How to Minimize Rounding Error in Calculating the Percentage Mean Deviation

Here's a reminder brought to you by Sig Fig.

Whenever possible, carry out multi-step calculations completely in your calculator, and round only the final result. The reason for this is that if you have several steps and you round every step of the way, each rounding can generate a little bit of error. This builds on itself, or propagates as we say, and can have the result of magnifying error. Round only once to minimize rounding error.

When calculating average deviations, rounding error can propagate dramatically if you don't carry an extra digit in intermediate calculations. Here's a way to minimize rounding error in calculating percentage mean deviation. Carry out the steps below in your calculator without rounding until the final step.

1. Calculate the mean and store it in your calculator. Let's call this value M.

2. Find the difference between the number of measurements less than the mean and the number greater than the mean. Let's call this difference n. For example if 2 measurements are less than M and 3 measurements are greater than M, n = 2 - 3 = -1.

3. Multiply M by n.

4. Add to the product nM all the measurements that are greater than M and subtract all the measurements that are less than M.

5. Divide the result by the number of measurements. This gives the average mean deviation.

6. Divide the result of part d by M. This gives the percentage mean deviation. At this point, round it to the proper number of significant figures.

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