1. Accuracy and Precision
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Accuracy and Precision
of Measurement
Introduction to Engineering Design
© 2012 Project Lead The Way, Inc.

2. Recording Measurements
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Recording Measurements
A measurement always includes a value
A measurement always includes units
A measurement always involves uncertainty
A measurement is the best estimate of a quantity
A measurement is useful if we can quantify the uncertainty

3. Uncertainty in Measurements
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Uncertainty in Measurements
Another (more definitive) method to indicate uncertainty is to use plus/minus notation
Example: ± .05 cm
3.79 ≤ true value ≤ 3.89
This means that we are certain the true measurement lies between 3.79 cm and 3.89 cm

4. Accuracy and Precision
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Accuracy and Precision
Accuracy = the degree of closeness of measurements of a quantity to the actual (or accepted) value
Precision (repeatability) = the degree to which repeated measurements show the same result
High Accuracy
Low Precision
Low Accuracy
High Precision
High Accuracy
High Precision

5. Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Example
A washer for a spaceships needs to be ± .100 mm or it could fail during launch. Two companies make a set of washers. Which company would you buy from one if you were in charge of NASA?
Company A
Company B
85.104mm mm mm mm mm mm mm

6. Example Plot Company A’s data on a number line
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Example
Plot Company A’s data on a number line
Plot Company B’s data on a number line
Company A
Company B
85.104mm mm mm mm m mm mm

7. Example Accepted Value 85.0 to 85.2
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Example
Company A’s part ranges from mm to mm
Company B’s data ranges from mm to mm
The accepted length of the washer is ± .1 mm
Accepted
Value 85.0 to 85.2

8. Example Which company’s part is more accurate?
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Example
Which company’s part is more accurate?
Which company’s part is more precise?
Which company should have their washer in the spaceship?
Company A
Company B
Company A

9. Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Quantifying Accuracy
The accuracy of a measurement is related to the error between the measurement value and the accepted value. Mathematically accuracy can be measured by the Error Equation
Error = |mean of measured value – accepted value|
Company A:
Mean = x A = mm
Company A
Company B
85.104mm mm mm mm mm mm mm
Company B:
Mean = x B = mm

10. Quantifying Accuracy Calculate the error of Company A’s washer
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Quantifying Accuracy
Calculate the error of Company A’s washer
Error A = |mean of measured values – accepted value|
Error A = | mm – mm| = mm
Error
|+0.004|
x A =
x B =
Accepted
Value
85.100

11. Quantifying Accuracy Calculate the error of Company B’s washer
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Quantifying Accuracy
Calculate the error of Company B’s washer
Error B = |mean of measured values – accepted value|
Error B = | mm – mm| = mm
Error A
|+0.004|
x A =
x B =
Error B
| |
Accepted
Value
85.100

12. Quantifying Accuracy Calculate the error of Company B’s washer
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Quantifying Accuracy
Calculate the error of Company B’s washer
Error B = mean of measured values – accepted value
Error B = | mm – mm| = mm
Error A
|+0.004|
0.004
x A =
Error B
| |
0.1948
x B =
Accepted
Value
85.100

13. Company A has an error of. 004 and Company B has an error of
Company A has an error of .004 and Company B has an error of Company A is more accurate

14. ± .100
Another way to test accuracy 4 out of 4 parts from company A are between 85.0 and /4 x 100 = 100% 0 out of 4 parts from company b are between 85.0 and /4 x 100 = 0% Company A is more accurate
Company A
Company B
85.104mm mm mm mm mm mm mm

15. Quantifying Precision
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Quantifying Precision
Precision is related to the variation in measurement data

16. Quantifying Precision
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Quantifying Precision
The precision of a measurement device can be related to the rang of repeated measurement data. Mathematically range can be used to measure precision.
Range = high - low
Company A:
RA= – = .085 mm
Student A
Student B
85.104mm mm mm mm mm mm mm
Company B:
RB = – = .003 mm

17. Company A has a range of .085 mm and Company B has a range of .003 mm
Company B is more precise