Find the mean absolute deviation of the data in the pictograph shown.
First of all, let’s think about what kind of data this pictograph is showing us. We have a list of five different people. And based on the title, we can tell that the data being shown is the number of apples each person has. Since each image of an apple does represent one apple, our first step before we do anything else is tally how many apples each person has. Jennifer has four. Noah and Amelia each have three. Daniel has two. And James has five.
But from there, we wanna think about what the mean absolute deviation is. If you think of the data on a number line, somewhere, there’s a mean and then there’s data points all along that line. The absolute deviation measures the distance from each of those points back to the mean. And the mean of absolute deviation is the average distance all the data points are from the mean. Any time we’re solving a problem like this, the first step is to find the mean of the data.
We want to know the average number of apples each person has. To do that, we add all the values of apples each person has and divide it by the number of values there are. Here, we have five different people. So we have four plus three plus three plus two plus five divided by five, which is 3.4. This is telling us that the average number of apples per person is 3.4. We can use that information to calculate the absolute deviation of each person from the mean. To do that, we take the absolute value of the mean minus that person’s data point.
So for Jennifer, it will be the absolute value of 3.4 minus four, which is 0.6. For Amelia, her distance from the mean will be equal to the absolute value of 3.4 minus three, which is 0.4. The same thing is also true for Noah. For Daniel, we’ll have the absolute value of 3.4 minus two, which is 1.4, and for James, the absolute value of 3.4 minus five, which is 1.6.
And now, to find the average absolute deviation or the mean absolute deviation, we take all five of our deviation values and we find the mean of those: 0.6 plus 0.4 plus 0.4 plus 1.4 plus 1.6 all divided by five, which is 0.88. And so we can say that the mean absolute deviation of the data given in this pictograph is 0.88.