How to Calculate Mean Deviation About Mean (for Ungrouped Data)

Let's learn how to calculate mean deviation about mean for raw or ungrouped data.

Steps

  1. Say we need to find the mean deviation about mean for the following data set:

    6, 7, 10, 12, 13, 4, 8, 12
  2. Find the mean of the given data.

    Mean = (Sum of observations) / (Number of observations)

    = (6 + 7 + 10 + 12 + 13 + 4 + 8 + 12) / 8 = 72/8 = 9
    Calculate Mean Deviation About Mean Step 1.jpg
  3. Subtract the mean from each of the observations and record your results. These results are the respective deviations of the observations from the mean.

    6 – 9, 7 – 9, 10 – 9, 12 – 9, 13 – 9, 4 – 9, 8 – 9, 12 – 9

    or, -3, –2, 1, 3, 4, –5, –1, 3
    Calculate Mean Deviation About Mean Step 2.jpg
  4. Find absolute values of the deviations obtained above.

    |-3|, |–2|, |1|, |3|, |4|, |–5|, |–1|, |3|

    or, 3, 2, 1, 3, 4, 5, 1, 3
    Calculate Mean Deviation About Mean Step 3.jpg
  5. Add the absolute values obtained above.

    3 + 2 + 1 + 3 + 4 + 5 + 1 + 3 = 22
    Calculate Mean Deviation About Mean Step 4.jpg
  6. Divide the result of last step by the number of observations. This will give you the final answer.

    Thus, the mean deviation about mean for the given ungrouped data is = 22/8 = 2.75
    Calculate Mean Deviation About Mean Step 5.jpg

Tips

  • Keep practicing and you will be able to do it quickly.

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