Descriptive Statistics Calculator

Enter Your DataLoad Example

Accepts numbers separated by commas, spaces, tabs, or new lines

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Start with the observations

Enter at least two finite numerical values, separated by commas, spaces or new lines, and calculate. Invalid tokens are rejected; the tool does not silently drop a malformed entry. It reports center, spread, position, shape summaries and sorted values.

The sample variance and SD use n−1; the population summaries use n. The displayed standard error uses sample SD/√n and needs independent sampling for its usual interpretation.

Worked example: quartile convention matters

Enter 2,3,4,7,8,10,12,20. Count is 8, sum 66, mean 8.25, median 7.5, minimum 2 and maximum 20. Sample variance is 34.5000 and sample SD approximately 5.8737.

Quartiles use linear interpolation at zero-based index (n−1)p. Q₁ is 3.75 and Q₃ is 10.5, giving IQR 6.75. Median-of-halves rules can instead give Q₁=3.5 and Q₃=11. State the convention when comparing tools; a different convention is not automatically an arithmetic error.

Shape and relative spread need conditions

Adjusted sample skewness needs at least three observations and nonzero SD. Adjusted excess kurtosis needs at least four and nonzero SD. Where these are undefined, the tool says so. A near-zero excess kurtosis does not establish normality, and a sample shape estimate can be unstable with few observations.

Coefficient of variation is sample SD/mean expressed as a percentage and is shown only with a positive mean here. It is meaningful for suitable ratio-scale quantities; changing an arbitrary origin, as in Celsius, changes the ratio without changing spread.

The five-number display is schematic. Its marker spacing is not a scaled box plot; use the reported values and an actual distribution plot to assess gaps or clusters.

Continue

Read percentiles and quartiles and data visualization, then inspect the histogram. Descriptive summaries alone do not establish representativeness or causal relationships.