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In the data set below, what is the mean absolute deviation? $\newline$ $2, 5, 2, 1, 7, 4$ $\newline$ 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

2, 5, 2, 1, 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 $2, 5, 2, 1, 7, 4$ . $\newline$ Sum of the data points: $2 + 5 + 2 + 1 + 7 + 4 = 21$ . $\newline$ Number of data points: $6$ . $\newline$ Mean = $\frac{21}{6} = 3.5$ .
Calculate Absolute Deviations: Calculate the absolute deviations from the mean for each data point. $\newline$ Absolute deviation for $2$ = $|2 - 3.5| = 1.5$ . $\newline$ Absolute deviation for $5$ = $|5 - 3.5| = 1.5$ . $\newline$ Absolute deviation for $2$ = $|2 - 3.5| = 1.5$ . $\newline$ Absolute deviation for $1$ = $|1 - 3.5| = 2.5$ . $\newline$ Absolute deviation for $7$ = $|7 - 3.5| = 3.5$ . $\newline$ Absolute deviation for $|2 - 3.5| = 1.5$ $0$ = $|2 - 3.5| = 1.5$ $1$ .
Calculate Mean of Deviations: Calculate the mean of the absolute deviations. $\newline$ Sum of absolute deviations: $1.5 + 1.5 + 1.5 + 2.5 + 3.5 + 0.5 = 11$ . $\newline$ Number of data points: $6$ . $\newline$ Mean absolute deviation = $\frac{11}{6} = 1.8333$ .
Round Mean Absolute Deviation: Round the mean absolute deviation to the nearest tenth. $\newline$ $1.8333$ rounded to the nearest tenth is $1.8$ .

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