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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.\newline13,0,14,36,18,9 13,0,14,36,18,9 \newlineFind the mean absolute deviation (MAD) of the data set.\newlineminutes

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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.\newline13,0,14,36,18,9 13,0,14,36,18,9 \newlineFind the mean absolute deviation (MAD) of the data set.\newlineminutes
  1. Calculate Mean: First, we need to calculate the mean (average) of the data set.\newlineData set: 13,0,14,36,18,913, 0, 14, 36, 18, 9\newlineNumber of terms: 66\newlineMean (μ)=sum of the termsnumber of the terms(\mu) = \frac{\text{sum of the terms}}{\text{number of the terms}}\newlineMean (μ)=(13+0+14+36+18+9)6(\mu) = \frac{(13 + 0 + 14 + 36 + 18 + 9)}{6}\newlineMean (μ)=906(\mu) = \frac{90}{6}\newlineMean (μ)=15(\mu) = 15
  2. Calculate Absolute Deviations: Next, we calculate the absolute deviations from the mean for each data point.\newlineAbsolute deviation for each term = ∣term−mean∣|\text{term} - \text{mean}|\newlineAbsolute deviations: ∣13−15∣,∣0−15∣,∣14−15∣,∣36−15∣,∣18−15∣,∣9−15∣|13 - 15|, |0 - 15|, |14 - 15|, |36 - 15|, |18 - 15|, |9 - 15|\newlineAbsolute deviations: 2,15,1,21,3,62, 15, 1, 21, 3, 6
  3. Find Sum of Deviations: Now, we find the sum of the absolute deviations.\newlineSum of absolute deviations = 2+15+1+21+3+62 + 15 + 1 + 21 + 3 + 6\newlineSum of absolute deviations = 4848
  4. Calculate Mean Absolute Deviation: Finally, we calculate the mean absolute deviation (MAD) by dividing the sum of absolute deviations by the number of terms.\newlineMAD=sum of absolute deviationsnumber of terms\text{MAD} = \frac{\text{sum of absolute deviations}}{\text{number of terms}}\newlineMAD=486\text{MAD} = \frac{48}{6}\newlineMAD=8\text{MAD} = 8

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