Go to content
  • Distribution A is created from a fixed parent population, grouped into 10 intervals of equal width.
  • Distribution B displays a single random sample from the parent population, and with the same grouping. Its size is varied by clicking the "Sample Size +" and "Sample Size -" buttons. A new sample is taken every time any button is clicked.
  • Distribution C is the distribution of the sample means. In other words, a number of samples are taken, the means of the samples are calculated, and their distribution is drawn, on the same horizontal scale as the population above, but grouped into much narrower intervals.
  • Section D is the Data section, and shows the statistics of the 3 distributions.
  • Clicking the "Number of Samples +" or "Number of Samples -" buttons changes the number of samples taken each time.
  • Clicking the "New Samples" button takes a new batch of samples without changing the sample number or sample size.
  • Clicking the "Show Normal +/-" button displays or hides a Normal curve on Distribution C, to enable you to decide how close a fit it is.

You now have at your disposal all you need to investigate the Central Limit Theorem, one of the cornerstones of mathematical statistics. Have fun!

Software/Applets used on this page

Copyright © R F Barrow, 2000-2003 Waldomaths


central limit theorem

The mean of a random sample of size n from a distribution of mean m and variance v will be normally distributed with mean m and variance v/n, for large n.


the value that a function f(x) approaches as the variable x approaches a value such as 0 or infinity


A line passing through a curve at a point that is perpendicular to the tangent to the curve at that same point.


A collection, group or set of individuals or objects.


A collection of sampling units drawn from a sampling frame.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)S1EstimationCentral Limit Theorem-
AQA A2 Further Maths 2017StatisticsCentral Limit Theorem - ExtraCentral Limit Theorem-
AQA AS/A2 Further Maths 2017StatisticsCentral Limit Theorem - ExtraCentral Limit Theorem-
CCEA A-Level (NI)S2EstimationCentral Limit Theorem-
CIE A-Level (UK)S2EstimationCentral Limit Theorem-
Edexcel A-Level (UK - Pre-2017)S3EstimationCentral Limit Theorem-
Edexcel A2 Further Maths 2017Further Statistics 1Central Limit TheoremCentral Limit Theorem-
Edexcel AS/A2 Further Maths 2017Further Statistics 1Central Limit TheoremCentral Limit Theorem-
I.B. Higher Level7EstimationCentral Limit Theorem-
Methods (UK)M15EstimationCentral Limit Theorem-
OCR A-Level (UK - Pre-2017)S2EstimationCentral Limit Theorem-
OCR A2 Further Maths 2017StatisticsHypothesis Tests and Confidence IntervalsCentral Limit Theorem-
OCR MEI A2 Further Maths 2017Statistics BSample Mean and Central Limit TheoremCentral Limit Theorem-
OCR-MEI A-Level (UK - Pre-2017)S3EstimationCentral Limit Theorem-
Universal (all site questions)EEstimationCentral Limit Theorem-
WJEC A-Level (Wales)S2EstimationCentral Limit Theorem-