How it works
The mean is the sum divided by the count. Variance is the average squared distance from the mean, divided by n − 1 for a sample or by n for a whole population, and the standard deviation is its square root.
Quartiles follow the NIST e-Handbook definition: the p-th percentile sits at rank p × (n + 1) in the sorted data, interpolated between neighbours. Outliers are values beyond 1.5 × IQR below Q1 or above Q3 (Tukey fences).
What each figure means
- Mean: the arithmetic average. Median: the middle value, half the data below and half above.
- Mode: the value that occurs most often. A data set can have several modes or none.
- Standard deviation: the typical distance from the mean, in the same unit as the data.
- Quartiles and IQR: Q1 and Q3 cut off the lowest and highest quarter; the IQR between them holds the middle half.
- Standard error: how precisely the sample mean estimates the population mean (s ÷ √n).
s = √( Σ(x − x̄)² ÷ (n − 1) )
Tips
- Use “sample” when your numbers are part of a larger group (survey answers, test runs), “whole population” only when you have every value.
- If mean and median are far apart, the data is skewed and the median is usually the better typical value.
- Spreadsheets compute quartiles in different ways (QUARTILE.INC, QUARTILE.EXC), so Q1 and Q3 can differ slightly from Excel.
Standards and sources
- NIST/SEMATECH e-Handbook of Statistical Methods: measures of location
- NIST/SEMATECH e-Handbook: measures of scale (variance, standard deviation, IQR)
- NIST/SEMATECH e-Handbook: percentiles
- NIST/SEMATECH e-Handbook: what are outliers in the data?
- NIST/SEMATECH e-Handbook: measures of skewness and kurtosis
Last reviewed October 17, 2026
Frequently asked questions
Sample or population standard deviation?
Use sample (divide by n − 1) when your data is a subset of a larger group, which is almost always the case. Use population (divide by n) only when you have measured every member.
How are quartiles calculated?
With the NIST e-Handbook method: sort the data, find rank p × (n + 1) and interpolate between the two nearest values. Spreadsheet functions use slightly different rules, so results can differ in small data sets.
How are outliers found?
Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are flagged. This is Tukey’s rule, a common screening test, not proof that a value is wrong.
Can I paste a column from Excel?
Yes. Values on separate lines work, and header text is skipped. With decimal commas, use semicolons or new lines between values.