Mathematics
Grade 8
15 min
Calculate mean absolute deviation
Calculate mean absolute deviation
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Introduction & Learning Objectives
Learning Objectives
Define mean absolute deviation and explain what it measures.
Accurately calculate the mean of a given data set.
Determine the absolute deviation of each data point from the mean.
Follow a multi-step process to calculate the mean absolute deviation for a data set.
Interpret the meaning of the mean absolute deviation in the context of a real-world problem.
Compare the variability of two different data sets using their mean absolute deviations.
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In this tutorial, you will learn how to calculate the Mean Absolute Deviation, or MAD. MAD is a measure of variability that tells us the avera...
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Key Concepts & Vocabulary
TermDefinitionExample
Mean (Average)The sum of all the values in a data set divided by the number of values in the set. It represents the 'center' of the data.For the data set {4, 6, 8}, the mean is (4 + 6 + 8) / 3 = 6.
Deviation from the MeanThe difference between a specific data point and the mean of the data set. It can be positive, negative, or zero.If the mean is 6, the deviation for the data point 4 is 4 - 6 = -2.
Absolute ValueThe distance of a number from zero on a number line. It is always a non-negative number. The symbol is two vertical lines: |x|.The absolute value of -5 is |-5| = 5. The absolute value of 5 is |5| = 5.
Absolute DeviationThe absolute value of the deviation. It measures the distance between a data point and the mean, and it is always positive or zero.I...
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Core Formulas
Formula for the Mean
\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}
Use this to find the mean (average) of your data set. Here, \bar{x} is the mean, \sum means 'sum of', x_i represents each value in the data set, and n is the total number of values.
Formula for Mean Absolute Deviation (MAD)
MAD = \frac{\sum_{i=1}^{n} |x_i - \bar{x}|}{n}
This is the complete formula for MAD. It tells you to: 1) find the mean (\bar{x}), 2) find the distance of each value from the mean (|x_i - \bar{x}|), 3) add up all those distances (\sum), and 4) divide by the number of values (n).
4 more steps in this tutorial
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Challenging
Consider the data set {10, 12, 14, 16, 18}. If the data point 100 is added to this set, what will be the most significant effect?
A.The mean will increase significantly, and the MAD will also increase significantly.
B.The mean will stay the same, but the MAD will increase.
C.The MAD will decrease because the range is larger.
D.The mean will increase, but the MAD will stay roughly the same.
Challenging
A data set of three numbers has a mean of 20 and a Mean Absolute Deviation of 8. Which of the following could be the data set?
A.{20, 20, 20}
B.{10, 20, 30}
C.{8, 20, 32}
D.{12, 20, 28}
Challenging
Data Set X is {5, 15, 25} and Data Set Y is {14, 15, 16}. Both sets have a mean of 15. Which statement accurately compares them?
A.They have the same MAD because they have the same mean.
B.Set X has a larger MAD, indicating greater variability than Set Y.
C.Set Y has a larger MAD, indicating greater variability than Set X.
D.The MAD cannot be calculated if the means are the same.
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