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A Note on the Normal Curve of Error and the Average Deviation

Published online by Cambridge University Press:  27 November 2014

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Extract

In the discussion that followed the reading of a paper on graduation A. Henry gave the following proof which leads to the equation for the “Normal Curve of Error” (A) and to an expression for the average deviation (irrespective of sign) from the most probable result (B).

Let the probability of the happening of a certain event be p and that of its failing q. Then in n trials the most probable number of occasions on which the event will happen will be np.

Type
Papers
Information
Journal of the Staple Inn Actuarial Society , Volume 1 , Issue 2 , 1912 , pp. 44 - 50
Copyright
Copyright © Institute of Actuaries Students' Society 1912

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References

* It may be mentioned that the tendency in statistical work is to discard expression B, and also ·67449 (the probable error), and to use (the standard deviation) instead. It might be well for actuaries to do the same.

† As an example of the possibility of this it may be mentioned that the standard deviation of the normal curve derived from the binomial is , and that this expression is the same for the binomial series itself whatever the values of n, p, and q.