What is the mean absolute deviation of the following set:
{16, 2, 5, 20, 14, 6, 21}
46
7
12
6.57
To find the mean absolute deviation of a set of numbers, we must first find the mean of the set. The mean is calculated by adding up all the numbers and dividing by the total number of numbers in the set.
16 + 2 + 5 + 20 + 14 + 6 + 21 = 84
There are 7 numbers in the set, so the mean is 84/7 = 12.
Next, we must find the absolute difference between each number and the mean, and then find the mean of those absolute differences.
|16 - 12| = 4
|2 - 12| = 10
|5 - 12| = 7
|20 - 12| = 8
|14 - 12| = 2
|6 - 12| = 6
|21 - 12| = 9
Adding up all these absolute differences, we get 4 + 10 + 7 + 8 + 2 + 6 + 9 = 46.
To find the mean absolute deviation, we divide this sum by the total number of numbers in the set, which is 7.
Mean absolute deviation = 46/7 ≈ 6.57
Therefore, the mean absolute deviation of the set {16, 2, 5, 20, 14, 6, 21} is approximately 6.57.