Grubbs' test statistic calculator
The Grubbs' test statistic calculator computes grubbs' test statistic from the relation G = max|x - xbar| / s. It takes a single input (values) and returns the grubbs g. Written for students working through a statistics course, analysts and researchers who need to describe a data set, weigh a probability or test a difference before reporting it, and people in quality control, lab work or operations deciding whether a batch, group or period differs enough from another to act on. Enter your values below and the result updates instantly, and you can share a permalink that pre-fills the exact calculation. Enter values in the form each tool asks for, whether that is a complete list of observations or summary figures such as counts, means, spreads or probabilities; keep any measurements in the same unit and on the same measurement scale, pick the right option where a tool distinguishes a sample from a whole population because that changes the formula and can shift the answer noticeably on small data sets, and scan for typos and stray extreme values first, since one mistyped figure can move a result a long way. For example, with values = 1,2,3,4,5, the grubbs g works out to 1.264911, and the worked example further down the page shows every step so you can follow the arithmetic and reproduce it by hand. The method is the standard form documented by NIST/SEMATECH e-Handbook of Statistical Methods, and the figure above each result carries the date it was last verified. These tools work only from the numbers and assumptions you give them: they cannot tell you whether the data was gathered in a way that supports a wider conclusion, whether the measure or distribution you picked fits the situation, or whether a result that looks convincing reflects a real effect rather than ordinary variation, so treat every output as a summary to interpret in context and never as proof of a cause.
With Values = 1,2,3,4,5, the result is 1.264911.
Applies to: any numeric inputs. Method source: NIST/SEMATECH e-Handbook of Statistical Methods, checked 2026-06-22.
The formula
G = max|x - xbar| / s
Worked example
With Values = 1,2,3,4,5:
- G = max|x - xbar| / s
- Grubbs G = 1.264911
This worked example is one of the automated golden-value tests this calculator must pass before it can publish.
What this assumes
- Inputs are real numbers in the units shown.
- The result is the exact value of G = max|x - xbar| / s; general information, not professional advice.
Frequently asked questions
What formula does this use?
G = max|x - xbar| / s, the standard form documented by NIST/SEMATECH e-Handbook of Statistical Methods.
Does the result ever change over time?
No. This is a pure formula with no external rate, so the same inputs always give the same result.
Official sources and verification
- Method: NIST/SEMATECH e-Handbook of Statistical Methods, checked 2026-06-22.
Reviewed by the CalculatorHub team, edited by James Graham, 2026-06-22. See our methodology. General information, not professional advice.