STATISTICS & PROBABILITY TS 4512

1. STATISTICS & PROBABILITYTS 4512 Herlina Setiyaningsih Petra Christian University Wednesday, 7.30 – 9.20

2. Expectations • Attend class regularly  attendance min 75%. • Tolerance of coming late 15 minutes. • Do your assignment, exam by your self.

3. Grading Policy • Assignments 20% • Midterm exam 40% • Final exam 40%

4. Textbooks • Ang, A. H-S., and Tang, W. H., 1975, Probability Concepts in Engineering Planning and Design, Volume I Basic Principles, John Wiley & Sons, New York. • Ang, A. H-S., and Tang, W. H., 1984, Probability Concepts in Engineering Planning and Design, Volume II Decision, Risk and Reliability, John Wiley & Sons, New York. • Devore, J. L., 2000, Probability and Statistics for Engineering and The Sciences 5th ed, Duxbury, California.

5. Benjamin, J. R., and Cornell, C. A., 1970, Probability, Statistic, and Decision for Civil Engineers, McGraw-Hill, New York.

6. Basic Course Outline • Descriptive Statistics • Theory of Probability • Random Variables • Discrete Distribution (Bernoulli, Binomial, Poisson) • Continuous Distribution (Normal, Exponential, etc) • Estimation and Hypothesis (Uniform Test, Comparison Test, “t” Test, etc)

9. Statistics • Method for collecting, processing, and enterprising data for getting some conclusions. (Johnson, 1996) • Populations: consist of all individuals and all objects with particular type . • Samples: subset of population.

10. Data • Ungrouped Data The data is not collected in group. • Grouped Data The data is collected in group, use frequency distribution table.

11. Branches of Statistics • Descriptive Statistics: calculation of numerical measure and graphical. • Inferential Statistics: use sample information to draw some types of conclusion about population.

12. Descriptive Statistics • Measure of location: • Center location: mean, median, mode • Other location: quartiles, percentiles, desil • Measure of variability: • Range, variance, standard deviation, variation coefficient • Measure of form: • Skewness, plot box

13. Ungrouped DataRange • Range: is the difference between the largest and smallest sample data. k = the largest value – the smallest value

14. Mean • Mean is an average of all data. • Populations: • Samples:

15. Variance • is measure for showing statistic dispersion (the extent of spread data from the mean). • Populations: • Samples:

16. Standard Deviation • is the (positive) square root of the variance . • Populations: • Samples:

17. Mode: the data has the biggest frequency/ data often appears. • Median: the middle of data after sorted.

18. Grouped Data • Range/ r: difference between upper limit of the highest class and lower limit of the lowest class. • j = 1 + 3.3 log n j: total of class intervals n: total of data • k= r/j

19. Mean

20. Variance Population: Samples

21. Variance Coefficient • For showing kind of data in some group data. • Populations Data: • Sample Data:

22. Mode Lo = bottom limit mode class i.e. class has the highest frequency k = range mode class b1 = mode class frequency minus class interval frequency before mode class b2 = mode class frequency minus class interval frequency after mode class

23. Median • Lo = bottom limit median class, • Me = median value, • n = data amount, • Fk = cumulative frequency before median class, • fo = frequency median class, • k = range

24. Quartiles • Measure of location that divide data into 4 equal parts. • Determine the location (if N odd): (i= 1,2,3)

25. Quartiles Determine the location (if N even): (N odd) (N even)

26. Desil • Measure of location that divide data into 10 equal parts. • Determine the location (if N odd): (i=1,2,…,9)

27. Desil Determine the location (if N even): (N odd) (N even)

28. Dibagi menjadi 100 bagian yang sama Persentil • Measure of location that divide data into 100 equal parts. • Determine the location (if N odd): (i= 1,2,..,99)

29. Persentil Determine the location (if N even): (N odd) (N even)

30. Skewness Coefficient • Measure of asymmetrical (skewed) distribution • Mean = median = modus : Symmetrical • Mean < median < modus : Skewed to the left • Mean > median > modus : Skewed to the right

32. BOXPLOTS • A pictorial summary to describe several data most prominent features. These features include: • Center • Spread • The extent and nature of any departure from symmetry • Identification of outliers

33. Lower fourth: • Median of the smallest n/2 observations, n even • Median of the smallest (n+1)/2 observations, n odd • Upper fourth: • Median of the largest n/2 observations, n even • Median of the largest (n+1)/2 observations, n odd • Fourth spread, fs fs = upper fourth – lower fourth

34. The simplest boxplot is based on the following five-number summary: smallest xi – lower fourth – median – upper fourth – largest xj • Outlier: any observation father than 1.5 fs from the closest fourth. • Extreme outlier: more than 3 fs from nearest fourth. • Mild outlier: observation between 1.5 fs ad 3 fs.

35. 3fs 3fs 1.5fs 1.5fs Extreme outlier Mild outlier xi Lower forth median Upper forth xj Extreme outlier Mild outlier

36. Example 1 The research of concrete compressive strength at 28 days, resulted: 20, 22, 21, 24, 21, 23, 21, 22, 25 (MPa). Compute the following: mean, variance, standard deviation, median, modus, variance coefficient. (i.e. populations and samples), and draw boxplot.

37. Answer Data sorted: 20, 21, 21, 21, 22, 22, 23, 24, 25 Mean: Populations: μ = 22,11 MPa Samples: = 22,11 MPa Variance: Populations : = 2,32 Samples : s2 = 2,61

38. Standard deviation: Populations:σ = 1,52 Samples : s = 1,62 Median:22 Mode: 21 Variation Coefficient : Populations: Cv = 0,07 Samples : Cv = 0,07

39. UF 20 21 21 21 22 22 23 24 25 fs = 23,5-21 = 2,5 1.5 fs = 1.5 x 2,5 = 3,75 3 fs = 3 x 2,5 = 7,5 Xi Me LF Xj

40. 3fs = 7.5 3fs = 7.5 1.5fs = 3.75 1.5fs = 3.75 17,25 Xi UF Xj 27.25 LF Me

41. Example 2 • The value of tensile strength (MPa) wood from markets, resulting in the following sample observations :

43. Answer • Mean= 1679/50 = 33,58 • Variance & standard deviation & Cv populations: = = 131,99 = = 11,49 Cv = (11,49/ 33,58) x 100% = 34,22%

44. Variance & standard deviation & Cv samples: = = 134,69 = = 11,61 Cv = 11,61/33,58 = 34,57%

45. Mode: f = 17 class = 24-31 b1 = 17-10 = 7 b2 = 17-7 = 10 k = 7 Lo = 23,5 = 26,38

46. Median: location = x = 50/2 = 25 class 24-31, fo = 17, Fk = 10, Lo = 23,5 k = 7 = 29,68

47. Positively Skewed

48. Assignment 24 Feb 2010 • Determine (samples) • Mean • Variance • Standard deviation • Variance coefficient • Median • Modus • Skewness and picture • Boxplot.