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The mean absolute deviation 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.
2.8
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.
Since there are 10 values in our set, to calculate the mean we have to divide the sum by 10. Mean: 115/10 = 11.5
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=11.5 and n=10. Let's use a table to find the sum of the absolute values of the differences.
| x_i | x-x_i | |x-x_i| |
|---|---|---|
| 9 | 11.5- 9=2.5 | |2.5|=2.5 |
| 9 | 11.5- 9=2.5 | |2.5|=2.5 |
| 14 | 11.5- 14=- 2.5 | |- 2.5|=2.5 |
| 7 | 11.5- 7=4.5 | |4.5| = 4.5 |
| 12 | 11.5- 12=- 0.5 | |- 0.5|=0.5 |
| 8 | 11.5- 8=3.5 | |3.5|=3.5 |
| 11 | 11.5- 11=0.5 | |0.5|=0.5 |
| 19 | 11.5- 19=- 7.5 | |- 7.5|=7.5 |
| 15 | 11.5- 15=- 3.5 | |- 3.5|=3.5 |
| 11 | 11.5- 11=0.5 | |0.5|=0.5 |
| Sum of Values | 28 | |
Finally, we need to divide by 10. Mean Absolute Deviation (MAD) 28/10=2.8