What is the mean absolute deviation of the following data set?
{5,12, 14, 18}
To find the mean absolute deviation of a data set, follow these steps:
1. Find the mean of the data set.
mean = (5 + 12 + 14 + 18) / 4 = 49 / 4 = 12.25
2. Subtract the mean from each data point and find the absolute value.
|5 - 12.25| = 7.25
|12 - 12.25| = 0.25
|14 - 12.25| = 1.75
|18 - 12.25| = 5.75
3. Calculate the mean of the absolute values obtained in the previous step.
mean absolute deviation = (7.25 + 0.25 + 1.75 + 5.75) / 4
mean absolute deviation = 15 / 4
mean absolute deviation = 3.75
Therefore, the mean absolute deviation of the given data set {5,12, 14, 18} is 3.75.