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In the data set below, what is the mean absolute deviation? $\newline$ $4, 3, 2, 4, 4$ $\newline$ 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

4, 3, 2, 4, 4

\newline

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

\newline

mean absolute deviation (MAD):

\_\_

Calculate Mean: Step $1$ : Calculate the mean of the data set $4, 3, 2, 4, 4$ . $\newline$ Sum of data points: $4 + 3 + 2 + 4 + 4 = 17$ . $\newline$ Number of data points: $5$ . $\newline$ Mean calculation: $17 / 5 = 3.4$ . $\newline$ Mean: $3.4$
Find Absolute Deviation: Step $2$ : Find the absolute deviation for each data point from the mean. Absolute deviation for $4$ = $|4 - 3.4| = 0.6$ . Absolute deviation for $3$ = $|3 - 3.4| = 0.4$ . Absolute deviation for $2$ = $|2 - 3.4| = 1.4$ . Absolute deviation for another $4$ = $|4 - 3.4| = 0.6$ . Absolute deviation for the last $4$ = $|4 - 3.4| = 0.6$ . Absolute deviations: $|4 - 3.4| = 0.6$ $0$
Calculate Mean of Absolute Deviations: Step $3$ : Calculate the mean of the absolute deviations. $\newline$ Sum of absolute deviations: $0.6 + 0.4 + 1.4 + 0.6 + 0.6 = 4.6$ . $\newline$ Number of data points: $5$ . $\newline$ Mean of absolute deviations: $4.6 / 5 = 0.92$ . $\newline$ Rounded to the nearest tenth: $0.9$

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