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) 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