## Accuracy, Precision, Variation, and Tolerance: A Five Day Unit Plan

Problem Statement: (For Davea students) You are asked by your employer at the automotive shop you work to perform cylinder head services for several types of vehicles. After you measure the valve guides and valve stems, you record your measurements, and you compare them with the factory specifications. Find the tolerance (the range of variation permitted in maintaining a specified dimension in machining a piece). Compare the tolerance for several cars that are manufactured from the same company. Enter the data to a spreadsheet so that high students from the DuPage county can access them. The question for everyone is: Do you find any trends in the variation of the tolerance for certain manufactures?

Day 1: Accuracy vs. Precision:
To become familiar with the difference between accuracy and precision, students will simulate measurements of some quantity, such as cylinder compression, by dropping pennies on a target on the floor. Each penny will represent a compression measurement and the bull's eye will represent the actual compression. Students from Davea will also measure the cylinder diameter from different cars, as they perform cylinder head service, and they will compare the accuracy and the precision of their measurements.

Day 2: Tolerance, an automotive lab:
Students at Davea measure valve guides and valve stems and record the measurements to a spreadsheet in the Internet--so that all high school students in DuPage county can have access to them. Then all the students explore the significance of tolerance in automotive technology. (Optional lab for the students in DuPage county) The Penny Lab. Students will calculate the densities of pre-1983 (copper) pennies and post-1983 (copper/zinc) pennies. After measuring masses and volumes, students will enter their data in tables or on a spreadsheet, prepare a stem-and-leaf diagram, and use the tables and diagram to analyze the variation in the data.

Days 3 and 4: Variation, an automotive lab.
Students will use a spreadsheet to analyze automotive data and discover how both individual measurements and team averages vary. The instructor will have some options when it comes to deciding which automotive quantity will be measured. During this lab students will be introduced to several important spreadsheet features including data entry and analysis.

Day 5: Variation, Variance and Standard Deviation.
Without actually exposing them to the rather foreboding formulae for variance and standard deviation, students will be introduced to these concepts and use them to describe sets of data simulated on a spreadsheet.