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For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?
For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?
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Practice Questions
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Q1
For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?
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Mean = 7.5; MAD = (|5-7.5| + |7-7.5| + |8-7.5| + |9-7.5| + |10-7.5|) / 5 = 1.
Questions & Step-by-step Solutions
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Q
Q: For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?
Solution:
Mean = 7.5; MAD = (|5-7.5| + |7-7.5| + |8-7.5| + |9-7.5| + |10-7.5|) / 5 = 1.
Steps: 6
Show Steps
Step 1: Find the mean (average) of the data set. Add all the numbers together: 5 + 7 + 8 + 9 + 10 = 39.
Step 2: Divide the total by the number of values in the data set. There are 5 numbers, so 39 / 5 = 7.5. This is the mean.
Step 3: Calculate the absolute deviation for each number. This means finding the distance from each number to the mean (7.5).
Step 4: For each number, subtract the mean and take the absolute value: |5 - 7.5| = 2.5, |7 - 7.5| = 0.5, |8 - 7.5| = 0.5, |9 - 7.5| = 1.5, |10 - 7.5| = 2.5.
Step 5: Add all the absolute deviations together: 2.5 + 0.5 + 0.5 + 1.5 + 2.5 = 7.5.
Step 6: Divide the total absolute deviation by the number of values in the data set: 7.5 / 5 = 1. This is the mean absolute deviation (MAD).
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