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A Panorama of Statistics by Peter Petocz, Eric Sowey

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14 The normal distribution: history, computation and curiosities

When we began our statistical studies at university, last century, we bought, as instructed, a booklet of ‘Statistical Tables’. This booklet contained all the standard tables needed for a conventional undergraduate degree programme in statistics, including the ‘percentage points’ of a variety of standard distributions, critical values for various statistical tests, and a large array of random numbers for sampling studies. We were soon made aware of one particular table, titled ‘Areas under the standard normal curve’, and were left in no doubt that we would be referring to it frequently. We used this booklet of tables in classwork throughout our studies, and had clean copies of it issued to us at every statistics examination. From our vantage point today, that booklet of Statistical Tables has become a rather quaint historical artefact from the mid‐20th century, at a time when calculators were the size of typewriters (both of these, too, being artefacts of that era).

That vital standard normal area table was to be found also in the Appendix of every statistics textbook on the market at that time. That is still the case today. It suggests that this printed tabulation from the past is still being consulted by students and, perhaps, also by professional statisticians. Need this still be so?

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Before considering this question, let’s look at the history of the normal distribution and of the construction ...

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