QQuestionMathematics
QuestionMathematics
What is the mean absolute deviation of the following set of numbers: 6, 2, 8, 4, 8, 6, 8, 8?
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Answer
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Step 1: Calculate the absolute deviation from the mean for each number.
First, find the mean (average) of the numbers: Now, calculate the absolute deviation of each number from the mean: \begin{align*} \text{deviation}(6) &= |6 - 6| = 0 \ \text{deviation}(2) &= |2 - 6| = 4 \ \text{deviation}(8) &= |8 - 6| = 2 \ \text{deviation}(4) &= |4 - 6| = 2 \ \text{deviation}(8) &= |8 - 6| = 2 \ \text{deviation}(6) &= |6 - 6| = 0 \ \text{deviation}(8) &= |8 - 6| = 2 \ \text{deviation}(8) &= |8 - 6| = 2 \end{align*}
Step 2: Find the mean absolute deviation.
Calculate the mean absolute deviation by finding the average of the absolute deviations: \begin{align*} &= \boxed{1.5} \end{align*}
Final Answer
The mean absolute deviation of the set of numbers is 1.5.
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