In the data set below, what is the mean absolute deviation?33586292486216If 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?33586292486216If the answer is a decimal, round it to the nearest tenth.mean absolute deviation (MAD): Submit
Solution
To calculate the Mean Absolute Deviation (MAD), follow these steps:
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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 3, 3, 5, 8, 6, 2, 9, 2, 4, 8, 6, 2, 1, 6. The sum of these numbers is 65 and there are 14 numbers, so the mean is 65 / 14 = 4.6 (rounded to the nearest tenth).
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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: |3 - 4.6| = 1.6, |3 - 4.6| = 1.6, |5 - 4.6| = 0.4, |8 - 4.6| = 3.4, |6 - 4.6| = 1.4, |2 - 4.6| = 2.6, |9 - 4.6| = 4.4, |2 - 4.6| = 2.6, |4 - 4.6| = 0.6, |8 - 4.6| = 3.4, |6 - 4.6| = 1.4, |2 - 4.6| = 2.6, |1 - 4.6| = 3.6, |6 - 4.6| = 1.4.
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Now, calculate the mean of these deviations. Add all the deviations together and then divide by the count. The sum of the deviations is 30.4 and there are 14 numbers, so the mean absolute deviation is 30.4 / 14 = 2.2 (rounded to the nearest tenth).
So, the Mean Absolute Deviation (MAD) of this data set is 2.2.
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