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The following data points represent the number of alligators in each body of water near Tom's house.

8,5,12,15
Find the mean absolute deviation (MAD) of the data set.
alligators

The following data points represent the number of alligators in each body of water near Tom's house. $\newline$ $8,5,12,15$ $\newline$ Find the mean absolute deviation (MAD) of the data set. $\newline$ alligators

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

Full solution

Q. The following data points represent the number of alligators in each body of water near Tom's house.

\newline

8,5,12,15

\newline

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

\newline

alligators

Calculate Mean: Calculate the mean of the data set. $\newline$ The data set is: $8, 5, 12, 15$ $\newline$ The number of data points is $4$ . $\newline$ Mean $(\mu) = \frac{\text{Sum of all data points}}{\text{Number of data points}}$ $\newline$ Mean $(\mu) = \frac{8 + 5 + 12 + 15}{4}$ $\newline$ Mean $(\mu) = \frac{40}{4}$ $\newline$ Mean $(\mu) = 10$
Calculate Absolute Deviations: Calculate the absolute deviations from the mean for each data point. Absolute deviation for each data point is the absolute value of the difference between that data point and the mean. For $8$ : $|8 - 10| = |−2| = 2$ For $5$ : $|5 - 10| = |−5| = 5$ For $12$ : $|12 - 10| = |2| = 2$ For $15$ : $|15 - 10| = |5| = 5$
Calculate Mean of Absolute Deviations: Calculate the mean of the absolute deviations. $\newline$ Sum of absolute deviations = $2 + 5 + 2 + 5 = 14$ $\newline$ Number of data points = $4$ $\newline$ Mean absolute deviation (MAD) = $(\text{Sum of absolute deviations}) / (\text{Number of data points})$ $\newline$ MAD = $14 / 4$ $\newline$ MAD = $3.5$

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