Have you ever experienced a situation that people's perceptions of what happened or how that happened were different despite the fact that all saw the same scene?

A similar phenomenon can be observed in laboratory when different students measure the same physical quantity. Not only that; it may happen that when you measure the same quantity twice, you get different results.

No matter how precise you try to be, there are always some measurement errors. That is called the statistical or random error and is based on factors that we cannot control: changing temperature, limitations of instruments (e.g. the smallest subdivision seen from different angle, because of the thickness of a ruler, may show different value), or limitations of the human eye.

In this lab, we will learn how to deal with experimental results that vary. The video below explains statistical methods that are used to deal with the random error.

Statistical Error

As an example, we will measure the length of one quantity (an abject will be determined in class) and collect the results in a table provided in class.

After collecting the data in one excel sheet, we can perform statistical analysis. The steps are as follows:

As you noticed, the average, absolute deviation, and its square and the sum of it was automatically calculated in the Excel sheet. Based on that we will calculate the sample variance and the sum of squares. In order to calculate sample variance, take the sum of squares , divide by (n-1), and square the quotient. Note the sample variance.

Finally, to find a standard error of the mean, divide sample variance by a square root of n.

Now, we may present the results of our measurement:

Accuracy and Precision

Error and difference

Percent Error (Relative Error)

Now, when we know the most accurate value of our measurement, we may report how much a particular measurement was different form this one. To state that, we calculate percent error.

Error in physics is the difference between a measurement and the actual or true value for that measurement.

Percent Difference

We will calculate percent error almost every time we measure anything in the physics lab. Sometimes, however, we do not know the accepted value. In that case, a similar formula of percent difference may be used.