Chapter 5, Problem 5.1P

To determine

The differences between an error and an uncertainty and the ways in which uncertainty can be estimated for a measured value.

Explanation of Solution

An error is the difference between measured value and the actual value of the measured quantity. Since we do not know the exact value, or the true value is unknown, the error is estimated. This numerical estimation is called an uncertainty. Errors are regarded as the effects whereas uncertainties are the numbers which define the amount of errors. Errors are caused due to number reasons, but the uncertainty is a number which the amount of error from the true value.

Ways to estimate the uncertainty for a measured value:

Systematic Uncertainty: The error due to systematic uncertainty remains constant under fixed operating conditions. It might cause a high offset or a low offset in the determined estimate of the true value of the measured variable. Since the value of systematic error is constant, it difficult to estimate and to recognize its presence. The systematic error is represented by an interval, b. The value b is the estimate of the systematic standard uncertainty. The interval defined by the systematic uncertainty at the 95% probability level is written as $\pm B=\pm 2b$

• Random Uncertainty: The probable range of the random error is estimated by random uncertainty.

The random uncertainty level is $\pm s_{\overline{x}}$.

Where,

  $s_{\overline{x}}=s_x/\sqrt{N}$

The degrees of freedom are, $\nu =N-1$.