1. STATISTICS AND PROBABILITY IN CIVIL ENGINEERING
TS4512
Doddy Prayogo, Ph.D.

2. Statistics
Science of data collection, summarization, presentation and analysis for better decision making.
How to collect data?
How to summarize it?
How to present it?
How do you analyze it and make conclusions and correct decisions?

3. Role of Statistics
Many aspects of Engineering deals with data – product and process design
Identify sources of variability
Essential for decision making

4. Data Collection Observational study
Observe the system
Historical data
The objective is to build a system model usually called empirical models
Design of experiment
Plays key role in engineering design

5. Data Collection Sources of data collection:
Observation of something you can’t control (observe a system or historical data)
Conduct an experiment
Surveying opinions of people in social problem

6. Data Collection Example: traveling time and frequency in site layout
experimental data in concrete laboratory

7. Statistics Divided into : Descriptive Statistics
Inferential Statistics

8. Forms of Data Description
Point summary
Tabular format
Graphical format
Diagrams

9. Point Summary Sample Mean x =  xi/n Population Mean(µ)
1) Central tendency measures
Sample Mean x =  xi/n
Population Mean(µ)
Median --- Middle value
Mode --- Most frequent value
Percentile

10. Point Summary Range = Max xi - Min xi
2) Variability measures
Range = Max xi - Min xi
Variance = V = S 2 =  (xi – x )2/ n-1
also =
Standard deviation = S
S = Square root (V)
Coefficient of variation = S/ x
Inter-quartile range (IQR)
 (xi 2) – {[( xi ) 2]/n}
n -1

11. Diagrams: Dot Diagram
A diagram that has on the x-axis the points plotted : Given the following grades of a class:
50, 23, 40, 90, 95, 10, 80, 50, 75, 55, 60, 40. . . . . 50
100

12. Graphical Format Time Frequency Plot
The Time Frequency Plot tells the following :
1) The Center of Data
2) The Variability
3) The Trends or Shifts in the data
Control Chart

13. Time Frequency Plot

14. Control Charts Central Line = Average ( X )
Lower Control Limit (LCL)= X – 3S
Upper Control Limit (UCL)= X + 3S

15. Control Charts Upper control limit = 100.5 x = 91.50
Lower control limit = 82.54

16. Population and Sample
Population is the totality of observations we are concerned with.
Example: All Engineers in the Kingdom,
All CE students etc.
Sample : Subset of the population
50 Engineers selected at random, 10 CE students selected at random.

17. Mean and Variance Sample mean X-bar Population mean µ
Sample variance S2
Population variance σ2

18. Percentiles
Pth percentile of the data is a value where at least P% of the data takes on this value or less and at least (1-P)% of the data takes on this value or more.
Median is 50th percentile. ( Q2)
First quartile Q1 is the 25th percentile.
Third quartile Q3 is the 75th percentile.

19. Percentile Computation : Example
Data : 5, 7, 25, 10, 22, 13, 15, 27, 45, 18, 3, 30
Compute 90th percentile.
1. Sort the data from smallest to largest
3, 5, 7, 10, 13, 15, 18, 22, 25, 27, 30, 45
2. Multiply 90/100 x 12 = 10.8 round it to to the next integer which is 11.
Therefore the 90th percentile is point # 11 which is 30.

20. Percentile Computation : Example
If the product of the percent with the number of the data came out to be a number. Then the percentile is the average of the data point corresponding to this number and the data point corresponding to the next number.
Quartiles computation is similar to the percentiles.

21. Pth percentile = (P/ 100)*n = r
double (round it up & take its rank)
(r)
integer (take Avg. of its rank & # after)
Inter-quartile range = Q3 – Q1
Frequency Distribution Table :
1) # class intervals (k) = 5 < k < 20
k ~ n
2) The width of the intervals (W) = Range/k
= (Max-Min) /n

22. Data Table 1.1 Compressive Strength of 80 Aluminum Lithium Alloy (psi)

23. Cumulative Relative Frequency
Class Interval
(psi)
Frequency
Relative Frequency =
(Frequency/ n)
Cumulative Relative Frequency
70 ≤ x < 90 2
0.0250
90 ≤ x < 110 3
0.0375
0.0625
110 ≤ x < 130 6
0.0750
0.1375
130 ≤ x < 150 14
0.1750
0.3125
150 ≤ x < 170 22
0.2750
0.5875
170 ≤ x <1 90 17
0.2125
0.8000
190 ≤ x < 210 10
0.1250
0.9250
210 ≤ x < 230 4
0.0500
0.9750
230 ≤ x < 250
1.0000

24. Histogram 2 5 20 15
Frequency 10 5 70 90
190
210
230
250
Compressive Strength (
psi )

25. Histogram: is the graph of the frequency distribution table that shows class intervals V.S. freq. or (Cumulative) Relative freq.

26. 2nd Assignment Due date: August 30rd Group of 2 persons
Please download Concrete Data on UCI repository:

27. 2nd Assignment
Provide data description of the Concrete Data (8 input variables and 1 output variable). Provide at least (but not limited to) upper bound, lower bound, mean, standard deviation
Please make histogram of 2 selected input variables and 1 output variable