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For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?

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Question: For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?

Options:

  1. 1
  2. 2
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  4. 4

Correct Answer: 2

Solution: 

Mean = 7.5; MAD = (|5-7.5| + |7-7.5| + |8-7.5| + |9-7.5| + |10-7.5|) / 5 = 1.

For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?

Practice Questions

Q1
For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?
  1. 1
  2. 2
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Questions & Step-by-Step Solutions

For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?
Correct Answer: 1
  • 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).
  • Mean – The average of a set of numbers, calculated by summing the numbers and dividing by the count.
  • Absolute Deviation – The distance between each data point and the mean, expressed as a positive value.
  • Mean Absolute Deviation (MAD) – The average of the absolute deviations from the mean, providing a measure of variability in the data set.
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