Mathematics
Grade 9
15 min
Mean absolute deviation
Mean absolute deviation
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1
Introduction & Learning Objectives
Learning Objectives
Define mean absolute deviation (MAD) and its purpose.
Calculate the mean of a given data set.
Determine the absolute deviation of each data point from the mean.
Calculate the mean absolute deviation for a set of data.
Interpret the meaning of the MAD in the context of a real-world scenario.
Compare the variability of two different data sets using their MADs.
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In this tutorial, you will learn how to calculate and interpret the Mean Absolute Deviation (MAD). MAD is a measure of variability that tells us the average distance of each data point from the mean of the set. It's a powerful way to...
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Key Concepts & Vocabulary
TermDefinitionExample
Mean (μ)The average of a set of numbers. It is found by adding all the numbers in the data set and then dividing by the count of numbers in the set.For the data set {2, 4, 6, 8}, the mean is (2+4+6+8) / 4 = 20 / 4 = 5.
Data Point (xáµ¢)A single value or number within a larger data set.In the data set {10, 20, 30}, the number 20 is one data point.
Deviation from the MeanThe difference between a specific data point and the mean of the data set. This value can be positive, negative, or zero.If the mean of a data set is 15, and a data point is 12, its deviation is 12 - 15 = -3.
Absolute Value (|x|)The distance of a number from zero on a number line. It is always a non-negative value.The absolute value of -5, written as |-5|, is 5. The absolute value of 5, written as |5|, i...
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Core Formulas
Formula for the Mean (μ)
μ = (Σxᵢ) / n
Use this to find the average of the data set. Here, 'Σxᵢ' means 'the sum of all data points' and 'n' is the total number of data points.
Formula for Absolute Deviation
|xᵢ - μ|
Use this for each data point to find its distance from the mean. First, find the deviation (xᵢ - μ), then take its absolute value.
Formula for Mean Absolute Deviation (MAD)
MAD = (Σ|xᵢ - μ|) / n
This is the main formula. It means 'the sum of all the absolute deviations, divided by the number of data points'. This gives you the average distance from the mean.
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Challenging
If every number in a data set is increased by 10, what is the effect on the mean absolute deviation (MAD) of the set?
A.The MAD increases by 10.
B.The MAD increases by 10 times the original MAD.
C.The MAD decreases by 10.
D.The MAD remains unchanged.
Challenging
The data set {4, 6, 14, x} has a mean of 9. If the mean absolute deviation is 3, what is the value of x?
A.10
B.12
C.14
D.8
Challenging
A data set is given by the algebraic expressions {x, x+4, x+8}. What is the mean absolute deviation of this set in terms of x?
A.x+4
B.8/3
C.4
D.0
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