Download The mean absolute deviation (or MAD)

Mean Absolute
Deviation
Let’s get MAD!
Get it? M.A.D.?
What is the mean absolute deviation (MAD)?
• The mean absolute deviation (or MAD) is the
average distance between each data value and the
mean.
• It other words, how far away, on average is each data
value from the average?
Why is it useful?
• If the MAD is a small number, then we can conclude that
the mean is a good representation of the data because most
of the data values will be close to the mean.
• If the MAD is a large number, then we can conclude the
mean is a poor representation of the data because most of
the data values will be far from the mean.
How to find the MAD
1) Find the mean of the entire data set
2) Subtract the mean from each data value and find its
absolute value
3) Find the average of the absolute values
Examples, please!
• Just a note: I’ll be using a small data sample to make calculations
easier
• Consider the following heights (inches) of a 7th grade class:
49, 51, 53, 54, 56, 58, 59, 59, 60
Start by finding the mean:
𝟒𝟗𝟗 ÷ 𝟗 = 𝟓𝟓. 𝟒
• This now gives us a claim: “The average height in this 7th grade class
is 55.4 inches.”
Mean: 55.4
• Then, subtract the mean from each data value and find its absolute value:
49 − 55.4 = 6.4
51 − 55.4 = 4.4
53 − 55.4 = 2.4
54 − 55.4 = 1.4
56 − 55.4 = 0.6
58 − 55.4 = 2.6
59 − 55.4 = 3.6
59 − 55.4 = 3.6
60 − 55.4 = 4.6
Find the average of the absolute values
• Now, take all the numbers you got from taking the
absolute values and find their average.
6.4 + 4.4 + 2.4 + 1.4 + 0.6 + 2.6 + 3.6 + 3.6 + 4.6
9
We get an average of 3.3
What does 3.3 mean?
• It means that the average distance of each data value is
about 3.3 units away from the mean, 55.4.
• So if all our data values are, on average, 3.3 units away from
55.4 inches, is the mean a good representation of our data
set? Does the data support our claim?
Things to remember:
• For the sake of practice, we’re dealing with small data sets.
Unless all the data is close to the same number, smaller data
sets are usually more difficult to summarize in one number
than larger data sets.
• The other measures of center and measures of variation
give us a bigger picture and put other numbers in context.
Statisticians use a variety of ways to quantify and represent
data.
Comparing MADs
• We can also use the MAD to compare populations:
• Suppose we’re looking at the heights of 7th grade girls and 7th grade
boys:
The MAD of the girls is 1.75. The MAD of the boys is 4. What can
we conclude about the data of the girls vs the boys?
The data of the girls is closer together than the boys. Their heights
are more uniform, and the boys are more varied, on average.