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In the data set below, what is the mean absolute deviation? $\newline$ $6,3,1,6,6$ $\newline$ 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

6,3,1,6,6

\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. $\newline$ To find the mean, add all the numbers together and divide by the number of data points. $\newline$ Mean = $(6 + 3 + 1 + 6 + 6) / 5$ $\newline$ Mean = $22 / 5$ $\newline$ Mean = $4.4$
Find Absolute Deviation: Find the absolute deviation for each data point. $\newline$ The absolute deviation is the absolute value of the difference between each data point and the mean. $\newline$ Absolute deviation for $6$ = $|6 - 4.4| = 1.6$ $\newline$ Absolute deviation for $3$ = $|3 - 4.4| = 1.4$ $\newline$ Absolute deviation for $1$ = $|1 - 4.4| = 3.4$ $\newline$ Absolute deviation for the other two $6$ s will be the same as the first one, which is $1.6$ each.
Calculate Mean Absolute Deviation: Calculate the mean of the absolute deviations. $\newline$ Add all the absolute deviations together and divide by the number of data points. $\newline$ Mean absolute deviation (MAD) = $(1.6 + 1.4 + 3.4 + 1.6 + 1.6) / 5$ $\newline$ Mean absolute deviation (MAD) = $9.6 / 5$ $\newline$ Mean absolute deviation (MAD) = $1.92$
Round MAD: Round the mean absolute deviation to the nearest tenth. $\newline$ $1.92$ rounded to the nearest tenth is $1.9$ , since the digit in the hundredths place is $2$ , which is less than $5$ .

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