Writing a descriptive statistics analysis means summarizing your data’s key features, typically the center, spread, and shape of each variable, then translating those numbers into clear sentences and tables. Whether you’re working on a research paper, a class assignment, or a workplace report, the process follows the same core steps. Below is a practical walkthrough, ending with a full written example you can adapt.
Know Your Variable Types First
Before you calculate anything, sort your variables into two camps: categorical and continuous. Categorical variables are things like gender, treatment group, or yes/no responses. Continuous variables are measurements on a numeric scale, like age, test scores, or blood pressure. The type of variable determines which statistics you report.
For categorical variables, you report frequencies (counts) and percentages. For continuous variables, you report a measure of center and a measure of spread. Getting this distinction right at the start prevents the most common rookie mistake: trying to calculate a mean for a variable like “department” or “diagnosis.”
Choose the Right Center and Spread
The three measures of center are the mean, median, and mode. The measures of spread include the range, interquartile range, variance, and standard deviation. You don’t report all of them. You pick the pair that fits your data’s distribution.
If your continuous variable is roughly symmetrical (a bell-shaped distribution), report the mean and standard deviation. The mean tells you the average value; the standard deviation tells you how tightly or loosely individual values cluster around that average. In a normal distribution, about 68% of values fall within one standard deviation of the mean, and about 95% fall within two.
If your data is skewed or contains outliers, switch to the median and interquartile range (IQR). The median is the middle value when all observations are lined up, and the IQR captures the spread of the middle 50% of your data. Income data is a classic example: a handful of extremely high earners can pull the mean far above what most people actually earn, making the median a much more honest summary. The rule is straightforward: always use the median when the distribution is skewed, and use either the mean or median when it’s symmetrical, because the two will be nearly identical.
Check Distribution Before Reporting
A surprisingly common mistake in published research is jumping straight to reporting the mean and standard deviation without first checking whether the data is normally distributed. Standard deviation only meaningfully describes spread in a roughly normal variable. When the distribution is skewed, standard deviation can mislead readers about how scattered the data really is.
Run a quick normality check. Most statistics software gives you skewness and kurtosis values, or you can look at a histogram. If the data is clearly lopsided, report the median and IQR instead.
Avoid the Standard Error Trap
One of the most frequently documented errors in biomedical literature is reporting the standard error instead of the standard deviation. The standard error is always smaller than the standard deviation, and substituting it makes your data look more precise than it actually is. Some researchers do this by accident; others do it deliberately to make results appear tighter.
The standard deviation describes how spread out individual data points are in your sample. The standard error describes the precision of the sample mean as an estimate of the population mean. When you’re writing a descriptive statistics section, you want the standard deviation. Save the standard error for inferential statistics.
Format Numbers Correctly
APA style, which most social and health sciences follow, has specific rules for decimal places. Report means and standard deviations to one decimal place when the original data comes from integer scales (like survey ratings from 1 to 5). For other continuous measurements, report to two decimal places. Percentages typically get one decimal place. The general principle is to round as much as possible while preserving useful precision. Readers absorb numbers with fewer decimal places more easily.
When writing statistics inline, use the standard abbreviations: M for mean, SD for standard deviation, Mdn for median, n for subsample size, and N for total sample size. These abbreviations are universally recognized in statistical writing and don’t need to be defined. Format them in italics. Present them with an equals sign: M = 34.2, SD = 5.7.
One formatting note: avoid writing results as mean ± SD (for example, 34.2 ± 5.7), because this notation looks identical to a confidence interval and creates confusion. Instead, write mean (SD), like 34.2 (5.7), or spell it out: M = 34.2, SD = 5.7.
Build a Summary Table
A well-designed table is the backbone of any descriptive statistics section. Use a standard format rather than inventing your own layout. Readers are accustomed to certain conventions and will scan your table faster if you follow them.
A typical descriptive statistics table has variables listed as rows and statistics as columns. For continuous variables, columns might include n, M, SD, Min, and Max. For categorical variables, columns include n and %. If your study has groups (say, a treatment group and a control group), create columns for each group so readers can compare at a glance.
Here’s what a simple table might look like for a hypothetical study of 120 college students:
Table 1
Demographic and Academic Characteristics of Participants (N = 120)
- Age: M = 21.3, SD = 2.4, Range = 18–35
- GPA: M = 3.14, SD = 0.52, Range = 1.80–4.00
- Weekly study hours: Mdn = 12.0, IQR = 8.0–18.5 (skewed distribution)
- Gender: Female, n = 72 (60.0%); Male, n = 41 (34.2%); Nonbinary, n = 7 (5.8%)
- Class standing: Freshman, n = 18 (15.0%); Sophomore, n = 30 (25.0%); Junior, n = 38 (31.7%); Senior, n = 34 (28.3%)
Notice that weekly study hours uses the median and IQR because the distribution was skewed, while age and GPA use the mean and standard deviation because they were approximately normal. The categorical variables (gender, class standing) report counts and percentages.
Write the Narrative
Your written analysis does two things: it highlights the most important patterns in the table, and it gives context that raw numbers alone can’t convey. You don’t need to restate every number from the table. Instead, focus on findings that matter for the rest of your paper.
Here’s a full written example based on the table above:
The sample consisted of 120 undergraduate students (Mage = 21.3, SD = 2.4), with ages ranging from 18 to 35. The majority of participants were female (60.0%), and most were juniors or seniors (60.0% combined). Participants reported a mean GPA of 3.14 (SD = 0.52). Weekly study hours were positively skewed, so the median is reported: students studied a median of 12.0 hours per week (IQR = 8.0–18.5), with some students reporting as many as 45 hours. Table 1 presents the full demographic and academic profile of the sample.
This paragraph works because it opens with sample size and a key demographic, summarizes the categorical breakdown without listing every category, flags the skewed variable and explains why the median was used, and points readers to the table for the complete picture.
Putting It All Together: Step by Step
If you want a repeatable process, here are the steps in order:
- Sort variables into categorical and continuous.
- Check distribution of each continuous variable (histogram, skewness values).
- Pick your statistics: mean and SD for normal data, median and IQR for skewed data, frequencies and percentages for categorical data.
- Build the table with clearly labeled rows and columns, using standard formatting.
- Write the narrative by highlighting key patterns, noting sample size, and explaining any non-obvious choices (like switching to the median).
- Double-check that you reported the SD (not the standard error), used the correct number of decimal places, and matched the right center-spread pair to each variable’s distribution.
The entire descriptive statistics section of a typical paper runs one to three paragraphs plus a table. Keep it tight. Your job is to give the reader a mental picture of who was in the study and what the data looks like before you move into testing hypotheses or building models.