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In the data set below, what is the mean absolute deviation? $\newline$ $5, 8, 5, 3, 7$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ mean absolute deviation (MAD): $\_\_$

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Calculate mean absolute deviation

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Q. In the data set below, what is the mean absolute deviation?

\newline

5, 8, 5, 3, 7

\newline

If the answer is a decimal, round it to the nearest tenth.

\newline

mean absolute deviation (MAD):

\_\_

Calculate Mean: Calculate the mean of the data set $5, 8, 5, 3, 7$ . Add all the numbers: $5 + 8 + 5 + 3 + 7 = 28$ . Divide by the number of data points: $28 / 5 = 5.6$ . Mean = $5.6$
Find Deviations: Find the absolute deviations from the mean for each data point. $\newline$ For $5$ : $|5 - 5.6| = 0.6$ . $\newline$ For $8$ : $|8 - 5.6| = 2.4$ . $\newline$ For $5$ : $|5 - 5.6| = 0.6$ . $\newline$ For $3$ : $|3 - 5.6| = 2.6$ . $\newline$ For $7$ : $|7 - 5.6| = 1.4$ . $\newline$ List of absolute deviations: $|5 - 5.6| = 0.6$ $0$
Calculate Mean Deviations: Calculate the mean of the absolute deviations. Add all the absolute deviations: $0.6 + 2.4 + 0.6 + 2.6 + 1.4 = 7.6$ . Divide by the number of data points: $\frac{7.6}{5} = 1.52$ . Mean absolute deviation = $1.52$
Round Mean Deviation: Round the mean absolute deviation to the nearest tenth. $\newline$ $1.52$ rounded to the nearest tenth is $1.5$ . $\newline$ Final mean absolute deviation = $1.5$

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