Mean Absolute Deviation

Determine the absolute
value of each number.

1.

Determine the mean of
each data set. Explain what
this number tells you.

2.

How are the two data
sets similar?

3.

Explain why the two data
sets have the same mean.

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What is the formula to solve for the mean?

Discuss with a partner to try and figure it out based on the previous example.

Determine the mean of the data set below using the
formula you and your partner created for mean to
test to see if it is valid.

a.) 5, 3, 93, 13, 418, 12, 6

b.) 6, 25, 2356, 8, 35, 346, 7

Formula for solving for the mean of a given data set:

1.

Based on the dot plots, which player do you think Coach
Harris should choose?

Lesson 1: March MADness

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When analyzing a data set, measures of center give you an idea of
where the data is centered, or what a typical data value might be.
There is another measure that can help you analyze data. Measures
of variation describe the spread of the data values. Just as there
are several measures of central tendency, there are also several
measures of variation.

The deviation of a data value indicates how far that data value is
from the mean. To calculate the deviation, subtract the mean from
the data value:

deviation = data value – mean

Lesson 1: March MADness

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2.

Describe the deviations. Record your results in the tables.

Lesson 1: March MADness

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3.

What is the meaning if a deviation is positive? Is negative? Is 0?

4.

What do you notice about the deviations for each player?

Lesson 1: March MADness

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The sum of all the deviations less than 0 is equal to the sum of the
deviations greater than 0. Because the mean is the balance point, the
sums of data points on either side of the balance point are equal to
each other.

In order to get an idea of the spread of the data values, you can take
the absolute value of each deviation and then determine the mean of
those absolute values. The absolute value of each deviation is called
the absolute deviation. The mean absolute deviation(MAD) is the
mean of the absolute deviations.

Lesson 1: March MADness

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6.

Record the absolute deviations for the points scored in the tables.

Lesson 1: March MADness

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3.

Complete each table. Then, compare the data sets and
interpret your results.

Lesson 1: March MADness

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2.

Create a dot plot for each data set.