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QuestionStatistics
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:
First, we need to calculate the absolute deviation for each number in the set. The absolute deviation is the absolute difference between each number and the mean of the set.
Step 2:
\text{Mean} = \frac{6 + 2 + 8 + 4 + 8 + 6 + 8 + 8}{8} = \frac{54}{8} = 6.75
Calculate the mean of the set:
Step 3:
|8 - 6.75| = 1.25
Now, calculate the absolute deviation for each number:
Step 4:
\text{Mean Absolute Deviation} = \frac{0.75 + 4.75 + 1.25 + 2.75 + 1.25 + 0.75 + 1.25 + 1.25}{8} = \frac{15}{8} = 1.875
Next, find the mean absolute deviation by summing the absolute deviations and dividing by the number of data points:
Final Answer
The mean absolute deviation of the set is 1.875.
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