INTERACTIVE TOOL · LABORATORY STATISTICS
Probability distribution viewer
Explore how distribution shape, sample size and extreme observations affect the summaries used to describe laboratory data.
By Stephen MacDonald PhD FRCPath · Guide updated 17 October 2026
The viewer uses simulated examples. Keep this guide open alongside the application.
A short exploration
1 · Start with a normal model
Choose Normal, then Interactive Lab. Move Sample Size (n) from 100 towards 1,000. Compare the standard deviation with the interval around the mean.
A larger sample can make the estimated mean more precise. The model’s spread of individual observations is a different quantity. Use this comparison to explain SD versus standard error.
2 · Explore a long right tail
Choose Log-Normal. Examine the shape, then compare the mean and median. A small number of large observations can matter to the mean and to the upper tail.
For a laboratory turnaround-time question, report summaries that describe the part of the service you need to understand. Retain information about unusually long delays.
3 · Look for more than one group
Choose Bimodal and look for two clusters. Consider whether different populations, conditions or processes might have been combined.
One overall mean and SD can hide structure. Investigate the grouping before deciding how to summarise or pool real observations.
4 · Explain what changed
Describe the centre, spread, tail and any separate clusters. State which summary answers your question and what that summary leaves out.
Use the viewer for discussion and visual exploration. Its scenario text and automatic labels are teaching prompts, not an assessment of your laboratory’s own data.
Keep the model and the laboratory question separate
A simulated distribution is an illustration
The viewer includes Normal, Log-Normal, Bimodal, Poisson, Exponential, Chi-Squared and Binomial examples. Select a model to explore its behaviour; the model choice is part of the example.
A histogram’s appearance changes with the sample and display settings. Apparent symmetry alone does not establish normality.
Reference intervals need their own evidence
A simulated sodium example does not establish a reference interval for a patient population. Likewise, between-person variation and analytical variation describe different sources of variation.
This viewer does not provide a reference-interval establishment or verification workflow. Use the relevant study design and guidance for that work.
Continue with the related question
SD, CV, standard error and confidence intervals · Using routine performance data in measurement uncertainty · Search all practical resources
Sources and method context
NIST/SEMATECH: the normal distribution explains the normal model. NIST/SEMATECH: location and scale parameters explains how parameters affect a distribution.
Fictional teaching examples. Suggest a correction and identify the passage or application screen concerned.