#### Mean Absolute Deviation - DecisionMakingwithRealWorldData

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Mean Absolute Deviation - DecisionMakingwithRealWorldData

FAMILY SIZE
How many members were in your family when you
were in the fourth grade?
Gather the number of Unifix Cubes that matches
your family size.
Assemble the cubes to form a “tower.”
Place your “tower” on the table in the front of the
room.
Place a Post-It Note on the dot/line plot on the
board.
DATA DISPLAYS
How are the two representations different?
Is there anything “lost in transition” from one display
to another?
What could we do with the towers to help link one
display with the other?
MEAN ABSOLUTE DEVIATION
Create
distributions of 9 family sizes with a
mean of 5.
Display
your data on a dot/line plot.
Use Post-It Notes as your “x’s” or “dots.”
HOW IS MAD HELPFUL?
By knowing the MAD, we can distinguish among
different distributions with the same means.
Think – four classes from Dr. Howard’s data
yesterday
A precursor to Standard Deviation – both measures
produce similar values
VARIATION/MEAN ABSOLUTE VARIATION
What kind of distribution would have the least
variation (with reference to the mean)?
With data, though, we expect variation.
There exists a need to quantify this variation from
the mean.
MAD – On average, how different are the data
values from the mean?
DEVIATIONS OF DATA VALUES FROM THE MEAN
Deviation = Value – Mean
Absolute Deviation =
MAD = Total of all absolute deviations
Number of Data Values (or n)
Value Mean
Using the Family Size dot/line plot, label the
distances of each data point from the mean.
COOL FACTS ABOUT THE MAD
Distances below and above the mean are equal
If the number of values below and above the mean
are the same, the median and mean are equal.
If the number of values below and above the mean
are not the same, the median and mean are not the
same.
If we sum the total distances, half of the values are
below the mean and half are above.
MAD = 1.8
MAD = 2
MAD = 2.7
MAD = 1.1
CCGPS Source:
Task: How Many People are in Your Family: A
Deeper Look at Mean Absolute Deviation
Sixth Grade
Unit 6
p. 18 - 21