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  • Updated Version 02/11/2011

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  • 1. Introduction to Statistics for Built Environment Course Code: AED 1222 Compiled by DEPARTMENT OF ARCHITECTURE AND ENVIRONMENTAL DESIGN (AED) CENTRE FOR FOUNDATION STUDIES (CFS) INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
  • 2. Lecture 6 Summarizing Quantitative Data 2 Today’s Lecture:  Summarizing Quantitative Data:  Histograms & Polygons  The Stem-and-Leaf plot  Ogives
  • 3. Contingency Table Contingency Table Data Qualitative Quantitative TabularTabular GraphicalGraphical TabularTabular GraphicalGraphical Frequency Distribution Frequency Distribution Rel. Freq. Dist. Rel. Freq. Dist. Bar GraphBar Graph Pie ChartPie Chart Frequency Distribution Frequency Distribution Rel. Freq. Dist. Rel. Freq. Dist. Cumulative Freq. Dist. Cumulative Freq. Dist. Histograms & Polygons Histograms & Polygons Stem and Leaf Plot Stem and Leaf Plot An overview OgivesOgives LECTURE 5 An overview of common data presentation: LECTURE 4
  • 4. Histograms What is a Histograms? • The histogram is a summary graph showing a count of the data points falling in various ranges. • The groups of data are called classes, and in the context of a histogram they are known as bins, because we can think of them as containers that accumulate data and "fill up" at a rate equal to the frequency of that data class • Consists of a set of rectangles • Bases at X axis, • Centers at the midpoints, • Lengths equals to the class interval size, • Areas proportional to the class frequencies. Graphical Graphical
  • 5. Histograms cont. • Unlike a bar graph, a histogram has no natural separation or gap between rectangles of adjacent classes. • The class boundaries are marked on the horizontal axis (X Axis) and the frequency is marked on the vertical axis (Y Axis). Thus a rectangle is constructed on each class interval. • If the intervals are equal, then the height of each rectangle is proportional to the corresponding class frequency. • If the intervals are unequal, then the area of each rectangle is proportional to the corresponding frequency density. Graphical Graphical
  • 6. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. How Many Class Intervals? • Many (Narrow class intervals) • may yield a very jagged distribution with gaps from empty classes • Can give a poor indication of how frequency varies across classes • Few (Wide class intervals) • may compress variation too much and yield a blocky distribution • can obscure important patterns of variation. 0 2 4 6 8 10 12 0 30 60 More Temperature Frequency 0 0.5 1 1.5 2 2.5 3 3.5 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 More Temperature Frequency (X axis labels are upper class endpoints) Histograms cont. Graphical Graphical
  • 7. Histograms cont. Draw a histogram for the following data set: Example of Histograms: Graphical Graphical
  • 8. Histograms cont. Graphical Graphical Draw a histogram for the following data set: Example of Histograms:
  • 9. Distribution of shops according to the number of wage - earners employed at a shopping complex When the intervals are unequal, we construct each rectangle with the class intervals as base and frequency density as height. Frequency Density Histograms cont. Graphical Graphical Draw a histogram for the following data set: Example of Histograms:
  • 10. Histograms cont. Graphical Graphical Distribution of shops according to the number of wage - earners employed at a shopping complex
  • 11. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Histogram 0 3 6 5 4 2 0 0 1 2 3 4 5 6 7 5 15 25 36 45 55 More Frequency Class Midpoints 0 10 20 30 40 50 60 Class Endpoints Example (Cont.): DATA ARRAY 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Sorted raw data from low to high: Insulation manufacturer 20 days high temperature record. Histograms cont. Graphical Graphical No gaps between bars, since continuous data (Note that we use the same example from Lecture 5)
  • 12. Information conveyed by Histograms Why use Histograms? -Histograms are useful data summaries that convey the following information: • The general shape of the frequency distribution • Symmetry of the distribution and whether it is skewed • Modality: unimodal, bimodal, or multimodal Graphical Graphical -A histogram may become more appropriate as the data size increases. -The ease with which histograms can now be generated on computers.
  • 13. Comparison between Histograms & Bar GraphsGraphical Graphical
  • 14. Polygons What is a Polygons? • A polygon is a line graph of the class frequency plotted against the class midpoint. • Obtained by connecting the midpoints of the tops of the rectangles in the histogram. • However, frequency Polygons can be drawn independently without drawing the histograms. • In drawing a histogram/polygon of a given frequency distribution, we take the following steps: Graphical Graphical
  • 15. Polygons cont. Graphical Graphical Step 1. : If the frequency table is in the inclusive form, we first convert it into an exclusive form and make it a continuous interval. Step 2. :To complete the polygon we assume a class interval with zero frequency preceding the first class interval and a class interval with zero frequency succeeding the last class interval. Step 3. : Taking a suitable scale, we represent the class mid- points or (class marks) along X axis. Step 4. : Taking a suitable scale, we represent frequency along Y axis. Step 5. : We plot the corresponding points and join it with the help of line segment. Procedure
  • 16. Polygons cont. Example of Polygons: Graphical Graphical Draw a Polygons for the following data set:
  • 17. Polygons cont. Example of Polygons: Graphical Graphical
  • 18. The Stem-and-Leaf plot What is a Stem-and-Leaf Plot? • The Stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. • Unlike histograms, stemplots retain the original data. • A basic stemplot contains two columns separated by a vertical line. The left column contains the stems and the right column contains the leaves. • Consists of a set of a : Stem: Leading Digits Leaf: Trailing digits Graphical Graphical
  • 19. Step 1. : Separate the sorted data series into leading digits (the stem) and the trailing digits (the leaves). Step 2. : List all stems in a column from low to high. Step 3. : For each stem, list all associated leaves. Procedure The Stem-and-leaf plot cont. Graphical Graphical
  • 20. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. • Here, use the 10’s digit for the stem unit: Data sorted from low to high: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58  12 is shown as  35 is shown as Stem Leaf The Stem-and-leaf plot cont. Graphical Graphical 1 2 3 5
  • 21. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Using other stem units – Round off the 10’s digit to form the leaves The Stem-and-leaf plot cont. Graphical Graphical • Here, use the 100’s digit for the stem unit:  613 would become  776 would become  1224 would become Stem Leaf 6 1 12 2 7 8
  • 22. Example (Let’s do it together with the Class) 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Display the following data with a Stem and Leaf Plot The Stem-and-leaf plot cont. Graphical Graphical Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. 4 5 2 1 0 1 3 3 1 2 Stem Leaf 3 7 4 4 2 5 3 4 6 7 7 8 6 8 7 . . . . .
  • 23. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Why use Stem-and-Leaf Plot? • A simple way to see distribution details from quantitative data The Stem-and-leaf plot cont. Graphical Graphical • Stemplots are useful for giving the reader a quick overview of distribution, highlighting outliers and finding the mode.
  • 24. Ogives What is an Ogives? • An Ogive is a graph of the cumulative relative frequencies from a relative frequency distribution. • Ogives are sometime shown in the same graph as a relative frequency histogram. • Also known as Cumulative Frequencies Graph. Graphical Graphical Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc.
  • 25. Example of an Ogives: Draw an Ogives for the following data set: Ogives cont. Graphical Graphical
  • 26. Example (Cont.): DATA ARRAY 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Constructing an Ogives table Sorted raw data from low to high: Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Add a Cumulative Relative Frequency New column: Graphical Graphical Insulation manufacturer 20 days high temperature record.
  • 27. Example (Cont.): Constructing an Ogives table cont. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Graphical Graphical Histogram 0 1 2 3 4 5 6 7 5 15 25 36 45 55 More Frequency Class Midpoints 100 80 60 40 20 0 CumulativeFrequency(%) / Ogive 0 10 20 30 40 50 60 Class Endpoints Insulation manufacturer 20 days high temperature record. / Construct an Ogive
  • 28. PYRAMID CHART LINE CHART SCATTER DIAGRAM RADAR CHART Other Graphical Data Presentation 1 What is other types of Graphical Data Presentation? Graphical Graphical
  • 29. PIE CHART BUBBLE CHART AREA CHART DOUGHNUT Other Graphical Data Presentation 2 More types of Graphical Data Presentation. Graphical Graphical