Purpose:

The purpose of this lab is to explore the characteristics of a set of data and understand it's relationship to "reality". Along the way we will talk about precision, accuracy, averages, medians, and confidence.

Equipment:

To complete this lab independently you will need some form of linear measuring device. A meter stick would be ideal but fairly unlikely to be in your closet. As a result you're probably going to make your measurements in feet and inches with a tape measure. All measurements MUST be converted to meters or cm after they are made. Just because.

COVID:

This lab is usually done in groups of 3. You will be doing most of this lab on your own so modify any instructions that apply to the group as a whole.

Procedure:

For this lab you will need paper and pencil to record raw data along with meter sticks and a sense of humor. There is a tendency in society to think of science as being completely focused on incredibly precise measurements. This tends to obscure some important ideas about data and how science uses it. In this lab I am going to try and force you to take fuzzy data so certain ideas will be more apparent. Below is an outline of the process we will follow but it is deliberately general since there is a lot to discuss in class before we start. As always in lab, you will need your minds (or at least some significant portion of them). The following are the steps we will take:

• I) Process Description: In any field of work it is important to be able to clearly describe what you are doing. Our first task in this lab was to figure out how to calibrate our measurement tool. Describe each of the important steps in your groups process for determining how long their “pace” is. Be sure to note where you decided to start and stop the measurement, how many times you collected the data, and how you will use that data. No calculations or numbers at this point – that’s the next step.

Commentary: Formally a pace, to a forester, is two steps. This is because our left and right steps are not the same especially if we've ever been injured. That doesn't mean your can't decide to call 1 step a pace but recognize there is some uncertainty in that. Every year when I do this in a school building somebody decides they want to call a 'pace' the length of their foot as they walk toe to heel down the hall. If you make this choice you will be driven crazy by the last part of this lab where you need to figure out a fairly long distance. This lab is NOT about precision. Relax.

• II) Calibration: We have a cultural expectation that when you write things down you should be clean and tidy. This often leads novice scientists to tidy up their data before putting it in the lab report. At a fundamental level this is considered unethical in science. In any report of scientific results the actual data should be presented without manipulation or modification. This allows others who are trying to understand or appreciate your work to make their own judgements about the decisions you made in gathering the data.

  For this part of the lab you will do the process you described in the first section. You will present the actual data you and your classmates collect in its full and original glory. This is done by creating a table to organize and enter the data so that you are also aware of who took/generated each data point. You will need to label each column and/row so you know what the data represents and be sure to note the units. You will have at least three sets of data and multiple measurements of each participant. Because you are working in a group there is data for each member of your group (perhaps a column) and then there are mutiple experiments that each of you do in the process of determining the length of your pace (perhaps these are rows).

  Commentary: It will not work well to take one step or a single two step pace and measure how long it is. As humans we make all sorts of interesting adjustments as we walk that will not be the same as when we 'pace off' a longer distance. The goal here is to be able to walk consistently over reasonable distances, uphill and downhill, over rough terrain or smooth, while maintaining a consistent 'pace'. When you calibrate your pace do it in a space where you aren't adjusting for walls and obstacles (outside?). Be sure you're already moving before you start the measurement and don't stop until you've gone past the end of your measurement. You may need help to do this. Try dropping bean bags or coins to mark the beginning and the end of your measurement zone. Be sure your measurement spans 3 - 4 paces at least to smooth out any irregularities.

• III) Calculation: Now take the numbers from the previous data table and show me how you calculated the length of your pace. Show at least one of the calculations completely so your reader understands how you did it. Since this calculation will be included in your lab report think about how to organize it so it's readable in the picture or scan. Calculate the length of your pace for each test individually so you know the extremes and the average results. Enter those extremes and the average into the table at the bottom (min, max, and average) That this gives you is a unit coversion that says something like 1 pace = 1.34 m (yours will be unique to you).

Commentary: In your data table you will have your actual measurements (probably in inches or feet) which will then be converted to cm or m in a separate column. Your measurement will indicate that you took x number of paces which covered y number of cm. Do algebra until you have 1 pace = (some number) m. Take a picture of the calculation to include in your lab report.

• IV) Measurement of Hallway (or other feature of interest): Now it’s time to use your calibrated “pace”. Have each member of the group pace off the length of the hallway independently. Record the data and then repeat the measurement at least once. Each person will then convert the average number of paces for the hallway into m and then contribute that number to the group. Determine, for your group, the average, min, and max length (in meters) of the hallway consistent with the data. Show your actual conversion from paces to meter for at least one case. Remember that you will need the data from your groupmates later on.

  COVID: While we would normally measure a long hallway at the college using paces you are asked to take on a different measurement that is more accessible under COVID. Instead of a hallway you may measure the length of a city block, the distance between telephone poles, or the distance to your local coffee shop. Remember that you are asked to make the measurement multiple times - 4x would make sense. There and back twice.

  Commentary: You can average the number of paces for your measurement and then convert to a distance or convert all the paces to distances and average those results. It is the same either way. In the end you need the average estimated distance you measured as well as the minimum and maximum.

• V) Class Results: In a table show the calculated average hallway (or other feature of interest) length from all the other groups in the class. Identify each measurement with the name of the group or someone in the group. Calculate the classes average, min, and max lengths (in meters) for the hallway. We will probably put it up on the board and send a picture to everyone in the class.

  COVID: If we could reliably assume that we are all measuring the same object then this question makes sense. I don't see a reasonable way to do that at the moment. We will be skipping this part.

• VI) Meaning: So how long is the hallway (or other feature of interest)? What does this data say about this question? What is your best estimate? What is the range of possibility? How sure are you? Answer these questions in your own words.

  COVID: When we have a lot of measurements of the same distance by a group of students then there are some important things we can talk about. In this case I want you to reflect on the quality of your own measurement. Do you think it's reasonable? If you do the measurement tomorrow how different do you think your result would be? Why? Give me a distance you are sure is shorter than the actual distance you measured? What is a distance longer than your measurement? These are your upper and lower bounds and the difference between them is an indicator of your confidence in your measurement.

LAB DELIVERABLES: (Turn in on LMS)

I) Process: Your paragraph describing the process you plan to use to determine how long your pace is. This paragraph should include a clear description of what you define a pace to be.

II) Calibration: Present your calibration data for all the members of your group in a clearly organized and labelled table. Then show how you use this data to determine the length of your pace. Show the math clearly and be sure to show the units as well. What is the conversion factor for your pace?

III) Measurement Data: Present the data from each individual in your group showing the number of paces for the length of the hallway (or other feature of interest). Multiple measurements are required from each group member. Present the data in a clear and well labeled table. Show how you converted paces to meters mathematically as well as the min, max, and average for your group.

IV) Meaning: Present the average hallway (or other feature of interest) lengths as determined by each group. What is the average prediction of the class (in m)? What is a reasonable expectation of the actual length of the hallway? Why is this consistent with the data and the variation in that data?