# The Central Limit Theorem

Statistics - investigating the Central Limit Theorem for a distribution which is non-Normal but whose variance is known.

###### Author and programmer: Ron Barrow

UK Year 13, KS5, GCE A Level Mathematics - Statistics

TweetInstructions below See also: Symmetric Confidence Intervals

## How to Use this Applet

This is a busy applet, and there is a great deal that can be
learnt from it. It is sometimes a little slow, as there are a great
many calculations to be done at each stage.

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!