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What is the MAD (Mean Absolute Deviation) of the following data set: 13, 14, 14, 16, 16, 16, 16, 18, 18, 19?
The mean of the data set is 16.
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Answer
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Step 1:I'll solve this step-by-step using the Mean Absolute Deviation (MAD) method:
Step 2:: Calculate the Mean
\bar{x} = \frac{13 + 14 + 14 + 16 + 16 + 16 + 16 + 18 + 18 + 19}{10} = 16
The mean is already given as 16. Let's verify:
Step 3:: Calculate the Absolute Deviations
- $$|19 - 16| = 3
Subtract the mean (16) from each data point and take the absolute value:
Step 4:: Calculate the Mean of Absolute Deviations
MAD = \frac{3 + 2 + 2 + 0 + 0 + 0 + 0 + 2 + 2 + 3}{10} = \frac{14}{10} = 1.4
Sum the absolute deviations and divide by the number of data points:
Final Answer
The Mean Absolute Deviation (MAD) is 1.4.
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