1. Copyright © 2014 Pearson Education. All rights reserved. 2.2-1 2.2 Dealing with Errors LEARNING GOAL Understand the difference between random and systematic errors, be able to describe errors by their absolute and relative sizes, and know the difference between accuracy and precision in measurements.

2. Copyright © 2014 Pearson Education. All rights reserved. 2.2-2 Two types of Measurement Errors Slide 1.1- 2

3. Copyright © 2014 Pearson Education. All rights reserved. 2.2-3 Slide 2.2- 3 Types of Error: Random and Systematic Two Types of Measurement Error Random errors occur because of random and inherently unpredictable events in the measurement process. Systematic errors occur when there is a problem in the measurement system that affects all measurements in the same way.

4. Copyright © 2014 Pearson Education. All rights reserved. 2.2-4 Slide 2.2- 4

5. Copyright © 2014 Pearson Education. All rights reserved. 2.2-5 EXAMPLE 1 Errors in Global Warming Data Scientists studying global warming need to know how the average temperature of the entire Earth, or the global average temperature, has changed with time. Consider two difficulties in trying to interpret historical temperature data from the early 20th century: (1) Temperatures were measured with simple thermometers and the data were recorded by hand, and (2) most temperature measurements were recorded in or near urban areas, which tend to be warmer than surrounding rural areas because of heat released by human activity. Discuss whether each of these two difficulties produces random or systematic errors, and consider the implications of these errors. Slide 2.2- 5

6. Copyright © 2014 Pearson Education. All rights reserved. 2.2-6 Size of Error: Absolute versus Relative Absolute and Relative Errors The absolute error describes how far a claimed or measured value lies from the true value: absolute error = claimed or measured value – true value The relative error compares the size of the absolute error to the true value. It is often expressed as a percentage: relative error = x 100% absolute error true value Slide 2.2- 6

7. Copyright © 2014 Pearson Education. All rights reserved. 2.2-7 EXAMPLE 2 Absolute and Relative Error Find the absolute and relative error. Your true weight is 100 pounds, but a scale says you weigh 105 pounds. Solution: Slide 2.2- 7

8. Copyright © 2014 Pearson Education. All rights reserved. 2.2-8 Describing Results: Accuracy and Precision Definitions Accuracy describes how closely a measurement approximates a true value. An accurate measurement is close to the true value. (Close is generally defined as a small relative error, rather than a small absolute error.) Precision describes the amount of detail in a measurement. Slide 2.2- 8

9. Copyright © 2014 Pearson Education. All rights reserved. 2.2-9 Slide 1.1- 9 Accuracy and Precision

10. Copyright © 2014 Pearson Education. All rights reserved. 2.2-10 Slide 1.1- 10 Accuracy and Precision

11. Copyright © 2014 Pearson Education. All rights reserved. 2.2-11 EXAMPLE 3 Accuracy and Precision in Your Weight Suppose that your true weight is 102.4 pounds. The scale at the doctor’s office, which can be read only to the nearest quarter pound, says that you weigh 102¼ pounds. The scale at the gym, which gives a digital readout to the nearest 0.1 pound, says that you weigh 100.7 pounds. Which scale is more precise? Which is more accurate? Slide 2.2- 11

12. Copyright © 2014 Pearson Education. All rights reserved. 2.2-12 Summary: Dealing with Errors The ideas we’ve covered in this section are a bit technical, but very important to understanding measurements and errors. Let’s briefly summarize how the ideas relate to one another. Errors can occur in many ways, but generally can be classified into one of two basic types: random errors or systematic errors. Whatever the source of an error, its size can be described in two different ways: as an absolute error or as a relative error. Once a measurement is reported, we can evaluate it in terms of its accuracy and its precision. Slide 2.2- 12