Calculate the mean absolute deviation for the data set: 1, 2, 3, 4, 5.

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Q: Calculate the mean absolute deviation for the data set: 1, 2, 3, 4, 5.

Solution: Mean = 3. Mean Absolute Deviation = (|1-3| + |2-3| + |3-3| + |4-3| + |5-3|)/5 = (2 + 1 + 0 + 1 + 2)/5 = 1.5.

Steps: 8

Step 1: Write down the data set: 1, 2, 3, 4, 5.
Step 2: Calculate the mean (average) of the data set. Add all the numbers together: 1 + 2 + 3 + 4 + 5 = 15.
Step 3: Divide the total by the number of values in the data set. There are 5 numbers, so: 15 / 5 = 3. This is the mean.
Step 4: Find the absolute deviation for each number. This means subtracting the mean from each number and taking the absolute value: |1-3|, |2-3|, |3-3|, |4-3|, |5-3|.
Step 5: Calculate each absolute deviation: |1-3| = 2, |2-3| = 1, |3-3| = 0, |4-3| = 1, |5-3| = 2.
Step 6: Add all the absolute deviations together: 2 + 1 + 0 + 1 + 2 = 6.
Step 7: Divide the total absolute deviation by the number of values in the data set: 6 / 5 = 1.2.
Step 8: The mean absolute deviation is 1.2.