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In the data set below, what is the mean absolute deviation? $\newline$ $7, 7, 1, 1, 8$ $\newline$ 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

7, 7, 1, 1, 8

\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 $7, 7, 1, 1, 8$ . $\newline$ Sum of data points: $7 + 7 + 1 + 1 + 8 = 24$ . $\newline$ Number of data points: $5$ . $\newline$ Mean = $\frac{24}{5} = 4.8$ .
Calculate Absolute Deviations: Calculate the absolute deviations from the mean for each data point. $\newline$ Absolute deviation for $7$ = $|7 - 4.8| = 2.2$ . $\newline$ Absolute deviation for $7$ = $|7 - 4.8| = 2.2$ . $\newline$ Absolute deviation for $1$ = $|1 - 4.8| = 3.8$ . $\newline$ Absolute deviation for $1$ = $|1 - 4.8| = 3.8$ . $\newline$ Absolute deviation for $8$ = $|8 - 4.8| = 3.2$ .
Calculate Mean of Absolute Deviations: Calculate the mean of the absolute deviations. $\newline$ Sum of absolute deviations: $2.2 + 2.2 + 3.8 + 3.8 + 3.2 = 15.2$ . $\newline$ Mean absolute deviation = $\frac{15.2}{5} = 3.04$ .
Round Mean Absolute Deviation: Round the mean absolute deviation to the nearest tenth. $3.04$ rounded to the nearest tenth is $3.0$ .

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