1. Accuracy and Precision
Understanding measurements

2. Directions Click F5 to view this power point as a presentation.
This allows you to see the practice math problems done step by step.
If you get the presenter view (see below), you can click on the three dots and then click hide presenter view.

3. Some mathematical STATEMENTS are 100% true
Understanding Error
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.

4. Error can occur because:
The equipment isn’t working properly
The person using the equipment is not using it properly
Something interfered with the equipment.

5. Examples of Interference
Vibrations, drafts, changes in temperature, electronic noise etc.

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

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

8. 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.

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

10. Absolute Value Symbol | |
The two vertical lines represent absolute value.
Absolute value is the magnitude of a real number without regard to its sign.
What does this mean?
After solving, if you have a negative number, ignore the negative sign.
|15-18| = 3
15-18 = -3 but because of the || symbols, you ignore the negative sign and only record the 3!

11. Example #1 Test Results
Let’s suppose you took a 75 point test. You earned 65 points.
What is your absolute error in this case?
Abs Error = Accepted Value – Measured Value
= 75 – 65
= 10 points

12. Example #1 Test Results How large was your error for THIS test?
(in other words, what was your relative error?)
Rel Error = (Abs Error ÷ Accepted Value) x 100%
= (10/75)x100%
= %

13. Size of Error – Absolute vs Relative:
is the error big enough to be of concern or small enough to be unimportant?
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 pounds but it really weighs pounds.
Size of an error

14. AE = |accepted – measured| RE = (AE / accepted) x 100
AE = |accepted – measured| RE = (AE / accepted) x 100 *Round to the hundredths (2 decimal places)
Example A: 4 pounds is the measured value (what you got). AE = |6-4| AE = 2 pounds RE = (2 / 6) x 100 RE = 33.33%
Example B: pounds is the accepted value (set by car manual).
AE = | |
AE = 2 pounds
RE = (2 / 3132) x 100
RE = 0.06%

15. In which example was a more accurate measurement made?
Example B had a more accurate measurement because their Relative Error was lower.
Both had the same Absolute Error, but by changing it to a percentage (Relative Error), we can compare the error to the accepted value and get a better idea of which is more accurate.
Remember, accuracy is the opposite of error so the lower the error, the more accurate. The higher the error, the less accurate.
The percentage of accuracy would be 100 – RE, therefore A had a 66.67% accuracy while B had a 99.94% accuracy.

16. 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.

17. Deviation
Described mathematically using Absolute Deviation and Relative Deviation

18. 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.

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

20. AD (absolute deviation) and RD (relative deviation)?
Example The class average for a test was 89, and you scored a 96. What was your
AD (absolute deviation) and RD (relative
deviation)?
AD = |Average Value – Measured Value| =
= 7 points
RD = (Abs Dev / Average Value) x 100%
= (7/89)x100%
= %

21. ACCURACY vs. PRECISION
Accuracy is closeness to ACCEPTED VALUE, or being correct
Precision is closeness to the AVERAGE, or being close together

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

23. Accuracy vs. Precision
Medium accuracy - mark is averaged around the target.
Low Precision - grouping is scattered.

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

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

26. 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
A high Relative Error means low accuracy.
You can’t know accuracy unless you know the Accepted Value
If your measurements are inaccurate, you may want to take them again.

27. Summary
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
A low Relative Deviation means high precision.
Both Relative Error and Relative Deviation show a percentage, which allows us to compare two sets of data to see who is more accurate (using RE) or more precise (using RD).