Accuracy and Precision: A Game of Darts

 

Subject Area

 Physical Science, Quantitative Reasoning

Age or Grade

Elementary school to High school

Estimated Length

 One 45 minute class period

Prerequisite knowledge/skills

 Arithmetic, some concepts of simple statistics

Description of New Content

 This lesson will give a hands-on introduction to the concepts of 'accuracy' and 'precision'. 

Goals

 Students will gain a deeper understanding of the distinction between 'accuracy' and 'precision' as they are used scientifically.

Materials Needed

One dart board, with magnetic darts.

Procedure

 

 

 

Opener

Stand close to the dart board and throw four darts into one corner of the board, as far away from the bull’s-eye as possible, making sure to try and land them as close to each other as possible.  Ask the class for an evaluation of your performance.  Most will probably remark that the throws were quite poor.  Tell the students that, while none of the throw came very close to bull's-eye, they were, however, very precise.  Some students will probably express confusion at this.  

Keeping the first dart board as is, stand close to the second board and throw four darts relatively close to the bull’s-eye, making sure to space the landing point out as much as possible.  Again, ask the students to evaluate your performance.  Remark that while you are happy to have made it close to the bull’s-eye, your precision is much worse this time around.

Again, some students will express confusion.  Ask them to explain why they are confused.  It is likely that the source of the confusion is that they have not learned the distinction between accuracy and precision.

Development

Have the students break into teams of two members each.  Announce that each team will throw two darts at the board and there will be prizes for the most accurate and the most precise teams. 

Before the competition begins, ask the students how to go about measuring the accuracy and precision of the throws.  After some guidance, students should suggest assessing accuracy by measuring the distances between the bull’s-eye and each throw, while assessing precision by measuring the distance between the two throws.  

Have each team throw its two darts from approximately 10 feet from the board, measuring the distance of each dart from the bull’s-eye as well as the distance between the darts.  Have all students record this data as the competition is taking place.

Closure

At the end of the competition, have the students spend a few minutes calculating each team's average distance from the bull’s-eye.  Have them use these calculations to determine the winning teams in terms of accuracy and precision.  

Return to the central theme of the lesson.  By this point, students should understand that there is a significant distinction between accuracy and precision, and that it is possible to be extremely accurate without being precise, and vice versa.  

 

Evaluation

 Use student feedback to improve the darts competition.  

Accompanying worksheet:

Name: _________________

 

Accuracy and Precision: A Game of Darts

 

Team 1

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

Team 2

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

 Team 3

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

 Team 4

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

 Team 5

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

Team 6

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

Team 7

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

Team 8

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

Team 9

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

 Team 10

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

 Team 11

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

 Team 12

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

 Team 13

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

Team 14

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:

Team 15

 

First Throw

Second Throw

Average

Distance from Bull’s-eye

 

 

 

 Distance between the location of both throws:


Questions:

 

  1. Which is a measure of accuracy, the distance of the throws from the bull’s-eye or the distance between the throws themselves?  Which is a measure of precision?  Explain your reasoning in both cases.

 

  1. Which team’s dart throwing was the most accurate, and how do you know?  Which team’s throws were the least accurate?

 

  1. Which team’s dart throwing was the most precise, and how do you know?  Which team’s throws were least precise? 

 

  1. A chemist is in need of a new electronic scale to measure the mass of the chemicals to be used in his experiments.  He is given two scales from which to choose.   Before he makes his decision, he uses both scales to measure the mass of a sample of lead whose mass is known to be 10.437 grams.  He measures the mass of the lead sample three times with each scale, and then makes his decision.  Using the first scale, he obtains the following readings: 10.7122 g, 10.7158 g, and 10.7103.  On the second scale he measures:  10.54 g, 10.46, and 10.37 g.  Which scale is more precise?  Which is more accurate?  Which scale do you think the chemist should choose for his lab? 

Extensions

 Use the concepts of this lesson to introduce the concepts of systematic and random error.  Explain how, all things being equal, a systematic error will usually produce more precise data than random error.  Also explain that, in some cases, extremely precise yet inaccurate data may be more desirable than data that is accurate yet imprecise.  Highly precise measurements that are significantly inaccurate are often the product of systematic errors which may be subsequently corrected by simple calibration procedures, renderring the calibrated data both highly accurate and precise. 

References