Authentic Learning Task (ALT) #1: Tired Paper Clips

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Overview

In this Authentic Learning Task (ALT), you, working in a team, use exploratory data analysis techniques to examine fatigue data generated by breaking common office paper clips.

After obtaining the data, each team uses a variety of exploratory data analysis techniques to study collective fatigue life characteristics for the sample tested. You study data from each of the two packets individually, and then compare and contrast them. Then, you discuss differences in terms of underlying paper clip characteristics that might lead to longer/shorter fatigue lives.

After completing this ALT, you should be able to demonstrate the following competency:

• Use summary techniques such as box plots, stem and leaf plots, and percentiles to analyze and interpret data sets (Comp. 1).

Materials and Equipment
No materials or equipment are needed for this ALT.

Safety and Disposal
No special safety or disposal procedures are required.

Pre-Activity

In order to quantify the data collected in ALT#1: Tired Paper Clips, you use several data analysis techniques, including stem and leaf diagrams, percentiles, and box plots.

In addition to reading the informational materials found on pages 15-17 in the Probability, Sampling, & Hypothesis Testing Participant Journal, this Pre-Activity requires you visit several informational websites, then test your skills with two pre-activity practice problems. The answers and solutions are provided by in a link below.

Stem and Leaf Diagrams
An excellent starting point with examples of the use of stem and leaf diagrams is at Statistics Canada.

Another excellent site is located at the Shoder Educational Foundation website. This site has a stem and leaf plotter and an information page found at the What button and instructions on how to use the plotter under the How button. (You may have problems displaying the stem and leaf diagram if you do not have an up to date Java applet software. It will prompt you if you need a download.)

Additional sites include:
http://www.netmba.com/statistics/plot/stem/
http://regentsprep.org/Regents/math/data/stemleaf.htm
http://ellerbruch.nmu.edu/cs255/jnord/stemplot.html

Percentiles
In previous courses and modules, you have studied both the measures of central tendencies (Mean, Mode and Median) as a means to find the most representative value of the data set and the measures of variability (Range, Variance, and Standard Deviation), i.e. the spread of the data set. A statistic that you probably have not used to illustrate the spread of the data is quartiles or percentiles.

The root word in the word quartile is quarter, signifying fourths. In this section, we will focus on the points that determine the 25th and the 75th percentiles. The median reflects the 50th percentile.

Visit the Statistics Canada again for example of calculating quartiles and box plots (discussed below).

Box Plots
This graphical technique that illustrates the median, upper and lower quartiles, and outliers was published by a famous statistician John Tukey (1977). The box plot, also known as a box and whisker plot, provides us with another very effective graphical tool. Visit the following sites for examples of box plots:

http://ellerbruch.nmu.edu/cs255/jnord/boxplot.html
http://www.netmba.com/statistics/plot/box/

Two sites that provide excellent information and steps for constructing Box Plots can be found at can be found at NIST and Shoder Educational, which has several example data sets and their corresponding box plots using interactive box plotter.

Coventry University provides guidance in using Excel to create box plots.

Self Assessment

Work Problems 1 and 2 in Worksheet that Accompanies the “Stem-and-Leaf Plots” Lesson.

Using the same data, determine the quartiles and create Box Plots.

Click here for the solutions to practice problems.

Activity

In your team, perform the following steps to complete the activity:

1. In your team, generate fatique life data for all paper clips in both packets, making sure the data from each packet is kept separate. Record the data on notebook paper.
2. Record the characteristics for each sample (packet) in the notebook. For example, a large or small size, brand, serrated or smooth, etc.
3. Complete the Data Sheets in your Participant Journal.

Post-Activity

Your team should now post all of its results from the activity to the Discussion Board.

Assignment
There are no instructions to prepare for ALT #2: A Visit to Pennyville.

Assessment
Your facilitator may use Assessment Sheet: Tired Paper Clips to evaluate your results from the activity and your posting to the Discussion Board.

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