Mean Absolute Deviation
(MAD)
Warm Up
2.
1.
3.
Mean Absolute Deviation Formative
1) How do you find the mean absolute deviation of a set
of data? 1) Find the mean of the data. 2) Find the
absolute value of the difference between each
data point and the mean. 3) Find the average of
those absolute values.
2) Find the mean absolute deviation (MAD) of the height
of the following basketball players. (Heights are in inches.):
75, 73, 76, 78, 79, 78, 79, 81, 80, 82, 81, 84, 82, 84, 80, 84
MAD = 2.5
3) What does the MAD tell us about the heights of the
basketball players?
The average distance of each player’s height from
the mean height of the players is 2.5 inches. The
players are around the same height.
Standard MCC7.SP.2.
Use data from a random sample to draw
inferences about a population with an unknown
characteristic of interest. Generate multiple
samples (or simulated samples) of the same size
to gauge the variation in estimates or predictions.
For example, estimate the mean word length in a
book by randomly sampling words from the book;
predict the winner of a school election based on
randomly sampled survey data. Gauge how far off
the estimate or prediction might be.
Essential Questions
How can I describe the variation
within a data set?
How do I use measures of center
and measures of variability to make
generalizations about data?
How is random sampling used to
determine an argument or make a
decision?
Vocabulary
Measures of Center-
mean, median, mode
Measures of Variability-
range, interquartile range,
mean absolute deviation- the average
distance of each data value from the mean.
Absolute Value-
distance from zero
Mean Absolute Deviation
The average distance between each data value from the mean.
1. Find the mean.
2. Find the distance between each data value and the
mean. That is, find the absolute value of the
difference between each data value and the mean.
3. Find the average of those differences.
Have you ever heard of the bell curve? That is what MAD is.
ROLLER COASTERS
The table on the right shows
the maximum speeds of eight
roller coasters at an
amusement park.
a) Find the mean absolute
deviation of the set of data.
b) Describe what the mean
absolute deviation represents.
Double Trouble
Test Scores
Below are test scores from two of my classes
1st Period: 90, 85, 80, 80, 100, 80, 85, 40, 90, 90
3rd Period: 100, 90, 70, 80, 80, 100, 80, 80, 70, 70
a)
Find the mean absolute deviation for each class.
1st MAD = 9.6
b)
3rd MAD = 8.8
Make a comparison statement about the mean absolute
deviations.
The mean absolute deviation for first period is higher which means
that the scores are more varied. Looking at the scores, is that true?
No. The outlier skewed the MAD.
Salary Comparison
b.
Closing
How do you find mean absolute
deviation and what is its purpose?
Find the mean.
2. Find the distance between each data value and the
mean. That is, find the absolute value of the
difference between each data value and the mean.
3. Find the average of those differences.
1.
The purpose is to see the spread of the data. The
higher the MAD, the more varied the data is.
Homework