# 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.

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 using the very same ampount of water each time (measured with a super-high-quality meter). 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

Set-up the TIMER utility on your computer or mobile device. You should have a display able to show hundredths of a second.  Use your timer to record the time it takes for one complete period (back then forth once) of the pendulum. Record your value for the period. If you’re working with a partner, you should each record a period. Upload your result to Learning Catalytics.

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 most likely value for period of the pendulum (and why)? Are there values for the period that you can rule out (and why)? What do you think the source of the variability in the measurements is? Estimate the uncertainty of your measurment in light of this comparison to the class as a whole.

Marking Scheme

1 mark for anyone in a group that produces a graphical representation of the data.
1 mark for an explanation of what you learned in the invention activity, written in your lab notebook.

1 mark for your measurements of the pendulum period
3 marks for a graphical representation of the pendulum data (including figure caption, axis labels, units).
2 marks for making quantitative statements about the period of the pendulum.

1 mark for discussion of variability and uncertainty estimates.

1 mark for notebook basics: title, date, lab partner, notes on what you have been doing, what you are observing, and why