LESSON-2-Accuracy-and-Precision.pptxdsdssd

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1. Accuracy and Precision Lesson 2

2. Target competencies Differentiate accuracy from precision (STEM_GP12EU-Ia2) Differentiate random errors from systemic errors. (STEM_GP12EU-Ia3) Estimate errors from multiple measurements of physical quantity. (STEM_GP12EU-Ia4)

3. Let’s connect! A good result of measurement is achieved if error is less or limited Accuracy and Precisio n are prime consideration in every measurement made. Errors in measurement are unavoidable due to several factors and it can be random or systematics depending on how measurement is made.

4. Let’s connect! Dart! Imagine you are playing Dart and given five darts to hit the target. You are given four chances to play. The results of each play is illustrated below. 1 2 3 4

5. Let’s connect! Dart! interpretation Illustration 1 2 3 4 Accuracy Poor Good Poor Good Precision Poor Poor Good good 1 2 3 4

6. a C curacy C- Correct p R ecision R- Repeatable

7. Let’s discover! Have you tried cooking but failed with its taste? Did you use the right measurement of the ingredients? What could be the factors for the error(s) met?

8. Factors why errors occur in every measurement The kind of measuring device use. Methods in getting the measurement. Condition under which the measurement is made.

9. TYPES OF ERROR Random Error or unsystematic error. Random error has no pattern, it is inconsistent. Example, in your first reading, you taught it might be too small, then the next reading might be too large. So nobody can predict random error and this cannot be avoided, even scientist doing their experiments.

10. TYPES OF ERROR 2. Systematic Error Systematic error is consistent and repeatable error due to the kind of measuring device used as mentioned above. It is also due to flawed experimental design.

11. To minimize errors in measurement, more trials must be made. The mean or average value of these trials will be taken to represent the entire set of data. From this, the degree of accuracy and precision can be determined.

12. ACCURACY Accuracy is the closeness or nearness of measurement to the accepted value. In the imaginary dart game, the bullseye is the accepted value. The closer your measurement to the accepted value, the more accurate is your measurement. accuracy is express in terms of absolute error or percentage of error.

13. ACCURACY accuracy is express in terms of absolute error or percentage of error. =   Percentage of error = X 100 %   Percentage of accuracy = 100 % - %or error Where: - absolute error O – observed value/ measured value A – accepted value T he parallel lines indicates that the value is absolute.  

14. EXAMPLE 1. An experimenter dropped a stone from a 5 story building and hit the ground, taking the time to fall of 3 seconds. Based from the data collected, the experimenter was able to measure acceleration of the stone to be 9.7 m/ . The actual value of the acceleration due to gravity is 9.8 m/ . What is the percentage of accuracy of the experiment?   Given: Accepted value (A) = 9.8 m/ Observed value (O) = 9.7 m/   Solution: = = l 9.7 m/ - 9.8 m/ l = 0.1 m/   Percentage of error = X 100 % = x 100 % = 1.02 %   Percentage of accuracy = 100% - % error = 100 % - 1.02 % = 98.98 %

15. Example A length was measured to be 6.8 feet. However, the actual length was 6.72 feet. What is the absolute error, percentage error and Percentage of accuracy for the measured? Given: Accepted value (A) = 6.72 feet Observed value (O) = 6.8 feet Solution: = =l 6.8 ft - 6.72 ft l = 0.08 ft   Percentage of error = X 100 % = x 100 % = 1. 19 %   Percentage of accuracy = 100% - % error = 100 % - 1.19 % = 98.81 %

16. Example My height is measured as 182 cm but my actual height is 174 cm. What is the absolute error, percentage error and Percentage of accuracy for the measured? Given: Accepted value (A) = 174 cm Observed value (O) = 182 cm Solution: = = l 182 cm- 174 cm l = 8 cm   Percentage of error = X 100 % = x 100 % = 4.59 % or 4.60 %   Percentage of accuracy = 100% - % error = 100 % - 4.60 % = 95.4 %

17. Example I measured 33 g of a substance but there is actually 40 g. What is the absolute error, percentage error and Percentage of accuracy for the measured? Given: Accepted value (A) = 40 g Observed value (O) = 33 g Solution: = = = 7g   Percentage of error = X 100 % = x 100 % = 17.5 %   Percentage of accuracy = 100% - % error = 100 % - 17.5 % = 82.5 %

18. PRECISION Precision is the agreement of several measurements made in the same way. In illustration #3 of the dart game, the darts flocked in almost the same area, though far from the bullseye, we can say that the measurement made are precise. Precision is expressed in terms of deviation or percentage of deviation. 3

19. PRECISION Precision is expressed in terms of deviation or percentage of deviation. The formula below will help you determine the precision of one’s measurement. =   % of deviation = x 100 %   Percentage of precision = 100 % - % of deviation Where: - Absolute deviation O – Observed value/ measured value M – mean (ave) of several measurement   =measured value – accepted value   x 100 %  

20. EXAMPLE 2. A student is doing a laboratory experiment about falling body. He obtained three trials in measuring the time of fall of a ball 3 meters above the ground. The measurement are summarize below: Trial 1 = 0.80 s Trial 2 = 0.79 s Trial 3 = 0.77 s What is the percentage of precision of the student? Solution: First , determine the average of the three trials. M = = 0.787 s  

21. =0.001 s EXAMPLE 2. A student is doing a laboratory experiment about falling body. He obtained three trials in measuring the time of fall of a ball 3 meters above the ground. The measurement are summarize below: Trial 1 = 0.80 s Trial 2 = 0.79 s Trial 3 = 0.77 s What is the percentage of precision of the student? Then , find the average absolute deviation. AD=   =  

22. EXAMPLE 2. A student is doing a laboratory experiment about falling body. He obtained three trials in measuring the time of fall of a ball 3 meters above the ground. The measurement are summarize below: Trial 1 = 0.80 s Trial 2 = 0.79 s Trial 3 = 0.77 s What is the percentage of precision of the student? Solve for the percentage of deviation % of deviation = x 100 % = X 100 % = 0.13 %   Percentage of precision = 100 % - % of deviation = 100 % - 0.13% = 99.87 %

23. Example Problem Two students measure the density of an unknown metal three times each. Below are the data. Student 1 Student 2 6.34 7. 11 6.31 7.19 6.30 7.12 Student 1 Student 2 Calculate the error and percent for student 1. The accepted value for density of the metal is 7. 08  

24. Two students measure the density of an unknown metal three times each. Below are the data. Student 1 6.34 6.31 6.30 Student 1 Solution: First , determine the average of the three trials. M = = 6.32   The accepted value for density of the metal is 7. 08   = measured value – accepted value = 6.32 - 7.08 = -0.76   = x 100 = x 100 = - 11 %  

25. Two students measure the density of an unknown metal three times each. Below are the data. Solution: First , determine the average of the three trials. M = = 7.14   The accepted value for density of the metal is 7. 08   = measured value – accepted value = 7.14 - 7.08 = 0.06   = x 100 = x 100 = 0.85%   Student 2 7. 11 7.19 7.12 Student 2

26. B. In an outdoor experiment, Tokyo is testing his football robot kicking a ball and hitting the goal. She obtained 4 trials measuring the velocity of the ball. The measurements are summarized below: Trial 1: 4.712 m/s Trial 2: 5.080 m/s Trial 3: 5.210 m/s Trial 4: 4.810 m/s What is the percentage precision, error and percentage of error (A=4.9 m/s) of the robot? SHOW COMPLETE SOLUTION. A. John and Sally performed an experiment to measure the density of aluminum ( 2.7 g/mL ). John’s measurement is 2.649 g/ mL while Sally’s measurement is 2.731 g/ mL . Who is more accurate between the two. Compute of the percentage of accuracy for both measurements. SHOW COMPLETE SOLUTION.

27. Quiz 1. In an outdoor experiment, Tokyo is testing his football robot kicking a ball and hitting the goal. She obtained 3 trials measuring the velocity of the ball. The measurements are summarized below: Trial 1: 4.712 m/s ,Trial 2: 5.080 m/s ,Trial 3: 5.210 m/s 2. A length was measured to be 165cm. However, the actual length was 180cm. What is the absolute error, percentage error and Percentage of accuracy for the measured? Express the following values in scientific notation. Express the following values in decimal notation. 0.00290 6281 0.00700 6 x 10 7 4.20 x 10 -6 4.20 x 10 6