Find the mean absolute deviation of the data set.
{74, 81, 86, 92, 74, 85, 90, 89, 78, 80}
To find the mean absolute deviation of the data set, we first need to find the mean (average) of the data set.
Mean = (74 + 81 + 86 + 92 + 74 + 85 + 90 + 89 + 78 + 80) / 10
Mean = 849 / 10
Mean = 84.9
Next, we find the absolute deviations of each data point from the mean:
|74 - 84.9| = 10.9
|81 - 84.9| = 3.9
|86 - 84.9| = 1.1
|92 - 84.9| = 7.1
|74 - 84.9| = 10.9
|85 - 84.9| = 0.1
|90 - 84.9| = 5.1
|89 - 84.9| = 4.1
|78 - 84.9| = 6.9
|80 - 84.9| = 4.9
Now, we find the mean of these absolute deviations:
Mean Absolute Deviation = (10.9 + 3.9 + 1.1 + 7.1 + 10.9 + 0.1 + 5.1 + 4.1 + 6.9 + 4.9) / 10
Mean Absolute Deviation = 55.9 / 10
Mean Absolute Deviation = 5.59
Therefore, the mean absolute deviation of the data set {74, 81, 86, 92, 74, 85, 90, 89, 78, 80} is 5.59.