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

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?

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

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

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

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

Statistics Divided into : Descriptive Statistics Inferential Statistics

Forms of Data Description Point summary Tabular format Graphical format Diagrams

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

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

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

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

Time Frequency Plot

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

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

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.

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

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.

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.

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.

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

Data Table 1.1 Compressive Strength of 80 Aluminum Lithium Alloy (psi) 105 221 183 186 121 181 180 143 97 154 153 174 120 168 167 141 245 228 174 199 181 158 176 110 163 131 154 115 160 208 158 133 207 180 190 193 194 133 156 123 134 178 76 167 184 135 229 146 218 157 101 171 165 172 158 169 199 151 142 163 145 171 148 158 160 175 149 87 160 237 150 135 196 201 200 176 150 170 118 149

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

Histogram 2 5 20 15 Frequency 10 5 70 90 110 130 150 170 190 210 230 250 Compressive Strength ( psi )

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

2nd Assignment Due date: August 30rd Group of 2 persons Please download Concrete Data on UCI repository: https://archive.ics.uci.edu/ml/machine-learning-databases/concrete/compressive/

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