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Sebastian observed the number of minutes his dormmates spent on social media sites while they were at the library. He reported his data in the following list.

13,0,14,36,18,9
Find the mean absolute deviation (MAD) of the data set.
minutes

Sebastian observed the number of minutes his dormmates spent on social media sites while they were at the library. He reported his data in the following list. $\newline$ $13,0,14,36,18,9$ $\newline$ Find the mean absolute deviation (MAD) of the data set. $\newline$ minutes

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Mean, median, mode, and range: find the missing number

Full solution

Q. Sebastian observed the number of minutes his dormmates spent on social media sites while they were at the library. He reported his data in the following list.

\newline

13,0,14,36,18,9

\newline

Find the mean absolute deviation (MAD) of the data set.

\newline

minutes

Calculate Mean: First, we need to calculate the mean (average) of the data set. $\newline$ Data set: $13, 0, 14, 36, 18, 9$ $\newline$ Number of terms: $6$ $\newline$ Mean $(\mu) = \frac{\text{sum of the terms}}{\text{number of the terms}}$ $\newline$ Mean $(\mu) = \frac{(13 + 0 + 14 + 36 + 18 + 9)}{6}$ $\newline$ Mean $(\mu) = \frac{90}{6}$ $\newline$ Mean $(\mu) = 15$
Calculate Absolute Deviations: Next, we calculate the absolute deviations from the mean for each data point. $\newline$ Absolute deviation for each term = $|\text{term} - \text{mean}|$ $\newline$ Absolute deviations: $|13 - 15|, |0 - 15|, |14 - 15|, |36 - 15|, |18 - 15|, |9 - 15|$ $\newline$ Absolute deviations: $2, 15, 1, 21, 3, 6$
Find Sum of Deviations: Now, we find the sum of the absolute deviations. $\newline$ Sum of absolute deviations = $2 + 15 + 1 + 21 + 3 + 6$ $\newline$ Sum of absolute deviations = $48$
Calculate Mean Absolute Deviation: Finally, we calculate the mean absolute deviation (MAD) by dividing the sum of absolute deviations by the number of terms. $\newline$ $\text{MAD} = \frac{\text{sum of absolute deviations}}{\text{number of terms}}$ $\newline$ $\text{MAD} = \frac{48}{6}$ $\newline$ $\text{MAD} = 8$

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