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In the data set below, what is the mean absolute deviation? $\newline$ $2, 5, 9, 9, 5$ $\newline$ 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

Full solution

Q. In the data set below, what is the mean absolute deviation?

\newline

2, 5, 9, 9, 5

\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 $2, 5, 9, 9, 5$ .
Sum of data points: $2 + 5 + 9 + 9 + 5 = 30$ .
Number of data points: $5$ .
Mean = rac{30}{5} = 6.
Calculate Absolute Deviations: Calculate the absolute deviations from the mean for each data point. $\newline$ Absolute deviation for $2$ = $|2 - 6|$ = $4$ . $\newline$ Absolute deviation for $5$ = $|5 - 6|$ = $1$ . $\newline$ Absolute deviation for $9$ = $|9 - 6|$ = $3$ . $\newline$ Absolute deviation for another $9$ = $|9 - 6|$ = $3$ . $\newline$ Absolute deviation for another $5$ = $|5 - 6|$ = $1$ .
Calculate Mean of Absolute Deviations: Calculate the mean of the absolute deviations. $\newline$ Sum of absolute deviations: $4 + 1 + 3 + 3 + 1 = 12$ . $\newline$ Mean absolute deviation = $\frac{12}{5} = 2.4$ .
Round Mean Absolute Deviation: Round the mean absolute deviation to the nearest tenth. $2.4$ rounded to the nearest tenth is $2.4$ .

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