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In the data set below, what is the mean absolute deviation? $\newline$ $5, 9, 1, 7, 7, 4$ $\newline$ 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, 9, 1, 7, 7, 4

\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 $5, 9, 1, 7, 7, 4$ . $\newline$ Sum of data points: $5 + 9 + 1 + 7 + 7 + 4 = 33$ . $\newline$ Number of data points: $6$ . $\newline$ Mean = $\frac{33}{6} = 5.5$ .
Calculate Absolute Deviations: Calculate the absolute deviations from the mean for each data point. $\newline$ Absolute deviation for $5$ = $|5 - 5.5| = 0.5$ . $\newline$ Absolute deviation for $9$ = $|9 - 5.5| = 3.5$ . $\newline$ Absolute deviation for $1$ = $|1 - 5.5| = 4.5$ . $\newline$ Absolute deviation for $7$ = $|7 - 5.5| = 1.5$ . $\newline$ Absolute deviation for $7$ = $|7 - 5.5| = 1.5$ . $\newline$ Absolute deviation for $|5 - 5.5| = 0.5$ $0$ = $|5 - 5.5| = 0.5$ $1$ .
Find Mean of Deviations: Find the mean of the absolute deviations. $\newline$ Sum of absolute deviations: $0.5 + 3.5 + 4.5 + 1.5 + 1.5 + 1.5 = 13.5$ . $\newline$ Mean absolute deviation = $\frac{13.5}{6} = 2.25$ .
Round Mean Absolute Deviation: Round the mean absolute deviation to the nearest tenth. $2.25$ rounded to the nearest tenth is $2.3$ .

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