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QuestionStatistics
What is the mean absolute deviation of the following set: 3, 1, 5, 5, 2, 3, 2, 3, 4, 2?
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Answer
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Step 1:I'll solve this step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Calculate the Mean (Average)
\text{Mean} = \frac{3 + 1 + 5 + 5 + 2 + 3 + 2 + 3 + 4 + 2}{10} = \frac{30}{10} = 3
First, we need to find the arithmetic mean of the dataset.
Step 3:: Calculate the Absolute Deviations
- $$|2 - 3| = 1
Subtract the mean from each data point and take the absolute value:
Step 4:: Calculate Mean Absolute Deviation
\text{MAD} = \frac{0 + 2 + 2 + 2 + 1 + 0 + 1 + 0 + 1 + 1}{10} = \frac{10}{10} = 1
Sum the absolute deviations and divide by the number of data points:
Final Answer
The Mean Absolute Deviation is 1.
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