# Introduction to Uncertainty and Error Propagation Lab

This particular lab is going to focus on the fundamentals of measurement: what does it mean to make a good measurement and how do we quantify the uncertainty on that measurement? These questions are really going to be the focus of this lab. Along the way, you will also be introduced to fundamental statistics concepts like mean and standard deviation that you might have seen in a statistics course. You will also be thinking about how to represent uncertainty: you will explore different options including:

• significant figures – which most of you have probably seen.
• the crank three times method – simple to implement but somewhat limited.
• Monte Carlo error propagation – this is the error propagation technique that is actually used in most research in the modern times because it’s the easiest to implement with complex datasets and complex formulas.

In order to do Monte Carlo effectively, you are also going to learn several different spreadsheet techniques. As stated in the syllabus, we are going to use Google Sheets to teach you spreadsheets because it is the easiest for us to help you learn. The basic ideas, however, work for Excel or Numbers or any of the other spreadsheet programs out there. As was said in the introduction to the lab, spreadsheets area great skill that are used in many different careers and in many different contexts. So, along the way you’re going to learn some nice spreadsheet stuff.

The measurement that you’re going to do in this lab might seem relatively simple: all you’re going to measure is the volume of a U.S. nickel. You will need to measure the radius and the thickness of your nickel. All the materials you need are ten US nickels and a metric ruler (things that you can probably get pretty easily). Again, these measurements may seem relatively simple. They are. That is on purpose. We want to focus first on an easy-to-make measurement so that we can really think about what the uncertainties are and how these uncertainties, from just the radius and thickness, propagate through a calculation, into the volume. We want to do this with a simple measurement that we can fully understand first before we move to something more complex. I think, along the way, you will be surprised how hard measuring something that seems as relatively simple as the volume of a nickel actually can be.

As usual, the lab as usual will guide you through with a series of questions and instructional materials. Do not hesitate to reach out to your lab TA for help if you need it. For any multiple-choice question, you will get multiple attempts. There will be a way to check your answers. There is a small deduction in credit for each attempt (let’s be honest, we don’t want you just guessing!).

Have fun really thinking about how to make measurements and what uncertainty really means!