- 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

## Glossary

### 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.

### limit

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

### normal

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

### population

A collection, group or set of individuals or objects.

### sample

A collection of sampling units drawn from a sampling frame.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | S1 | Estimation | Central Limit Theorem | - |

AQA A2 Further Maths 2017 | Statistics | Central Limit Theorem - Extra | Central Limit Theorem | - |

AQA AS/A2 Further Maths 2017 | Statistics | Central Limit Theorem - Extra | Central Limit Theorem | - |

CCEA A-Level (NI) | S2 | Estimation | Central Limit Theorem | - |

CIE A-Level (UK) | S2 | Estimation | Central Limit Theorem | - |

Edexcel A-Level (UK - Pre-2017) | S3 | Estimation | Central Limit Theorem | - |

Edexcel A2 Further Maths 2017 | Further Statistics 1 | Central Limit Theorem | Central Limit Theorem | - |

Edexcel AS/A2 Further Maths 2017 | Further Statistics 1 | Central Limit Theorem | Central Limit Theorem | - |

I.B. Higher Level | 7 | Estimation | Central Limit Theorem | - |

Methods (UK) | M15 | Estimation | Central Limit Theorem | - |

OCR A-Level (UK - Pre-2017) | S2 | Estimation | Central Limit Theorem | - |

OCR A2 Further Maths 2017 | Statistics | Hypothesis Tests and Confidence Intervals | Central Limit Theorem | - |

OCR MEI A2 Further Maths 2017 | Statistics B | Sample Mean and Central Limit Theorem | Central Limit Theorem | - |

OCR-MEI A-Level (UK - Pre-2017) | S3 | Estimation | Central Limit Theorem | - |

Universal (all site questions) | E | Estimation | Central Limit Theorem | - |

WJEC A-Level (Wales) | S2 | Estimation | Central Limit Theorem | - |