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In the data set below, what is the mean absolute deviation? $\newline$ $5, 2, 1, 1, 4, 5, 3$ $\newline$ 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, 2, 1, 1, 4, 5, 3

\newline

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

\newline

mean absolute deviation (MAD):

\_\_

Calculate Mean: Calculate the mean (average) of the data set. $\newline$ Add all the numbers: $5 + 2 + 1 + 1 + 4 + 5 + 3 = 21$ $\newline$ Divide by the number of data points: $21 / 7 = 3$ $\newline$ Mean: $3$
Find Absolute Deviations: Find the absolute deviations from the mean for each data point. $\newline$ $|5 - 3| = 2$ , $|2 - 3| = 1$ , $|1 - 3| = 2$ , $|1 - 3| = 2$ , $|4 - 3| = 1$ , $|5 - 3| = 2$ , $|3 - 3| = 0$ $\newline$ Absolute deviations: $2$ , $1$ , $2$ , $2$ , $1$ , $2$ , $|2 - 3| = 1$ $3$
Calculate Mean of Deviations: Calculate the mean of these absolute deviations. $\newline$ Add the absolute deviations: $2 + 1 + 2 + 2 + 1 + 2 + 0 = 10$ $\newline$ Divide by the number of data points: $\frac{10}{7} \approx 1.4$ $\newline$ Mean absolute deviation: $1.4$

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