The students are comfortable with how to find the mean of a set of data. Add all the data values together and divide by the number of values. The other name for the mean is the average. I am seeing problems with them not double checking their work, therefore they make careless errors. I always tell them to add the set of numbers twice. If you get the same answer two times in a row, the chances are you added correctly. They are allowed to use a calculator.
What is the MAD (mean absolute deviation)? First, you have to find the mean of the data set. Then, you notice that some numbers in the data set can be the same as the mean, but some numbers are not the same as the mean. This is what the MAD examines. To find the MAD, you have to first find out how far each data value is from the mean. So you subtract the mean from the data value (or the difference or how much it DEVIATES from the mean). SOMETIMES, this is a negative number, but we find the absolute value of each difference (a numbers' absolute value is always positive; it tells how far from zero the number is). After finding the positive value of each difference, you add these together and divide by how many numbers you just added (it's finding the average again). This is the average of how far those numbers NOT exactly the mean are different from the mean (or the mean absolute deviation). In the picture below, you can see not only how we found the MAD, but the it identifies the five number summary as well. The data set used: 10, 15, 20, 22,22, 26, 30, 31, 35, 40.
What is the MAD (mean absolute deviation)? First, you have to find the mean of the data set. Then, you notice that some numbers in the data set can be the same as the mean, but some numbers are not the same as the mean. This is what the MAD examines. To find the MAD, you have to first find out how far each data value is from the mean. So you subtract the mean from the data value (or the difference or how much it DEVIATES from the mean). SOMETIMES, this is a negative number, but we find the absolute value of each difference (a numbers' absolute value is always positive; it tells how far from zero the number is). After finding the positive value of each difference, you add these together and divide by how many numbers you just added (it's finding the average again). This is the average of how far those numbers NOT exactly the mean are different from the mean (or the mean absolute deviation). In the picture below, you can see not only how we found the MAD, but the it identifies the five number summary as well. The data set used: 10, 15, 20, 22,22, 26, 30, 31, 35, 40.