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What is the mean absolute deviation of the following set of data: 10, 8, 10, 6, 6, 2, 10, 4?

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Step 1:

First, calculate the mean (average) of the data set. To do this, add up all the numbers and divide by the count of numbers. \begin{align*} &= 8.25 \end{align*}

Step 2:

Next, for each data point, calculate the absolute deviation from the mean. This is the absolute value of the difference between the data point and the mean. \begin{align*} \text{deviation}(10) &= |10 - 8.25| = 1.75 \ \text{deviation}(8) &= |8 - 8.25| = 0.25 \ \text{deviation}(10) &= |10 - 8.25| = 1.75 \ \text{deviation}(6) &= |6 - 8.25| = 2.25 \ \text{deviation}(6) &= |6 - 8.25| = 2.25 \ \text{deviation}(2) &= |2 - 8.25| = 6.25 \ \text{deviation}(10) &= |10 - 8.25| = 1.75 \ \text{deviation}(4) &= |4 - 8.25| = 4.25 \end{align*}

Step 3:

Now, calculate the mean absolute deviation by finding the average of the absolute deviations calculated in step 2. \begin{align*} &= \boxed{2.5625} \end{align*}

Final Answer

The mean absolute deviation of the data set is approximately 2.5625.

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