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