1. Descriptive Statistics Civil and Environmental Engineering Dept.
Islamic University of Gaza
Statistics and Probability for Engineers
(ENGC 6310)
Lecture 4:
Descriptive Statistics
Prof. Dr. Yunes Mogheir
Civil and Environmental Engineering Dept.
First Semester/2019

2. 6-1 Numerical Summaries
Definition: Sample Mean

3. 6-1 Numerical Summaries
Example 6-1

4. 6-1 Numerical Summaries
Figure 6-1 The sample mean as a balance point for a system of weights.

5. 6-1 Numerical Summaries Population Mean
For a finite population with N measurements, the mean is
The sample mean is a reasonable estimate of the population mean.

6. 6-1 Numerical Summaries
Definition: Sample Variance

7. 6-1 Numerical Summaries
How Does the Sample Variance Measure Variability?
Figure 6-2 How the sample variance measures variability through the deviations

8. 6-1 Numerical Summaries
Example 6-2

9. 6-1 Numerical Summaries

10. 6-1 Numerical Summaries
Computation of s2

11. 6-1 Numerical Summaries Population Variance
When the population is finite and consists of N values, we may define the population variance as
The sample variance is a reasonable estimate of the population variance.

12. 6-1 Numerical Summaries
Definition

13. Graphical Description of Data
Pie Chart:
How a given quantity is divided into subset
Present fractions, percentages, or proportions
Examples:
Transportation means
Population

14. Horizontal or vertical
Bar Chart:
1-2 independent Var.
Horizontal or vertical
(million gallons per day, mgd)

15. Graphical Description of Data
Column Chart:
Example 2-5

16. Scatter Plot - Flow v. Water Level
Scatter Chart
Both variables presented in intervals or ratio
Example 2-6 (yield Strength vs. carbon content
ASK
How good is this relationship? Is it linear? What would you do next?
Scatter Plot - Flow v. Water Level

17. Graphical Description of Data
Line Chart:
Illustrate mathematical equation
Used for design work
Example 2-7

18. Graphical Description of Data
Combination Charts
Two or more graphs are combined
Example 2-11 (excel: add trend line & equation)

19. 6-3 Stem-and-leaf Diagrams
Steps for Constructing a Stem and-Leaf Diagram

20. 6-3 Stem-and-leaf Diagrams
Example

21. 6-3 Stem-and-leaf Diagrams
Example

22. Ordered stem-and-leaf diagram

23. Ordered stem-and-leaf diagram
Find the following:
10th percentile (10 percent of values less than this value.
25th percentile =first quartile = q1
50th percentile =second quartile = median= q2
75th percentile =third quartile = q3
Inter-quartile range (IQR) = q3 – q1

24. Ordered stem-and-leaf diagram
calculates the first and third quartiles as the (n+1)/4 and 3(n+1)/4
For example, (80+1)/4 = and 3(80+1)/4 = Therefore, we interpolate between the 20th and 21st ordered observation to obtain q1=143.5 and between the 60th and 61st observation to obtain q3=181

25. 6-4 Frequency Distributions And Histograms

26. 6-4 Frequency Distributions And Histograms

27. 6-4 Frequency Distributions And Histograms

28. 6-5 Box Plots
The box plot is a graphical display that simultaneously describes several important features of a data set, such as center, spread, departure from symmetry, and identification of observations that lie unusually far from the bulk of the data.
Center / median
IQR
Symmetry or asymmetry
Outlier
Extreme outlier

30. 6-5 Box Plots
Figure 6-13 Description of a box plot.

31. 6-4 Box Plots
Figure 6-14 Box plot for compressive strength data in Table 6-2.

32. 6-4 Box Plots
Figure 6-15 Comparative box plots of a quality index at three plants.

33. Class Exercise Introduction to using excel for data summarizing: Mean
Introduction to using excel for data summarizing:
Mean SD
Variance
Quartiles
IQR