How many digits show when reporting mean ± SD?

Report the mean with one more decimal place than the first significant digit of the standard deviation.

Think of the standard deviation as how exact your spread number is, and you want the mean to show one extra digit of detail compared to that spread. If the standard deviation’s first important digit is in the tenths place, give the mean one more digit and report it to the hundredths place. If the standard deviation’s first important digit is in the ones place, give the mean one more digit and report it to the tenths place. This makes the mean and standard deviation look consistent and prevents giving a false sense of accuracy.

Students often write the mean with too many decimals compared with the standard deviation, which makes the numbers look more precise than they really are, so round the mean to match the rule above. Another common mistake is reporting the standard deviation with insignificant leading zeros and then matching the mean to an inappropriate place; remove those meaningless zeros and determine the first significant digit before deciding precision. A quick tip is to find the first nonzero digit in the standard deviation, count its decimal place, and then add one decimal place when rounding the mean.

For more examples and practice problems visit w w w dot gumball degree dot com to find videos and resources on reporting means and standard deviations.

Round Mean Precision to Match SD

1. Match mean precision to SD
2. Find SD’s first significant digit
3. If SD in tenths, use hundredths
4. If SD in ones, use tenths
5. Keep mean and SD consistent

Common Mean and SD Reporting Errors

1. Mean has too many decimals
2. Reporting SD with meaningless leading zeros
3. Matching mean to wrong decimal place

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