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In the data set below, what is the mean absolute deviation? $\newline$ $1, 9, 8, 7, 5, 6, 6$ $\newline$ 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

Full solution

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

\newline

1, 9, 8, 7, 5, 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 $1, 9, 8, 7, 5, 6, 6$ .
Sum of data points: $1 + 9 + 8 + 7 + 5 + 6 + 6 = 42$ .
Number of data points: $7$ .
Mean = rac{42}{7} = 6.
Calculate Deviations: Calculate the absolute deviations from the mean for each data point. $\newline$ Absolute deviation for $1$ = $|1 - 6| = 5$ . $\newline$ Absolute deviation for $9$ = $|9 - 6| = 3$ . $\newline$ Absolute deviation for $8$ = $|8 - 6| = 2$ . $\newline$ Absolute deviation for $7$ = $|7 - 6| = 1$ . $\newline$ Absolute deviation for $5$ = $|5 - 6| = 1$ . $\newline$ Absolute deviation for each $|1 - 6| = 5$ $0$ = $|1 - 6| = 5$ $1$ (two times).
Calculate Mean Deviations: Calculate the mean of the absolute deviations. $\newline$ Sum of absolute deviations: $5 + 3 + 2 + 1 + 1 + 0 + 0 = 12$ . $\newline$ Mean absolute deviation = $\frac{12}{7} = 1.71428571429$ .
Round Mean Deviation: Round the mean absolute deviation to the nearest tenth. $\newline$ $1.71428571429$ rounded to the nearest tenth is $1.7$ .

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