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

6-1 Numerical Summaries Definition: Sample Mean

6-1 Numerical Summaries Example 6-1

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

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.

6-1 Numerical Summaries Definition: Sample Variance

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

6-1 Numerical Summaries Example 6-2

6-1 Numerical Summaries

6-1 Numerical Summaries Computation of s2

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.

6-1 Numerical Summaries Definition

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

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

Graphical Description of Data Column Chart: Example 2-5

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

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

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

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

6-3 Stem-and-leaf Diagrams Example

6-3 Stem-and-leaf Diagrams Example

Ordered stem-and-leaf diagram

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

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 = 20.25 and 3(80+1)/4 = 60.75. 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

6-4 Frequency Distributions And Histograms

6-4 Frequency Distributions And Histograms

6-4 Frequency Distributions And Histograms

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

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

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

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

Class Exercise Introduction to using excel for data summarizing: Mean 1115 1310 1540 1502 1258 1315 1085 798 1020 865 2130 1421 1109 1642 Introduction to using excel for data summarizing: Mean SD Variance Quartiles IQR