What is the mean absolute deviation of the following data set?
{80, 90, 95,85, 70}
To find the mean absolute deviation (MAD) of a data set, follow these steps:
1. Find the mean of the data set.
The mean of the data set {80, 90, 95, 85, 70} is (80 + 90 + 95 + 85 + 70) / 5 = 84.
2. Subtract the mean from each data point and calculate the absolute value of the difference.
The differences are:
80 - 84 = -4
90 - 84 = 6
95 - 84 = 11
85 - 84 = 1
70 - 84 = -14
The absolute values of these differences are:
|-4| = 4
|6| = 6
|11| = 11
|1| = 1
|-14| = 14
3. Find the mean of the absolute values calculated in step 2.
The mean of the absolute values is (4 + 6 + 11 + 1 + 14) / 5 = 7.2.
Therefore, the mean absolute deviation of the data set {80, 90, 95, 85, 70} is 7.2.