- Descriptive statistics summarise a dataset through four measure types — frequency, central tendency, dispersion and position
- Contrary to a common myth, Python's standard library does include a median function: the statistics module, added in Python 3.4, provides mean, median, mode, variance and standard deviation
- Definitions here follow the NIST/SEMATECH e-Handbook and the Australian Bureau of Statistics.
A descriptive statistic is a summary value that quantitatively describes or summarises features from a collection of data, while descriptive statistics (as a field) is the process of using and analysing those summaries. Descriptive statistics involves summarising and organising data so it can be easily understood. Unlike inferential statistics, it seeks only to describe the data and does not attempt to make inferences from the sample to the whole population.
Here we typically describe the data in a sample. This means descriptive statistics, unlike inferential statistics, is not developed on the basis of probability theory. Such summaries may be either quantitative, meaning summary statistics, or visual, meaning simple graphs. For example, the shooting percentage in basketball is a descriptive statistic that summarises the performance of a player or a team: the number of shots made divided by the number of shots taken.
What Is Descriptive Statistics?
Descriptive statistics are summary measures that quantitatively describe and organise the features of a dataset. Unlike inferential statistics, they only describe the sample in hand and do not draw conclusions about a wider population. They condense large amounts of data into simple numerical summaries, tables and graphs that are easy to read and interpret quickly.
The use of descriptive and summary statistics has an extensive history, and the simple tabulation of populations and of economic data was one of the first ways the topic of statistics appeared. More recently, a collection of summarisation techniques has been formulated under the heading of exploratory data analysis; an example of such a technique is the box plot. In the business world, descriptive statistics provide a useful summary of many types of data.
Permutation and CombinationRead →How Do Descriptive and Inferential Statistics Differ?
Descriptive statistics summarise and present the data you actually collected, using numbers, tables and graphs to describe a chosen group. Inferential statistics go further: they take a sample and make generalisations or predictions about a larger population. In short, descriptive statistics describe what the data show, while inferential statistics infer what the wider data suggest.
- Descriptive statistics use the data to provide descriptions of a group, either through numerical calculations, graphs or tables.
- Inferential statistics use measurements from a sample of subjects to compare treatment groups and generalise to the larger population.
- Inferential statistics make inferences and predictions about a population based on a sample of data taken from that population.
- Descriptive statistics are straightforward to report, while inferential statistics require confidence that the sample accurately represents the population.
| Descriptive Statistics (2026) | Inferential Statistics (2026) |
|---|---|
| Used to summarise and graph the data for a group that you choose. | Takes data from the sample and makes inferences about the larger population. |
| Describes a sample in a fairly straightforward way. | Draws conclusions that extend beyond the sample. |
| Reduces a large number of data points to a few summary values. | Needs confidence that the sample accurately represents the population. |
| Helps you gain insight into and visualise the data. | Many requirements, such as random sampling, affect the process. |
What Are the Types of Descriptive Statistics?
Descriptive statistics fall into four main types. Measures of frequency show how often values occur; measures of central tendency (mean, median, mode) locate the centre; measures of dispersion (range, variance, standard deviation) show the spread; and measures of position (percentiles, quartiles) describe how a single score ranks relative to the others in the dataset.
Measures of Frequency
- Count, percent and frequency.
- Show how often something occurs.
- Use these when you want to show how often a response is given.
Measures of Central Tendency
- Mean, median and mode.
- Locate the distribution by various central points.
- Use these when you want to show an average or the most commonly indicated response.
Measures of Dispersion or Variation
- Range, variance and standard deviation.
- Identify the spread of scores by stating intervals; range is the high minus low points.
- Variance or standard deviation measures the difference between the observed scores and the mean.
- Use these when you want to show how spread out the data are, which also tells you when the spread affects the mean.
Measures of Position
- Percentile ranks and quartile ranks.
- Describe how scores fall in relation to one another, relying on standardised scores.
- Use these when you need to compare scores to a normalised score, such as a national norm.
How Do You Interpret Descriptive Statistics?
Interpretation uses the mean to describe the sample with a single central value, while the standard deviation shows how spread out the data are. Because outliers affect the mean more than the median, comparing the two reveals skew. Together, central tendency and dispersion tell you where the data sit and how variable they really are.
Many statistical analyses use the mean as a standard measure of the centre of the distribution of the data. But unusual values, called outliers, affect the median less than they affect the mean. Comparing the mean and the median therefore helps you judge whether the data are symmetric or skewed, and which measure of central tendency better represents your sample.
Python's standard library does include a median function: the statistics module, added in Python 3.4, provides median() alongside mean(), mode(), variance() and stdev(). The mean is calculated by summing all the values and dividing by the count, while the median is found by ordering the values and taking the middle one. If a dataset contains outliers, values much higher or lower than the rest, they can strongly distort the mean. The mean is therefore not robust to outliers, whereas the median, which ignores their magnitude, is.
How Do You Write a Descriptive Statistics Analysis?
Start by describing your sample size, then report the centre of the data with the mean or median. Next describe the spread using the standard deviation and range. Assess the shape of the distribution with a histogram or box plot to spot skew and outliers, then compare groups if a grouping variable exists in your data.
Step 1: Describe the size of your sample
You should collect a medium to large sample of data. Samples with at least 20 observations are often adequate to represent the distribution of your data. However, to better represent the distribution with a histogram, some practitioners recommend at least 50 observations. Larger samples also provide more precise estimates of the process parameters, such as the mean and standard deviation.
Step 2: Describe the center of your data
Use the mean to describe the sample with a single value that represents the centre of the data. The median and the mean both measure central tendency, but unusual values, called outliers, affect the median less than the mean. When you have unusual values, you can compare the mean and the median to decide which is the better measure to use. If your data are symmetric, the mean and median are similar.
Step 3: Describe the spread of your data
Use the standard deviation to determine how spread out the data are from the mean. A higher standard deviation value indicates a greater spread in the data, while a lower value indicates the observations cluster closely around the mean.
Step 4: Assess the shape and spread of your data distribution
Use the histogram, the individual value plot and the box plot to assess the shape and spread of the data and to identify any potential outliers. Examine the shape of your data to determine whether it appears skewed. When data are skewed, the majority of the values are located on the high or low side of the graph. Skewness is often easiest to detect with a histogram, while outliers are easiest to identify on a box plot.
Step 5: Compare data from different groups
If you have a group variable, you can use it to analyse your data by group or by group level. For example, a bank manager who collects wait-time data might split the histogram by customer task to reveal that check-cashing waits are shorter than home-equity-loan waits, a pattern hidden in the combined data.
Why Are Descriptive Statistics Important in Data Science?
Descriptive statistics are the essential first step in data science and machine learning. Before building predictive models, analysts summarise and visualise data to understand its structure, check its quality and spot outliers. Skipping this exploration often leads to wrong conclusions, so careful descriptive analysis produces cleaner inputs and better-performing models across the whole workflow.
Descriptive statistical analysis helps you understand your data and is a very important part of machine learning, because machine learning is all about making predictions while statistics is about drawing conclusions from data. Doing a descriptive statistical analysis of your dataset is crucial; many people skip this step and lose valuable insight, which often leads to wrong conclusions. Take your time, run the summaries carefully, and make sure the data meet the requirements for further analysis.