Descriptive Statistics Calculator
Free online descriptive statistics calculator. Enter your dataset and instantly get the mean, median, mode, range, variance, standard deviation, quartiles, IQR and outliers, for both sample and population.
What is descriptive statistics?
Descriptive statistics summarize the main features of a dataset. Measures of central tendency — the mean, median and mode — describe a typical value, while measures of spread — range, variance, standard deviation and the interquartile range — describe how much the values vary.
The variance and standard deviation are reported in two versions: population (dividing by n, used when your data are the whole group of interest) and sample (dividing by n − 1, used when your data are a sample that estimates a larger population).
Quartiles split the sorted data into four equal parts. The interquartile range (Q3 − Q1) is a robust measure of spread that ignores extreme values. Values lying below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are flagged as potential outliers.
How to use this calculator
Follow these steps:
- Enter your numbers separated by commas, spaces or line breaks.
- Read the summary statistics: mean, median, mode, spread measures and quartiles.
- Use the sorted data and outlier list to inspect your dataset, or copy the full results.
Worked example
A teacher records the scores of 9 students on a quiz:
Frequently Asked Questions
Have another question? Let us know.
When should I use the population versus the sample formula?
Use the population formulas when your dataset includes every member of the group you care about. Use the sample formulas when your data are a subset and you want to estimate the spread of the larger population; the n − 1 correction makes the sample variance unbiased.
What is the difference between mean, median and mode?
The mean is the arithmetic average, sensitive to extreme values. The median is the middle value when data are sorted, robust to outliers. The mode is the most frequent value. For skewed data, the median often represents the typical case better than the mean.
How are quartiles and outliers computed here?
The median splits the sorted data in half. Q1 is the median of the lower half and Q3 is the median of the upper half (excluding the median when n is odd). The IQR is Q3 − Q1, and a point is flagged as an outlier if it lies below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR.
Why is the standard deviation important?
The standard deviation tells you how tightly the values cluster around the mean. A small standard deviation means the data are consistent; a large one means they are widely spread. It is the foundation of many inferential statistics, such as confidence intervals and t-tests.
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