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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 temperature.
 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 allow.

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.

Acknowledgement

Some of the material presented here is reproduced by permission of Chris D Odom, George School, USA

[ Accuracy and precision  |  Measurement tools  |  Percentage Error and Percentage Difference  |   Instrument Uncertainty and Least Count  |  Error Propagation  |  An Introduction to Statistics on the TI-83  |  Back to Experiments  ]

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