What is the mean absolute deviation of the following set:
{10, 4, 12, 8, 6}
To find the mean absolute deviation (MAD), we first need to find the mean of the set. The mean is the sum of all the numbers in the set divided by the number of elements in the set.
In this case, the sum of the numbers in the set is 10 + 4 + 12 + 8 + 6 = 40. Since there are 5 numbers in the set, the mean is 40/5 = 8.
Next, we need to find the absolute deviation for each number in the set. To do this, we subtract the mean from each number and take the absolute value of the difference.
For the numbers in the set:
|10 - 8| = 2
|4 - 8| = 4
|12 - 8| = 4
|8 - 8| = 0
|6 - 8| = 2
Next, we find the sum of the absolute deviations:
2 + 4 + 4 + 0 + 2 = 12
Finally, we find the MAD by dividing the sum of the absolute deviations by the number of elements in the set:
12/5 = 2.4
Therefore, the mean absolute deviation of the set {10, 4, 12, 8, 6} is 2.4.