# Percent Uncertainty

In other science courses, you may have seen the concept of percent error:

However, as described in the Introduction to Statistical and Systematic Uncertainty, the true value is actually generally *unknowable*. Thus, this concept of percent error really only makes sense if there is some accepted value without an uncertainty to which you can compare.

A much more useful idea is the :

where x is the mean as already discussed in Mean and *σ* is the uncertainty (the reason for this choice of symbol will be made clear later).

Example

Consider two distance measurements each with an uncertainty of

The first is Dr. Toggerson’s height:

The second measurement is the height of the library

The percent uncertainty on Dr. Toggerson’s height is

Meanwhile, the same uncertainty on the library is

The same uncertainty leads to different percent uncertainty depending on the mean value.

The uncertainty on a measurement divided by the mean. Generally a more useful quantity than percent error which requires a true value.