Discovering Pi and its Measurement Variation: A Collaborative Cloud Activity

Scott Sinex and Ted Chambers

Department of Physical Sciences & Engineering

Prince George’s Community College

Conference on June 1-2, 2017 at The Community College of Baltimore County, Owings Mills

The measurement ...

2

diameter

circumference

Measure to nearest 0.1 cm or 1 mm

Directions are on the “directions” tab on spreadsheet.

What do students discover?

• Variation in the computation of pi and ways to assess variation
• A mathematical model from plotting - circumference as a function of diameter
• Computing the numerical value of pi from the data and slope of the model
• Determining the percent error from known value of pi
• Assessing the possible cause of error, both systematic & random
• Consider a standard object to assess accuracy and precision

3

Some definitions

Accuracy - closeness to true value, here the known value of pi

Precision - how reproducible is a measurement - range, standard deviation, %CV (coefficient of variation) = std. dev. * 100/mean

Percent Error = (experimental value - true value)*100/true value

Random Error = random scatter in data, can come from measurements, replicate measurements reduce

Systematic Error = bias in measurements

4

Types of Errors

Data collection and sharing ...

To get the spreadsheet - https://goo.gl/oYVQzS

For today the file can be edited to collect data

Normally can view, then go to File > Make a copy… to get your copy which you can edit!

5

Examining variation - numerically & graphically

6

Deriving a mathematical model C = 𝜋 d

7

Best-fit line by linear regression

y = mx + b

y = mx

Computing 𝜋

8

Percent Error = (experimental value - true value)*100

true value

Determining Accuracy & Precision

9

Students get to ...

• Engage in measurement & data collection/analysis
• Compare individual, whole class, and other classes via in
• Derive a mathematical model in terms of scientific variables:
• y = mx C = 𝜋d
• Examine goodness-of-fit with r-squared
• Investigate error and how it influences the model parameters
• Validate model via percent error using a standard via known value of pi

10

We speculate ...

Value of pi will have a positive systematic error or positive %error.

Why? Measurement of diameter if not through center of object will be low; hence, pi will be larger than true/known value

11

More on types of errors - S.A. Sinex (2005) Investigating Types of Errors, Spreadsheets in Education 2 (1) 115-124.

Rulers and Measurement Error (interactive Excel spreadsheet)

Scott Sinex Email: sinexsa@pgcc.edu