Day 1: Accuracy vs. Precision.

 

Let's begin with an explanation of the difference between accuracy and precision. Accuracy refers to how close a measurement is to the true value of what is being measured. Precision refers to how close measurements of the same quantity are to each other, even if they are not close to the true value. For example, the darts on the dart boards below represent sets of measurements. A bull's eye represents a perfect measurement--a measurement exactly the same as the true value.

 

NEITHER PRECISE NOR ACCURATE

Since none of the darts are close to the bull's eye, the measurements they represent are not very accurate. Also, since the darts are not very close to each other, the set of five measurements here is not very precise either.

 

BOTH PRECISE AND ACCURATE

 

The measurements are all close to the true value, so they are accurate. Also, the measurements are all close to each other, so they are precise.

 

PRECISE BUT NOT ACCURATE

 

Since all of the measurements are close together, they are precise, but since they are not close to the true value, they are not accurate.

Since all of the measurements are close together, they are precise, but since they are not close to the true value, they are not accurate.

Activity 1:

See if you can draw and describe (as done in the pictures and captions above) the case where a set of measurements is fairly accurate but not very precise.

Activity 2:

For Dave students: Each student measures the diameter of the cylinders various cars and record the measurements in a spreadsheet as following:

 

CAR 1

Cylinder
Diameter

Student Number

1

2

3

4

5

6

7

8

1

______

______

______

______

______

______

______

______

2

______

______

______

______

______

______

______

______

3

______

______

______

______

______

______

______

______

4

______

______

______

______

______

______

______

______

5

______

______

______

______

______

______

______

______

6

______

______

______

______

______

______

______

______

7

______

______

______

______

______

______

______

______

8

______

______

______

______

______

______

______

______

 

FOR ALL STUDENTS:

  1. Were the Measurements accurate? Why or why not?
  2. Were the measurements precise? Why or why not?
  3. Do you see any similarities or differences among cars manufactured by different companies?
    1. The equipment, tools, and technology available to you when you make measurements will affect your accuracy and precision. Depending on the design and age of a measuring instrument as well as other factors such as the skill of the people using the instruments, real-life measurements can be accurate or inaccurate, precise or imprecise, or any combination of these.
  4. What variable in your experiment corresponds to the reliability of your measurements (in terms of both accuracy and precision)?

For high school students in DuPage county: Draw a dart board on a sheet of paper and set it on the ground. Have each member in a group of about five drop a penny on the target from a height of about one meter, aiming for the bull's eye. Each penny represents a measurement of some quantity, say, the compression in the cylinder.

  1. What does the bull's eye represent?
  2. How many compression measurements were made?
  3. Were the measurements accurate? Why or why not?
  4. Were the measurements precise? Why or why not?

    Now simulate a new set of measurements by dropping pennies from a height of 2 meters.

  5. Has the accuracy and/or precision of your measurements changed? If so, how. Explain.
    1. The equipment, tools, and technology available to you when you make measurements will affect your accuracy and precision. Depending on the design and age of a measuring instrument as well as other factors such as the skill of the people using the instruments, real-life measurements can be accurate or inaccurate, precise or imprecise, or any combination of these.

 

Activity 3:

For high school students in DuPage county: Suppose your team is challenged to determine the mass of an object using a balance. Each member of the team measures the mass on the same balance. Here are you data:

Team member

Mass in Grams

1

39.97

2

40.06

3

39.98

4

39.97

5

40.02

Your team decides to report your mean (average) mass, which is 40.00g. Your instructor then informs you, however, that the actual mass is 45.00g.

  1. Who (or what) would your instructor blame for the fact that your reported mass was too low by 5/45 = 1/9 or about 11%?
  2. What can you conclude about the precision of your balance?
  3. What can you conclude about the accuracy of your balance?
  4. How might this type of error (called a systematic error) have been avoided?

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