Standard deviation is reported in text using the abbreviation SD, placed in parentheses after the mean: for example, “The average age was 39.5 years (SD = 10.1).” That parenthetical format is the most widely accepted convention in scientific and academic writing, but the details of formatting, decimal places, and context matter quite a bit depending on where and how you’re presenting your data.
The Standard Text Format
In running text, report the mean first, then the standard deviation in parentheses. The most common format looks like this:
- In text: The mean score was 74.2 (SD = 12.8).
- In tables: Use a column header labeled M (SD) and list values as 74.2 (12.8).
APA style, which dominates psychology, education, and the social sciences, treats SD as a standard statistical abbreviation that never needs to be defined. You can use it on first appearance without spelling it out. The letters S and D should be italicized when used as the abbreviation in text (as with all statistical symbols like M, t, F, and p). When writing in full sentences rather than parenthetical notation, spell out “standard deviation” instead of using the symbol: “The standard deviations were large across all conditions.”
Avoid the plus-or-minus symbol (±) in text. Writing “39.5 ± 10.1” is common in some medical journals, but it creates confusion because readers can mistake it for a confidence interval. The clearer convention is mean (SD), which leaves no ambiguity about what the number represents.
How Many Decimal Places to Use
The number of decimal places in your standard deviation should match the precision of your original measurements. If you measured height to the nearest centimeter (no decimals), report the SD to one decimal place at most. If your raw data already has one decimal place, the SD can have one or two. The general principle: don’t report a statistic with more precision than the instrument that generated the data, because those extra digits are meaningless.
APA guidelines draw a distinction based on the type of data. For integer scales like survey responses (rated 1 through 5, for instance), report the mean and SD to one decimal place. For continuous measurements like reaction times or biological markers, two decimal places is standard. These aren’t rigid rules, but they reflect a practical truth: extra decimal places imply a level of measurement accuracy that often doesn’t exist.
Sample SD vs. Population SD
The symbol you use depends on whether you’re describing a sample or an entire population. In almost all research contexts, you’re working with a sample, and the correct symbol is s or SD. The Greek letter sigma (σ) is reserved for the population standard deviation, which you’d only use if you had data on every member of a group rather than a subset.
This distinction matters beyond notation. Most statistical software calculates the sample standard deviation by default, dividing by n − 1 rather than n. That correction accounts for the fact that a sample tends to slightly underestimate the true spread of the population. You generally don’t need to specify which formula you used, since sample SD is the assumed default, but it’s worth verifying your software’s behavior if you’re working with very small datasets where the difference becomes meaningful.
When Standard Deviation Is the Wrong Choice
Standard deviation only describes spread meaningfully when your data follow a roughly normal (bell-shaped) distribution. If your data are heavily skewed, with a long tail in one direction, the SD can be misleading because it’s pulled by extreme values in the same way the mean is.
For non-normal data, the better practice is to report the median and interquartile range (IQR) instead of the mean and SD. The IQR captures the range between the 25th and 75th percentiles, giving readers a sense of where the middle half of your data falls. Report it the same way: median (IQR). Hospital length-of-stay data is a classic example. Most patients stay a few days, but a small number stay weeks, creating a strong right skew. Reporting a mean and SD in that case would suggest a symmetry that doesn’t exist.
Standard Deviation vs. Standard Error
One of the most common reporting mistakes is using standard error of the mean (SEM) when standard deviation is appropriate, or vice versa. They answer different questions. SD tells you how spread out the individual data points are. SEM tells you how precisely you’ve estimated the average.
SEM is always smaller than SD (it’s calculated by dividing SD by the square root of the sample size), which is why some researchers use it in figures to make their error bars look tighter. This is misleading if the goal is to show variability in the data. Use SD when you want to describe how much individual values vary within your sample: the ages of participants, the range of blood pressure readings, the spread of test scores. Use SEM when you’re making an inference about a population mean, such as estimating where the true average likely falls.
Whichever you report, label it explicitly. A table that shows “42.3 (5.1)” without indicating whether 5.1 is SD or SEM is incomplete, because the reader has no way to interpret that number correctly.
Reporting SD in Tables and Figures
In tables, the cleanest approach is a column header that reads M (SD), with values listed as compact pairs: 74.2 (12.8). This saves space and is immediately recognizable. If your table includes multiple statistics, you can use separate columns for M and SD instead.
In figures, standard deviation typically appears as error bars extending above and below the mean. Always note in the figure caption what the error bars represent, since they could be SD, SEM, or confidence intervals. A caption like “Error bars represent ±1 SD” removes all ambiguity. Some fields default to showing ±1 SD (covering roughly 68% of the data in a normal distribution), while others show ±2 SD (covering about 95%). State which convention you’re using.
Interpreting SD for Your Reader
Raw numbers gain meaning when you help the reader understand what the SD actually implies. A small SD relative to the mean indicates that most values cluster tightly around the average. A large SD means the data are spread out, with many values falling far from the center. One useful technique: express the SD as a percentage of the mean to give readers an intuitive sense of scale. If the average starting salary is $50,000 with an SD of $13,500, you can note that one standard deviation spans roughly 27% of the mean, so most salaries fall between about $36,500 and $63,500.
For normally distributed data, the 68-95-99.7 rule provides a quick interpretive framework. About 68% of values fall within one SD of the mean, 95% within two, and 99.7% within three. Mentioning this in a results section can make your findings far more accessible, especially for audiences outside your field.