1. Accuracy and Precision Understanding measurements

2. Some mathematical STATEMENTS are 100% true (ex: I have 2 sisters, you are 14 years, 7 months, and 6 days old, etc.) But … every MEASUREMENT encounters ERROR. Understanding Error

3. Examples of Measurement Error Vibrations, drafts, changes in temperature, electronic noise etc. Limitations of the measuring instrument

4. Accuracy When dealing with data collection, we must describe the accuracy of the measurements

5. Accuracy Is Correctness! how close your measurement is to the accepted value. A highly accurate measurement will be very close to the accepted value.

6. Error ERROR is Incorrectness! The size of the experimental error can be described using mathematics: Absolute Error (or AE for short) shows how far away the measurement is from the accepted value Relative Error (or RE for short) turns the size of the error into a percentage.

7. Formulas Absolute Error = | Accepted Value – Measured Value | Relative Error = | Absolute Error | x 100 Accepted Value

8. Example #1Test Results Let’s suppose you took a 75 point test. You earned 65 points. What is your absolute error in this case?

9. Example #1Test Results How large was your error for THIS test? (in other words, what was your relative error?)

10. Find the AE and RE for each: A. You ask for 6 pounds of hamburger and receive 4 pounds. B. A car manual gives the car weight as 3132 pounds but it really weighs 3130 pounds. Size of Error – Absolute vs Relative: is the error big enough to be of concern or small enough to be unimportant?

11. PRECISION It is consistency and agreement among many of the same measurements How close measurements are to each other Compares one measurement to the AVERAGE of the group of measurements. How spread out the data is The smaller the scatter, the greater the precision.

12. Deviation Described mathematically using Absolute Deviation and Relative Deviation

13. Absolute Deviation (AD) shows how far away one measurement is from the average value of many measurements Relative Deviation (RD) turns the size of the deviation into a percentage.

14. Absolute and Relative Deviation Absolute Deviation = | Average Value – Measured Value | Relative Deviation = | Absolute Deviation| x 100 Average Value

15. Example The class average for a test was 89, and you scored a 96. What was your AD (absolute deviation) and RD (relative deviation)?

16. ACCURACY vs. PRECISION Accuracy is closeness to ACCEPTED VALUE Precision is closeness of a set of measurements to each other or an AVERAGE

17. Accuracy vs. Precision Low Accuracy - but the mark misses the target. High precision - grouping is tight.

18. Accuracy vs. Precision Somewhat accurate - mark is averaged around the target. Low Precision - grouping is scattered.

19. Accuracy vs. Precision Low Accuracy - mark misses the target. Low Precision - grouping is scattered.

20. Accuracy vs. Precision High Accuracy - mark is averaged around the target. High precision - grouping is tight.

21. Summary All measurements have uncertainty Accuracy describes how close a measurement is to an ACCEPTED VALUE Accuracy is mathematically described using Absolute Error and Relative Error Precision describes how close a measurement is to the AVERAGE VALUE of a set of data Precision is mathematically described using Absolute Deviation and Relative Deviation