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In the data set below, what is the mean absolute deviation? $\newline$ $7, 7, 5, 7, 3$ $\newline$ 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

Full solution

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

\newline

7, 7, 5, 7, 3

\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 $7, 7, 5, 7, 3$ . Add all the numbers: $7 + 7 + 5 + 7 + 3 = 29$ . Divide by the number of data points: $29 / 5 = 5.8$ . Mean = $5.8$
Find Deviations: Find the absolute deviations from the mean for each data point. $\newline$ For $7$ : $|7 - 5.8| = 1.2$ $\newline$ For $7$ : $|7 - 5.8| = 1.2$ $\newline$ For $5$ : $|5 - 5.8| = 0.8$ $\newline$ For $7$ : $|7 - 5.8| = 1.2$ $\newline$ For $3$ : $|3 - 5.8| = 2.8$ $\newline$ Absolute deviations: $|7 - 5.8| = 1.2$ $0$ , $|7 - 5.8| = 1.2$ $0$ , $|7 - 5.8| = 1.2$ $2$ , $|7 - 5.8| = 1.2$ $0$ , $|7 - 5.8| = 1.2$ $4$
Calculate Mean Deviations: Calculate the mean of the absolute deviations. Add all the absolute deviations: $1.2 + 1.2 + 0.8 + 1.2 + 2.8 = 7.2$ . Divide by the number of data points: $7.2 / 5 = 1.44$ . Mean absolute deviation = $1.44$
Round Mean Deviation: Round the mean absolute deviation to the nearest tenth. $\newline$ $1.44$ rounded to the nearest tenth is $1.4$ . $\newline$ Final mean absolute deviation = $1.4$

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