There is little that can be scientifically investigated without taking measurements. By taking and analyzing data, we can develop models that inform us of how the world works. However, to be able to analyze data effectively, critical decisions need to be made regarding how the data are being taken in order to determine its validity.

This uncertainty is not a fault of experimental science, and does not give credence to “theory being more perfect than experiment.” The idea of uncertainty is found in every aspect of science – in experiment we call it *error* or *uncertainty*, in theory we are limited by the *assumptions* made, and in engineering we define our products to be within a *tolerance.* In all instances, these forms of uncertainty describe how *confident* the scientist is in their measurement – it defines the range of values within which they are *sure* the reported value falls.

Defining uncertainty is a skill that is developed over time and, like any other skill, takes practice. As it is a major tool used in nearly every aspect of science, it has become a major learning goal of DATA Lab, both this semester and next (should you take PHY 252).

In this workshop, you are tasked with taking a series of measurements. Your data will be pooled with the rest of the class – affording us a backdrop against which to discuss measurements and uncertainty. The discussions with the larger group will help inform your decisions in experiments as well as help you develop a deeper understanding of what uncertainty means and how it is used in science. Afterwards, you and your group will be presented with a final measurement that you will record and assign uncertainty to. By using the information in class, you will justify your experimental decisions and value reported.

In order to be productive in class, it would be helpful to research before class:

• What reported data means
• Why uncertainty is assigned to measured data
• How the assigned uncertainty reflects the confidence of the reported value
• The difference between random and systematic uncertainty
• How to calculate the mean of data set

Part 1 – Measurements

There are five measurements you are tasked with taking: the length of a metal block, the diameter of a bouncy ball, the length of a string, the mass of a weight, and the angle of a board. After you take these measurements, record the values you obtained on the white boards provided. It may be helpful to consider and document in your notebook

• How was each measurement taken?
• Were there any complications that arose while taking your measurements?
• Did the way you took your measurement affect the value you obtained?

Part 2 – Discussion of Uncertainty

Scientists will include values of uncertainty when they report data. Your group will be assigned one of the sets of measurement data to discuss. In this discussion, consider:

• What do the reported values mean?
• How difficult was the measurement to make? Why?
• What does the amount of variability tell you about the uncertainty in the measurement?
• Are there other things the variations tell you?
• Can you assign a quantitative value for the uncertainty of this set of data?

You will then report your group's discussion to the class.

Part 3 – Obtaining and Reporting Data

Your group will be tasked with taking one additional measurement. The experimental decisions your group makes will affect the value and uncertainty of your measurement. Document these decisions and determine a value for the measurement and its uncertainty. Justify your values based on the decisions you made and the discussions held in class.

At the end of the day, you will each turn in your notebook. While your entire entry will be evaluated, in order to narrow our scope feedback and assessment will primarily focus on what you submit for Part 3, especially

• The value reported and the uncertainty assigned.
• How you documented your measurement and the experimental decisions you made.
• Justification for your assigned value and uncertainty and how it related to the discussions held in class.