What is the mean absolute deviation of the following set:
{23, 15, 15, 7}
To find the mean absolute deviation, we first need to find the mean of the set.
To find the mean, we add up all the numbers in the set and then divide by the total number of numbers.
23 + 15 + 15 + 7 = 60
There are 4 numbers in the set, so we divide 60 by 4 to find the mean.
Mean = 60/4 = 15.
The mean of the set is 15.
Next, we find the absolute deviation for each number in the set by subtracting the mean from each number and taking the absolute value.
|23 - 15| = 8
|15 - 15| = 0
|15 - 15| = 0
|7 - 15| = 8
The absolute deviations are 8, 0, 0, and 8.
To find the mean absolute deviation, we find the average of these absolute deviations.
Mean absolute deviation = (8 + 0 + 0 + 8)/4 = 16/4 = 4.
Therefore, the mean absolute deviation of the set {23, 15, 15, 7} is 4.