The following table shows the number of classes taught by each teacher in the math
department at a high school. Find the mean absolute deviation (MAD) of the data set rounded to the nearest
hundredth if necessary.
To find the mean absolute deviation, we’ll follow three steps. First, we find the mean of the data set. Second, we’ll find the distance of each data point from the mean. And then, we’ll average the values we find in step two.
For step one, to find the mean, we’ll first need to know the total number of classes
in the math department. That means we’ll add two plus four plus two plus five. There’re 13 total classes. To find the mean, we’ll take the 13 total classes, divide it by four, the number of
teachers, 13 divided by four. And we could write that as a decimal. The average number of classes for a teacher in the math department is 3.25. And that completes step one.
For step two, we need to find out how far each data point the number of classes each
teacher taught is from the mean. How would we find out how far two is from 3.25? We would subtract. 3.25 minus two equals 1.25. The same thing goes for four. Four minus 3.25 is 0.75. Our next point is two again. 3.25 minus two equals 1.25. And for our last point, five minus 3.25 equals 1.75. These values complete step two.
And for step three, we’ll need to find the average of these values. That means we’ll need to add them together, 1.25 plus 0.75 plus 1.25 plus 1.75. When we add them together, we get five. The mean or average of these points is equal to the total five divided by the number
of things we added together, which was four. When we divide five by four, we get one and one-fourth.
We know we want to round to the nearest hundredth. And that means we’re interested in a decimal value. One and one-fourth written as a decimal is 1.25. It’s already to the hundredths place. There’s nothing to round, which finishes step three.
And we can say that the mean of absolute deviation of this data set is 1.25, one and