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Descriptive Statistics for Engineers: Sample Mean and Variance, Graphical Data Presentation

Learn about sample mean, sample variance, population mean, sample variance computation, graphical data presentation including pie charts, bar charts, scatter plots, stem-and-leaf diagrams, histograms, and box plots. The lecture explores numerical summaries, graphical descriptions of data, and practical exercises using Excel.

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Descriptive Statistics for Engineers: Sample Mean and Variance, Graphical Data Presentation

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  1. 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 NumericalSummaries Example 6-1

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

  5. 6-1 NumericalSummaries 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 NumericalSummaries Definition: Sample Variance

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

  8. 6-1 NumericalSummaries Example 6-2

  9. 6-1 NumericalSummaries

  10. 6-1 NumericalSummaries Computation of s2

  11. 6-1 NumericalSummaries 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 NumericalSummaries 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. 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 Chart Scatter Plot - Flow v. Water Level • Both variables presented in intervals or ratio • Example 2-6 (yield Strength vs. carbon content

  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 = 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

  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

  29. 6-5 Box Plots Figure 6-13Description of a box plot.

  30. 6-4 Box Plots Figure 6-14Box plot for compressive strength data in Table 6-2.

  31. 6-4 Box Plots Figure 6-15Comparativebox plots of a quality index at three plants.

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

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