
Finally, we need to divide by 3.
Mean Absolute Deviation (MAD)
2/3=0.67
