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Errors & statistics
Errors and statistics
Physics is a quantitative science, relying on accurate
measurements of fundamental properties such as time, length, mass and
Carl Friedrich Gauss
(1777-1855) German mathematician and physicist has discovered
the asteroid Ceres - he was able to accurately compute the
orbit after only three observations after the inventing of the
method of least squares. On another occasion, while interested
in the abstract problem of geodesics (shortest distance
between two points on a surface such as the Earth) he invented
the heliotrope, a surveying instrument that used the sun's
rays to obtain accurate measurements. He also developed the
mathematics of error analysis for measurements in general,
giving rise to probability analysis and hypothesis testing.
The normal probability curve is known as the Gaussian curve.
His work with Wilhelm Weber resulted in an advancement of the
theory of electromagnetism.
To ensure measurements of these properties are accurate and precise, instruments
such as metre sticks, Vernier calipers, micrometer calipers, triple-beam
balances and laboratory thermometers are often used. It is important to
understand how to use these devices properly. With any measurement tool, the
student should always try to achieve the greatest accuracy the apparatus will
This module also aims to:
explain briefly what "statistics" is;
introduce the reader to "exploratory data analysis";
show how to do this using a TI-83.
The intended readership is:
anyone who wishes to learn or revise the very beginnings of the
study of statistics.
Some of the material presented here is reproduced by permission of Chris
D Odom, George School, USA