IED Unit 3: Measurement & Statistics

Understanding precision, accuracy, and variability in engineering metrics


Engineers need to be able to design, measure, and build things that are very exact.  In this unit, we’ll look at different kinds of measurements and units.  We’ll also look at the precision, accuracy, and variability of measurements using statistics! The main topics of the unit are:

  • Units & Unit Conversion
  • Measurement Tools
  • Dimensioning
  • Statistics
  • Microsoft Excel

The skills we develop in this unit will be useful as we continue to design and build our own prototypes and solutions to different problems. The work in this unit will require some careful attention to the math of engineering as we complete three main parts:

  1. STEP 1: Collect a variety of measurements in different units to see how they compare and to get used to different measurement tools.  Then work to practice converting units mathematically.
  2. STEP 2: Work with your team to complete an instant design challenge, collect data on your success, and investigate the variability in your data with statistics!
  3. STEP 3: Design, measure, and build a puzzle cube that meets precise parameters!

When you’re done, you will have gotten practice with the mathematics of measurement and variability, and then also demonstrated those skills as you built a puzzle.


(25 pts) About 3 days

In different branches of math, science, and engineering we use different units for measurement.  In this part of our third unit, you will get to practice taking different kinds of measurements, practice converting between different metrics, and practice using calipers to properly dimension your drawings.


(25 pts) About 3 days

In addition to being able to measure individual dimensions, we also need to understand how both our measurements and the objects around us vary.  Here you will study variability and the ways that statistics can help quantify how precise or accurate our measurements and our results are.


(20 pts) About 3 days

Your final job is to combine the concepts of measurement and variability to create a puzzle cube toy that fits very precise parameters.  You will design your toy, measure and assemble the parts to meet specific criteria, and then sketch your puzzle cube parts using isometric and multiview sketching.

Part 1: Measurement & Units

Work with measurements with a variety of units and tools

Conversion Reference

It’s important that engineers be able to describe what they are trying to build.  Part of that is having a clear picture or diagram, and along with that is the importance of using the right units.  When we measure distances we have a choice between inches, feet, centimeters, or meters.  We have similar choices when we measure weights, volumes, and other forces.  In this first part, you will do some simply measuring, practice the math needed to convert between different kinds of units, and become familiar with the use of calipers to measure precisely.


Watch the video on measurement and units, and take a full page of careful notes in your engineering notebook

Complete the measurements activity for SI and US units

 Complete the Unit Conversion assignment

 Use a caliper to carefully measure and dimension a multiview drawing of some Automoblox pieces

 Have Mr. Benshoof approve your assignments and drawings

Measurement & Units

Unit Conversion

Calipers & Dimensioning

What’s Due In Part 1: Measurement & Units

  • Measurement Notes
  • Measurement Activity
  • Unit Conversion
  • Automoblox Diagrams
  • Mr. Benshoof’s Approval

Here’s what’s due in Part 1: Measurement & Units

  1. Notes on measurement and units in your engineering notebook
  2. Complete measurements activity
  3. Complete Unit Conversion assignment
  4.  Caliper dimensions for Automoblox diagram
  5. Have Mr. Benshoof approve your assignments and drawings

Part 2: Statistics & Variability

Describing the variability in our measurements and what we build

Calculations Reference


Nothing we make is ever perfect.  The job of an engineer is to understand how their solution is imperfect, and to be able to describe both the size of those imperfections as well as the impact of them.  As we continue our work in measurement we need to be able to quantify variability – the inconsistency – in our work.  In this part of the unit, we will collect some data on manufactured objects as well as our own creations and then use that to explore mean, median, and standard deviation.


 Start by taking careful notes on “Statistics Calculations” and “What is variability?” in your engineering notebook

 Collect your linear dimensions measurements and complete the activity in Excel

 Complete the Variability Statistics assignment

 With a partner, complete the “Fling Machine” instant design challenge, collect your data, and analyze your data in Excel

 Have Mr. Benshoof check-off your completed data collection and statistics work

Statistics Calculations

What is variability?

Statistics with Excel

What’s Due In Part 2: Statistics & Variability

  • Statistics Notes
  • Linear Dimension Analysis
  • Variability Assignment
  • Fling Machine Analysis
  • Benshoof’s Check-off

Here’s what’s due in Part 2: Statistics & Variability

  1. Watch the Statistics Calculations & Variability videos and take good notes in your engineering notebook
  2. Complete the first linear dimensions variability assignment including the Excel analysis
  3. Complete the Variability Statistics assignment
  4.  Complete the Fling Machine design challenge and Excel analysis
  5. Benshoof’s check-off of your completed work

Part 3: Puzzle Cube

Design, measure, and create a puzzle cube toy!

Puzzle Cube Overview

The final part of our unit in measurement and statistics involves the design and creation of a small logic puzzle.  The puzzle cube is made of 27 small wooden cubes that are glued together to form puzzle pieces.  When assembled correctly, the pieces make a perfect 3x3x3 cube.  Your job is to design the shape of your puzzle pieces, find blocks that fit the necessary parameters, and assemble your toy.  You’ll then collect data on how long it takes people to solve your puzzle so that you can analyze the difficulty of the puzzle.


 Take a page of notes on the Puzzle Cube Overview in your engineering notebook.  Clarify the challenge, the criteria, and the constraints!

 Plan out your 5 puzzle pieces and sketch them in your notebook

 Find 27 cubes that fit the necessary parameters and assemble your puzzle cube

 Have 10 students try to solve your puzzle cube and time them.  Record their time in your notebook and use Excel to analyze the statistics

 Have Mr. Benshoof confirm your puzzle cube

 If you have time, decorate your puzzle cube and make a box for it

What’s Due In Part 3: Puzzle Cube

  • Puzzle Cube Notes
  • Puzzle Piece Sketches
  • Build Your Puzzle
  • Excel Analysis
  • Mr. Benshoof’s Confirmation
  • + Decorate & Package!

Here’s what’s due in Part 3: Puzzle Cube

  1. Take a page of notes on the Puzzle Cube Overview in your engineering notebook.
  2. Plan and sketch your puzzle pieces
  3.  Collect properly sized cubes and build your puzzle
  4. Test your puzzle cube and analyze the data in Excel
  5. Have Mr. Benshoof confirm your puzzle cube
  6.  Add decorations and a custom box if you have time!

Double Check: Unit Expectations

Check what you need to have completed by the unit deadline

The purpose of this unit is to reinforce some of the basic math and statistics that engineers need to use when dealing with measurements.  The major focus is on units and unit conversions, with a secondary focus on using Excel to calculate measures of center and variability.  Together, these ideas get applied when we make a very precise puzzle cube and test its difficulty using statistics.  When you’re done, you will have gotten some good math practice and also built a fun puzzle!

Engineering Notebook:

(Part 1) You should have taken some detailed notes on measurement & units

 (Part 2) You should have taken some good notes about statistics & variability

(Part 3) You should have taken a page of careful notes on the puzzle cube overview

(Part 3) You should have drawn your puzzle cube pieces along with dimensions using isometric sketching

Building & Making:

(Part 1) You should have completed the measurement activity and the Automoblox Dimensioning Activity

 (Part 1) You should have completed the Unit Conversion Assignment

(Part 2) You should have completed the measurement & Fling Machine statistics analysis activities

 (Part 2) You should have completed the Variability Statistics Assignment

(Part 3) You should have planned and built your puzzle cube toy!

 (Part 3) 10 students should have tried to solve your puzzle, and you should have calculated the proper statistics in Excel

Checkpoints & Quizzes:

(Part 1) Mr. Benshoof should have checked-off your measurement and unit assignments

 (Part 2) Mr. Benshoof should have checked-off your statistics and variability assignments

 (Part 3) Mr. Benshoof should have confirmed your completed puzzle cube and statistical analysis