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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.\newline8,5,12,15 8,5,12,15 \newlineFind the mean absolute deviation (MAD) of the data set.\newlinealligators

Full solution

Q. The following data points represent the number of alligators in each body of water near Tom's house.\newline8,5,12,15 8,5,12,15 \newlineFind the mean absolute deviation (MAD) of the data set.\newlinealligators
  1. Calculate Mean: Calculate the mean of the data set.\newlineThe data set is: 8,5,12,158, 5, 12, 15\newlineThe number of data points is 44.\newlineMean (μ)=Sum of all data pointsNumber of data points(\mu) = \frac{\text{Sum of all data points}}{\text{Number of data points}}\newlineMean (μ)=8+5+12+154(\mu) = \frac{8 + 5 + 12 + 15}{4}\newlineMean (μ)=404(\mu) = \frac{40}{4}\newlineMean (μ)=10(\mu) = 10
  2. 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 88: 810=2=2|8 - 10| = |−2| = 2 For 55: 510=5=5|5 - 10| = |−5| = 5 For 1212: 1210=2=2|12 - 10| = |2| = 2 For 1515: 1510=5=5|15 - 10| = |5| = 5
  3. Calculate Mean of Absolute Deviations: Calculate the mean of the absolute deviations.\newlineSum of absolute deviations = 2+5+2+5=142 + 5 + 2 + 5 = 14\newlineNumber of data points = 44\newlineMean absolute deviation (MAD) = (Sum of absolute deviations)/(Number of data points)(\text{Sum of absolute deviations}) / (\text{Number of data points})\newlineMAD = 14/414 / 4\newlineMAD = 3.53.5

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