Descriptive statistics

The responses are in: 300 respondents, dozens of questions. Before testing hypotheses or building models, you need to understand what the data «looks like» overall: what the typical value is, how widely answers vary, and how they are distributed across options.

This is the job of descriptive statistics — summary measures that compress a sample into a few understandable numbers: mean, median, proportions, spread. Without it, it is hard to interpret both statistical significance and the figures in the report themselves.

Descriptive statistics does not draw conclusions about the population and does not test hypotheses — it only characterizes what you have already collected. Generalizing to a population requires confidence intervals, tests, and the margin of error. But the first step in any analysis is to describe the data.

What descriptive statistics is in simple terms

Descriptive statistics is the set of methods and measures that summarize and characterize sample data: central tendency (mean, median, mode), spread (variance, standard deviation, range), the shape of the distribution, as well as frequencies and proportions by category. The goal is to present compactly «how» the collected data is structured, without drawing conclusions about causes and without extrapolating to a wider population.

Put simply: from the data you compute the «typical» value, the «spread», and the proportions across groups — and based on this picture you decide what to do next (compare groups, build a regression, revise the questions).

Which measures it includes

• Central tendency. The arithmetic mean, median, and mode — «around what» the answers are concentrated. For ordinal and scale data people often look at both the mean and the median: with outliers the median is more robust. More on this in the separate article about scales and interpretation.
• Spread. Standard deviation, variance, range (min–max), interquartile range. They show how far the values «scatter» around the center. Without the spread, the same average score may mean «everyone answered 4» or «half answered 1, half answered 7».
• Frequencies and proportions. How many people chose each option (absolute frequencies) and what percentage (proportions). The basis for tables and charts of categorical and ordinal variables.
• Distribution. Histograms, proportions across intervals, and a check for normality when needed. It helps you understand whether the data is symmetric and whether there are outliers.

Survey reports most often present means by scale, the proportions of «agree / disagree», a breakdown by segments, and cross-tabulations. This is descriptive statistics in action.

A brief example. The question «Rate the quality of service from 1 to 5»: 200 responses. Descriptive statistics gives: mean 3.8, median 4, mode 4, standard deviation 0.9. Proportions: «1» — 2%, «2» — 5%, «3» — 20%, «4» — 48%, «5» — 25%. These figures show that the majority lean toward the positive ratings and the spread is moderate; if the mean were also 3.8 but with 50% «1» and 50% «5», the picture would be entirely different — and without the spread and proportions you would not see it.

When you need it

The first stage of any analysis. Before testing hypotheses, running a regression, or comparing groups, it is useful to look at the means, the spread, and the distribution. Outliers and odd distributions are best spotted right away.

Reports for the client. Management and colleagues usually need «numbers in one line»: the average satisfaction score, the share of those who recommend, a breakdown by region. All of this is descriptive statistics.

Data quality control. Proportions by gender and age, the number of missing values, completion time — these summaries help you tell whether there are collection glitches or skews in the sample.

Descriptive statistics does not answer questions like «does the mean in group A differ from group B in a statistically significant way» or «what is the population estimate at a given precision». That requires the methods of inferential statistics (tests, confidence intervals).

Describing by segments and subgroups

Often the overall summaries alone are not enough: you need to understand how the measures look in different groups — by gender, age, region, customer type. You compute the same means, proportions, and spread, but separately for each subgroup. This yields cross-tabulations and segment profiles. It is important to state the size of each subgroup: a mean over 15 respondents and over 150 carry different degrees of confidence. If a subgroup is very small, the descriptive figures for it are best accompanied by a caveat, or no firm conclusions should be drawn from it.

Common mistakes

Looking only at the mean. For ordinal and scale data, when there is skew or outliers, the median and mode are often more informative. Additionally, look at the spread: the same «average score of 3.5» may come from «all 3–4» as well as «half 1, half 6».

Confusing it with inferential statistics. Descriptive statistics characterizes only your sample. Statements like «the population mean equals 4.2» or «the difference between groups is significant» require confidence intervals and tests — that is already the next level.

Ignoring the sample size. A mean over 30 respondents and over 3,000 have different stability. In a report, always state the sample size and, where possible, the spread (for example, the standard deviation or a confidence interval for the mean).

Mixing scales. A mean over nominal categories (customer type, region) is meaningless. For categorical variables use only frequencies and proportions; for ordinal and interval ones use the mean, median, and spread, taking into account the type of scale.

Comparing groups without accounting for size. «In group A the mean is 4.2, in group B it is 3.9» is descriptively correct, but without stating N and without testing the significance of the difference it is merely a statement of fact. For the conclusion that «the groups differ» you need tests and confidence intervals; descriptive statistics leads up to the question but does not answer it.

How it looks in SurveyNinja

In the «Reports and responses» section, summaries for each question are shown by default: the number of responses, the proportions by option, and — for scales — the mean. This is the basic descriptive statistics. For cross-tabulations by segment or to compute the median or standard deviation, the data can be exported to CSV/XLSX and calculated in a spreadsheet or a statistical package. When exporting, it is convenient to use filters to describe only the subsample you need (for example, those who completed the survey or a particular region).

Practical recommendations

Always state N. Next to the mean and proportions, write the number of responses they are based on. For subgroups, give the subgroup size, otherwise the reader cannot judge the reliability of the figures.

Add a measure of spread. At least the standard deviation for means, or a confidence interval — that way both the «typical» value and its uncertainty are visible.

Explore before complex analysis. Histograms and summaries by variable help you spot outliers, missing values, and unexpected distributions before a regression or tests.

Do not limit yourself to a single measure of center. For symmetric data the mean and median are close; with skew or outliers the median is more robust. It makes sense to look at both and, when needed, explain in the report why you chose one or the other (for example, «the median is given due to the pronounced skew of the distribution»).

Connection with other types of analysis

Descriptive statistics is the foundation. On its basis people build correlation and regression analysis (first they look at the means and spread of the variables), test differences between groups (comparing means and proportions with the aid of tests), and interpret the results of quantitative surveys. Individual measures — mean, median, mode, standard deviation — are covered in their own glossary articles; here the key point is to establish that describing the data always comes first, and conclusions and generalizations come afterward.

Descriptive statistics is the first step of analysis: it compresses the data into understandable measures (mean, median, proportions, spread) and does not draw conclusions beyond the sample. Without it, it is hard to interpret both the report and the subsequent hypothesis tests; with it, the picture of the data becomes clear before any generalizations.