1. LECTURER PROF.Dr. DEMIR BAYKA AUTOMOTIVE ENGINEERING LABORATORY I

2. STATISTICAL TREATMENT OF EXPERIMENTAL DATA DISCRETE FREQUENCY DISTRIBUTIONS

4. FREQUENCY F( n j ) IS THE NUMBER OF OCCURRENCE OF THE j th MEASUREMENT VALUE j1234567 value13141516171819 nj1321021

5. j1234567 value13141516171819 nj1321021

6. RELATIVE FREQUENCY f j IS THE RELATIVE VALUES OF NUMBER OF OCCURRENCES WITH RESPECT TO TOTAL NUMBER OF OCCURRENCES &

7. RELATIVE FREQUENCY f j THERE ARE 7 GROUPS ie m = 7

8. FREQUENCY GRAPH

9. MEASURES OF CENTRAL TENDENCY ARITHMETIC MEAN IT PROVIDES THE BEST ESTIMATE OF AN UNBIASED DISTRIBUTION OF DATA

10. MEASURES OF CENTRAL TENDENCY MEDIAN IT IS THE VALUE AT THE MIDDLE POSITION OF A DISTRIBUTION OF DATA IT IS USUALLY USED WHEN THE DISTRIBUTION IS BIASED

11. MEASURES OF CENTRAL TENDENCY MODE IT IS THE VALUE HAVING THE HIGHEST FREQUENCY IN THE SAMPLE DISTRIBUTION

12. GEOMETRIC MEAN (Log - Mean) IT IS IMPORTANT WHEN DEALING WITH RATIOS OR PERCENTAGES

13. HARMONIC MEAN

14. QUADRATIC MEAN (ROOT - MEAN - SQUARE )

15. REPEATED MEASUREMENTS TIME  t = 0.5 s 8.60 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.65 8.70 8.20 THIS IS ASSUMED TO REPRESENT THE TRUE VALUE AS BEST AS POSSIBLE 8.45 TAKE AVERAGE 48.49 58.41 6 8.58 78.43 88.53 3 8.48 98.65 108.40 208.35 18.68 2 8.2519 8.56 188.28 178.23 138.31 118.48 128.37 168.50 15 8.50 148.52 START SAMPLING END SAMPLING RATE OF SAMPLING 5 ms (200 kHz)

16. MEASURES OF DISPERSION OF DATA VARIANCE (MEAN SQUARE DEVIATION )

18. MEASURES OF DISPERSION OF DATA STANDARD DEVIATION

19. REPEATED MEASUREMENTS TIME  t = 0.5 s 8.60 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.65 8.70 8.20 8.45 TAKE AVERAGE 8.45 +  = 8.57 8.45 -  = 8.33 65%  = 0.122352

20. MEASURES OF DISPERSION OF DATA RANGE IT IS THE DIFFERENCE BETWEEN THE LARGEST AND SMALLEST VALUES OF THE ENTIRE SET OF DATA

21. MEASURES OF DISPERSION OF DATA AVERAGE DEVIATION

22. UNBIASED ESTIMATES

23. A) THE SAMPLE MEAN x IS THE BEST AVAILABLE ESTIMATE OF THE UNKNOWN MEAN OF THE UNIVERSE 

24. UNBIASED ESTIMATES A) THE BEST AVAILABLE ESTIMATE OF THE UNKNOWN STANDARD DEVIATION OF THE UNIVERSE IS GIVEN BY 

25. THE USE OF THIS EXPRESSION BECOMES IMPORTANT ESPECIALLY WHEN n IS SMALL FOR LARGE VALUES OF n HOWEVER,  >  sample ALWAYS

26. C) IF MORE THAN ONE ( SAY m ) EQUAL-SIZED RANDOM SAMPLES ARE DRAWN FROM THE SAME UNIVERSE, THEN THEIR RESPECTIVE MEANS AND STANDARD DEVIATIONS ARE EXPECTED TO BE EQUAL TO EACH OTHER

28. STANDARD ERROR OF THE MEAN THIS QUANTITY REPRESENTS THE STANDARD DEVIATION OF x FROM 

29. REPEATED MEASUREMENTS TIME  t = 0.5 s 8.60 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.65 8.70 8.20 8.45 8.45 +  = 8.57 8.45 -  = 8.33 65%  = 0.122352

30. REPEATED MEASUREMENTS TIME  t = 0.5 s 8.60 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.65 8.70 8.20 8.45  = 0.122352 8.48 8.42 THE TRUE VALUE IS IN THIS RANGE WITH 68% CONFIDENCE

31. STANDARD ERROR OF THE STANDARD DEVIATION THIS QUANTITY REPRESENTS THE STANDARD DEVIATION OF  x FROM 

32. REPEATED MEASUREMENTS TIME  t = 0.5 s 8.60 8.25 8.30 8.35 8.40 8.45 8.50 8.55 8.65 8.70 8.20 8.45  = 0.122352

33. CONTINUOUS DISTRIBUTIONS IN ACTUAL EXPERIMENTS VALUES WILL BE LESS DISCRETE 23.26, 25.12, etc

34. CONTINUOUS DISTRIBUTIONS IF WE HAD A SET OF 100 DATA VALUES SUCH AS 23.26, 25.12..., etc THEN THE FREQUENCY GRAPH WOULD PROBABLY HAVE VERY FEW VALUES THAT WERE THE SAME

35. CONTINUOUS DISTRIBUTIONS

36. THE ONLY APPARENT MEANINGFUL QUANTITY APPEARS TO BE THE DENSITY OF THE “DOTS”

37. CONTINUOUS DISTRIBUTIONS 16 LET US DIVIDE THE DATA BY INCREMENTS

38. CONTINUOUS DISTRIBUTIONS NOW LET US COUNT HOW MANY DATA POINTS ARE BETWEEN 22.51 AND 23.50 16

41. IF MORE MEASUREMENTS WITH A MORE ACCURATE DEVICE WERE TAKEN

42. AND IF THE DATA WERE INCREASED

44. THE INTERVAL MUST BE CHOSEN *LARGE ENOUGH TO BE MEANINGFUL *SMALL ENOUGH TO GIVE DETAIL