# Physics 107 - - Statistical Distributions

Learning Goals

You will learn how to display and handle measurements that are subject to random variations.

Exercise I

With fresh water supplies diminishing, the use of flow meters to regulate water consumption will become increasingly important. You are a new technician at a metal working shop that frequently uses fresh water to cool and lubricate several of their machines. In anticipation of upcoming mandatory regulation, you have proposed to your new bosses that the shop determine its current level of water usage. They like your idea so much that they have put you in charge of making this measurement.

In researching this question you quickly learn that flow meters can be very costly to design and build so that they will always give the exact same measurement; however, less expensive ones also exist. These cheaper models do not always give the exact same reading for consecutive measurements, only close to the same. This is okay because your particular application has more generous tolerances - you do not need to break the bank and get the very best device.

You have found four different models (Schwartz Water Flow Meter, MegaBonn 3000, Wiemanator Carlatron, and Jimmy Dees' Flomometer), for the same lesser price, that all perform well enough for your intended application. The manufacturers have each provided data (below) on the flow rate of water (in units of millilitres per second), as measured by their device and through the same standardized test equipment. But a picture is worth a thousand words, and you want to convert these data into a useful graph for easy comparison.

Specifically, you must invent a procedure for graphically representing the water flow data for each of the four devices. There is more than one way to do this, but you have to use the same procedure for each device, so that a fair comparison may be made between graphs. Outline your procedure for converting the data provided below into a useful graphical representation, and show the resulting graph for each data set.

 Schwartz Water Flow Meter MegaBonn 3000 Wiemanator Carlatron Jimmy Dees Flomometer 10.03 9.77 11.15 9.91 9.73 9.72 10.55 9.88 10.06 10.30 10.68 10.00 9.93 10.15 10.76 9.97 10.26 10.05 11.05 10.43 10.16 10.23 11.19 9.41 9.99 9.99 10.96 10.57 9.50 9.98 11.18 9.22 10.13 10.25 11.32 10.26 9.61 9.90 11.03 9.05 10.51 9.84 10.18 9.85 9.81 10.07 9.45 10.08 9.83

Exercise II

Now that you have created a graphical representation of the water flow data, a decision needs to be made concerning which device to purchase. In the interest of being able to best recommend one of these devices over another to your bosses, you have decided to assign to each a numerical score that reflects how well the device measures the flow rate of water. Specifically, you must invent a procedure for computing the numerical score for each of the devices. There is no single way to do this, but you have to use the same procedure for each device, so that it is a fair comparison between the devices. Write your procedure and the numerical score you compute for each device using the data provided below.

Rules.

1. Use the data provided from Part 1 and your graphical representation.
2. Each device always performs reproducibly, so a device only gets a single score.
3. The exact same procedure must be used for each device to determine its score.
4. A small score implies that the device performs more reliably.

Exercise III

Set-up the TIMER utility on your computer. You should have a display able to show hundredths of a second. When everyone is ready, the instructor will release the pendulum. Use your timer to record the time it takes for one complete period (back then forth once) of the pendulum. and you then start your timer. Record your value for the period, together with an estimate of your uncertainty. If you’re working with a partner, you should each record a period. Write your result on the blackboard.

When all of the data from the entire class is available, devise a means of displaying this data. What can you say quantitatively about the period of the pendulum?

Marking Scheme

1 mark for anyone in a group that produces a graphical representation of the data.
1 mark for an explanation of your choice of graphical representation, written in your lab notebook.
2 marks for the numerical scores and justification/explanation of it.
2 marks for a graphical representation of the pendulum data.
2 marks for making a quantitative statement about the period of the pendulum.