Probability theory and statistics are two sides of the same coin.
In fact, one can use a coin to illustrate the connection. In
probability theory one assumes that a coin has a certain probability
of "heads", for example, supposing the coin is "fair" then the
probability of heads is 1/2. With this assumption one goes on
and studies features about coin tossing. In statistics on the other
hand, one studies actual data about the coin, for example, suppose
that one tosses a coin one hundred times and it happens that 53
of the tosses yielded heads and 47 gave tails. The question is:
Is the coin fair, that is, is the probability of heads equal to 1/2?
Thus, probability and statistics start with different points of view
and different questions. Probability theory is used to help statistics
in answering the question as to whether the coin is fair or not. For
example, given the above data, a statistician would be able to
answer the question as to whether the coin is fair and with what
probability one can have confidence in the statistician's decision?
It is not possible to do statistics without a theoretical base in
probability theory. Probability theory on the other hand can be
studied without reference to data, but the very idea of the
probability of an event is imbedded in considerations about data
(the probability of an event is the long run value of the relative
frequency of the event based on actual data).
Richard J. Griego
-----Original Message-----
From: Mike Robison <mrobison@voyager.net>
To: historia-matematica@chasque.apc.org
<historia-matematica@chasque.apc.org>
Date: Monday, March 29, 1999 8:17 AM
Subject: Re: [HM] Is Statistics Part of Mathematics?
>"Richard J. Griego" wrote:
>>
>> In response to James A. Landau's message of March 26, 1999 as to
>> whether statistics is part of mathematics:
>>
>> If one accepts that probability theory is part of statistics, then
>> certainly statistics has contributed mightily to parts of mathematics.
>
>This initial statement is where I would appreciate clarification. In
>developing a curriculum for a basic level (prerequisite basic HS
>algebra) statistics class, we are including a probability unit. This
>has been challenged as unnecessary. I guess I have two related
>questions.
>Is there a historical reason that probability is included in basic
>statistics?
>
>Has probability "always" been included in basic statistics classes?
>
>Thank you.
>
>Mike
>--
>Mike Robison
>Math graduate student and occasional amateur historian
>Michigan State University
>mrobison@voyager.net robiso12@pilot.msu.edu
>http://www.msu.edu/user/robiso12/index.htm
>"Expecting all children the same age to learn from the
>same materials is like expecting all children the same
>age to wear the same size clothing." M. Hunter
>