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

   
           

Instructions below   See also:   Symmetric Confidence Intervals

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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!