### Mean Absolute Deviation - DecisionMakingwithRealWorldData

```FAMILY SIZE

How many members were in your family when you

Gather the number of Unifix Cubes that matches

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.”

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.

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.