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.

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

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: 3.84 ± .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

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

Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Example A washer for a spaceships needs to be 85.100 ± .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 85.301 mm 85.023 mm 85.298 mm 85.187 mm 85.299 mm 85.102 mm

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 85.301 mm 85.023 mm 85.298 mm 85.187 m 85.299 mm 85.102 mm

Example Accepted Value 85.0 to 85.2 Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Example Company A’s part ranges from 85.023 mm to 85.187 mm Company B’s data ranges from 85.298 mm to 85.301 mm The accepted length of the washer is 85.1 ± .1 mm Accepted Value 85.0 to 85.2

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

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 = 85.104 mm Company A Company B 85.104mm 85.301 mm 85.023 mm 85.298 mm 85.187 mm 85.299 mm 85.102 mm Company B: Mean = x B = 85.2998 mm

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 = |85.104 mm – 85.100 mm| = 0.004 mm Error |+0.004| x A = 85.104 x B = 85.2998 Accepted Value 85.100

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 = |85.2998 mm – 85.100 mm| = 0.1998 mm Error A |+0.004| x A = 85.104 x B = 85.2998 Error B |+0.1948| Accepted Value 85.100

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 = |85.2998 mm – 85.100 mm| = 0.1998 mm Error A |+0.004| 0.004 x A = 85.104 Error B |+0.1948| 0.1948 x B = 85.2998 Accepted Value 85.100

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 .1998 Company A is more accurate

85.100 ± .100 Another way to test accuracy 4 out of 4 parts from company A are between 85.0 and 85.2 4/4 x 100 = 100% 0 out of 4 parts from company b are between 85.0 and 85.2 0/4 x 100 = 0% Company A is more accurate Company A Company B 85.104mm 85.301 mm 85.023 mm 85.298 mm 85.187 mm 85.299 mm 85.102 mm

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

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= 85.187 – 85.102 = .085 mm Student A Student B 85.104mm 85.301 mm 85.023 mm 85.298 mm 85.187 mm 85.299 mm 85.102 mm Company B: RB = 85.301 – 85.298 = .003 mm

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