Question

Math

Posted 5 months ago

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Find the mean absolute deviation (MAD) of the data in the dot plot below.
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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

Calculate the mean of the data set {22, 23, 23, 25, 27}

step 2

The mean (average) is the sum of the data points divided by the number of data points: $\frac{22 + 23 + 23 + 25 + 27}{5} = \frac{120}{5} = 24$

step 3

Calculate the absolute deviations from the mean for each data point: $|22 - 24|, |23 - 24|, |23 - 24|, |25 - 24|, |27 - 24|$

step 4

The absolute deviations are: $2, 1, 1, 1, 3$

step 5

Calculate the mean absolute deviation (MAD) by finding the mean of these absolute deviations: $\frac{2 + 1 + 1 + 1 + 3}{5} = \frac{8}{5} = 1.6$

Answer

The mean absolute deviation (MAD) of the data is 1.6.

Key Concept

Mean Absolute Deviation (MAD)

Explanation

MAD is the average of the absolute deviations from the mean of a data set. It measures the spread of the data points.

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