Question

In the data set below, what is the mean absolute deviation? 3 8 6 9 2 5

Answer 1

Answer:  Approximately 2.1667

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Explanation:

First we need to find the arithmetic mean.

Add up the values to get 3+8+6+9+2+5 = 33

Divide this over 6 because there are 6 values: 33/6 = 5.5

The mean is 5.5

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Subtract the mean from each data value. Apply absolute value to ensure the result is not negative.

• |3 - 5.5| = |-2.5| = 2.5
• |8 - 5.5| = |2.5| = 2.5
• |6 - 5.5| = |0.5| = 0.5
• |9 - 5.5| = |3.5| = 3.5
• |2 - 5.5| = |-3.5| = 3.5
• |5 - 5.5| = |-0.5| = 0.5

Each result represents how far that specific data value is from the mean. Absolute value is used to find distance on a number line.

Add up each of those results to get: 2.5+2.5+0.5+3.5+3.5+0.5 = 13

Then divide by 6 to find the average: 13/6 = 2.1667 which is approximate

The mean absolute deviation represents the average distance any given value is from the mean. The term "deviation" refers to how far each data value is from the mean, which is the center point we're after more or less.

The MAD (mean absolute deviation) effectively measures how spread out the data set is. The larger the MAD, the more spread out the data is likely to be. The range, standard deviation and variance are also measures of spread.