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In the data set below, what is the mean absolute deviation?927413548524If the answer is a decimal, round it to the nearest tenth.mean absolute deviation (MAD): Submit

Question

In the data set below, what is the mean absolute deviation?927413548524If the answer is a decimal, round it to the nearest tenth.mean absolute deviation (MAD): Submit

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Solution

To calculate the Mean Absolute Deviation (MAD), follow these steps:

  1. First, calculate the mean (average) of the data set. Add all the numbers together and then divide by the count of numbers. In this case, the numbers are 9, 2, 7, 4, 1, 3, 5, 4, 8, 5, 2, 4. The sum of these numbers is 54 and there are 12 numbers, so the mean is 54/12 = 4.5.

  2. Next, subtract the mean from each number in the data set and take the absolute value of each result. This gives you the deviation of each number. Here are the deviations: |9-4.5| = 4.5 |2-4.5| = 2.5 |7-4.5| = 2.5 |4-4.5| = 0.5 |1-4.5| = 3.5 |3-4.5| = 1.5 |5-4.5| = 0.5 |4-4.5| = 0.5 |8-4.5| = 3.5 |5-4.5| = 0.5 |2-4.5| = 2.5 |4-4.5| = 0.5

  3. Now, calculate the mean of these deviations. Add them all together and divide by the count. The sum of the deviations is 23.5 and there are 12 numbers, so the mean absolute deviation is 23.5/12 = 1.96.

  4. If we round this to the nearest tenth, the Mean Absolute Deviation (MAD) is 2.0.

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