Descriptive Statistics Calculator
Paste numbers or upload a CSV to calculate their center, spread, quartiles and potential outliers. Start with the example below, then explore your own data.
Your numbers
One dataset, up to 1,000 observations.
Results
8 values · example data
| Statistic | Result |
|---|---|
| Count (n) | 8 |
| Sum | 40 |
| Mean | 5 |
| Median | 4.5 |
| Mode | 4Each occurs 3 times. |
| Minimum | 2 |
| Maximum | 9 |
| Range | 7 |
| Sample variance | 4.571428571 |
| Sample standard deviation | 2.138089935 |
| First quartile (Q1) | 4 |
| Third quartile (Q3) | 6 |
| Interquartile range (IQR) | 2 |
| Lower outlier fence | 1 |
| Upper outlier fence | 9 |
Displayed results use up to 10 significant digits. Calculations use the unrounded input.
Potential outliers: 0
No values lie outside the 1.5 × IQR fences.
Flags are a prompt to investigate, not a reason to delete data. Every observation is included in the statistics.
Opens this dataset in the selected editor without changing your saved charts. The box plot keeps your quartile method.
Calculate a summary, then look at the distribution
- Enter one dataset, with up to 1,000 numerical observations. All numeric cells in an uploaded file are treated as observations in that same dataset.
- Choose sample or population statistics and the quartile method required by your course or analysis.
- Select Calculate statistics. If an entry is invalid, correct it before continuing; the calculator does not omit it.
- Open the same values in a histogram to examine shape or a box plot to inspect the median, quartiles and outlier flags.
Mean, median and mode describe different centers
The mean is the sum divided by the number of observations. The median is the middle sorted value, or the average of the two middle values when the count is even. The mode is the most frequent value. This calculator lists all tied modes when they repeat; if every value occurs once, it reports “No repeated value.”
A very large or small observation can pull the mean away from the median. Neither number shows the full distribution, so check the values and a chart before drawing conclusions.
For a compact view that keeps each observation visible, try the Stem-and-Leaf Plot Maker.
Sample or population standard deviation?
Choose Population when the entered values are the whole population you want to describe. Choose Sample when they are a sample from a larger population. The choice changes variance and standard deviation, not the mean, median or quartiles.
Population variance is the sum of squared differences from the mean divided by n. Sample variance divides by n − 1. Standard deviation is the square root of variance, in the original measurement units; variance has squared units.
For a single observation, sample variance and sample standard deviation are undefined. Population variance and standard deviation are zero. No inference about the wider population follows from that one observation.
Worked example: 2, 4, 4, 4, 5, 5, 7, 9
The eight values sum to 40, giving a mean of 40 ÷ 8 = 5. The two middle values are 4 and 5, so the median is 4.5. The mode is 4, which appears three times.
The squared differences from the mean sum to 32. Population variance is 32 ÷ 8 = 4 and population standard deviation is 2. Sample variance is 32 ÷ 7 ≈ 4.571429 and sample standard deviation is approximately 2.138090.
With exclusive median-of-halves quartiles, Q1 is 4 and Q3 is 6, so IQR is 2. The outlier fences are 1 and 9. A value exactly on a fence is not flagged; this example has no potential outliers.
Quartiles, IQR and potential outliers
The interquartile range is Q3 − Q1. This calculator flags values strictly below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. A flag is descriptive, not a statistical test or proof of an error. All observations remain in the calculations.
Quartile definitions differ. Exclusive median of halves leaves the overall median out of both halves for odd-sized datasets; inclusive median of halves includes it in both. Linear interpolation uses R type 7, at zero-based positions (n − 1) × p. Small datasets can produce different quartiles and flags under these methods. Match the method specified by your textbook or other software.
Input, precision and privacy
Use decimal points and ungrouped numbers: write 1000, not 1,000. Scientific notation such as 1.2e3 is accepted. Spaces, commas, tabs, semicolons and new lines separate observations; blank cells are ignored. A single first-line Value, Values or Data header is optional. Remove other headers and select only the measurement column you want to summarize.
Results are displayed to at most 10 significant digits. The calculations use JavaScript’s floating-point numbers, not arbitrary-precision arithmetic. Inputs too extreme for reliable finite results are rejected with a request to rescale. Very large integers and finely spaced decimals may lose precision.
Your numbers stay in the browser. Opening a chart transfers them locally to its editor without adding values to the URL. No account or upload to our servers is needed.
Definitions and further reading
- NIST: measures of location — mean, median and mode.
- NIST: measures of scale — variance, standard deviation, range and IQR.
- R documentation: sample quantiles — including the type 7 interpolation method.
Lessons and printable worksheets
Practise with original sample data, worked answers, and free classroom worksheets.