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# Aed1222 lesson 4

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• Updated Version 02/11/2011
• The table allows us to see at a glance that the proportion of men who are right-handed is about the same as the proportion of women who are right-handed although the proportions are not identical.
• There may also be more than two variables, but higher order contingency tables are difficult to represent on paper. The relation between  ordinal variables , or between ordinal and categorical variables, may also be represented in contingency tables, although such a practice is rare.
• Males are more likely to develop a tumor than females… The majority of kids like RED at the age of 4, however, their color preference shifts gradually as they grow to BLUE, which is the least favorite color for kids 4 and 8 years of age. YELLOW is not a favorite among kids regardless of their age.
• Raw data can be collected from students and written on the board. Then they can be arranged in an ascending array, and then grouped. A suggested grouping is: Less than 2, 2-3, 4-5, more than 5. The answers to questions 1 &amp; 2 are derived from the array. The answer to questions 3, 4 &amp; 5 are derived from the frequency table.
• ### Aed1222 lesson 4

1. 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. 2. What is/are Data Presentation? ●The data are summarised to enable researchers, managers and decision-makers to observe important features of the data, provide insight into the type of model and analysis that should be used. Data Presentation ●Data presentation is an essential step before further statistical analysis is carried out. ●and help them in making wise and effective decision.
3. 3. The need for summarizing data ●Summarizing data Data must be summarized and presented in a meaningful, readable and understandable ways so they are useful for decision making and problem solving. Common model of presenting data includes : andTabular SummaryTabular Summary Graphical SummaryGraphical Summary
4. 4. DATA Qualitative Quantitative TabularTabular GraphicalGraphical TabularTabular GraphicalGraphical Frequency Distribution Frequency Distribution Rel. Freq. Distribution Rel. Freq. Distribution Bar GraphBar Graph Pie ChartPie Chart Frequency Distribution Frequency Distribution Rel. Freq. Distribution Rel. Freq. Distribution Cumulative Freq. Dist. Cumulative Freq. Dist. Histograms & Polygons Histograms & Polygons Stem and Leaf Plot Stem and Leaf Plot An overview OgivesOgives An overview of common data presentation: Contingency Table Contingency Table
5. 5. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. What is a Frequency Distribution? • A frequency distribution is a list or a table. • containing the values of a variable (or a set of ranges within which the data fall)* • and the corresponding frequencies with which each value occurs (or frequencies with which data fall within each range)* Frequency Distribution *Ungroup and (Grouped Data) Tabular Tabular
6. 6. Frequency distribution >> a tabular models of data summary by showing categories/classes (or variables) together with the corresponding frequency (or number) of items in each of several non-overlapping classes. Frequency Distribution Objective >> to provide insights about the data that cannot be quickly obtained by looking only at the original data (raw data). Tabular Tabular Examples of Frequency Distribution table:
7. 7. Frequency Tables Category Category Frequenc y Tabular Tabular Frequency: What corresponding frequencies is in each category? Example 1 : A survey done to claim that Local graduate Architects perform better than Overseas graduate Architects.
8. 8. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Number of days read Frequency 0 44 1 24 2 18 3 16 4 20 5 22 6 26 7 30 TOTAL 200 Frequency TablesTabular Tabular Category Category Frequenc y Example 3 : An advertiser asks 200 customers how many days per week they read the daily newspaper.
9. 9. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. What is a Relative Frequency Distribution? • A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class. • The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class. Relative Frequency DistributionTabular Tabular
10. 10. Relative Frequency TablesTabular Tabular .20 100 20 = 20% of the respondent is Strongly Agree with the sample report. Relative Frequency: What proportion is in each category?
11. 11. Relative Frequency TablesTabular Tabular .4640 97 45 = 46.4% of the Academic Staff is respondent in the sample report. Relative Frequency: What proportion is in each category?
12. 12. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Relative Frequency: What is the proportion of each category? Number of days read Frequency Relative Frequency 0 44 .22 1 24 .12 2 18 .09 3 16 .08 4 20 .10 5 22 .11 6 26 .13 7 30 .15 TOTAL 200 1.00 .220 200 44 = 22% of the people in the sample report that they read the newspaper 0 days per week Relative Frequency TablesTabular Tabular
13. 13. Frequency Distribution Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Why use Frequency Distribution? • A frequency distribution is a way to summarize data. • The distribution condenses the raw data into a more useful form, • and allows for a quick visual interpretation of the data. Tabular Tabular
14. 14. Contingency Tables What is a Contingency Tables / Cross Tabulation? • A table showing the responses of subjects to one variable as a function of another variable. • A way of summarizing the relationship between variables. • A table of frequencies classified according to the values of two variables or more. • In statistics, contingency tables are used to record and analyze the relationship between two or more variables, most usually categorical variables. It may be enhanced by including the percentages that fall into each category. Tabular Tabular
15. 15. ●When a population/sample is classified according to two variables it is said to have been 'cross-classified' or subjected to a two-way classification. Suppose that we have two variables, Gender (male or female) and handedness (right- or left-handed). We observe the values of both variables in a random sample of 100 people. Then a contingency table can be used to express the relationship between these two variables, as follows: Contingency tables cont. Examples of Contingency Table:
16. 16. ●The figures in the right-hand column and the bottom row are called marginal totals and the figure in the bottom right-hand corner is the grand total. ●If the proportions of individuals in the different columns varies between rows (and, therefore, vice versa) we say that the table shows contingency between the two variables. If there is no contingency, we say that the two variables are independent (i.e. there is no relationship between them). Contingency tables cont.
17. 17. ●The example in the previous slide is for the simplest kind of contingency table, in which each variable has only two levels; this is called a 2 x 2 contingency table. ●In principle, any number of rows and columns may be used. Contingency tables cont.
18. 18. Contingency tables cont. What is the relationship between the factors gender and presence of tumor? What effect does a kid's age have on the color she/he likes?
19. 19. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. ●Bar graphs and Pie charts are often used for qualitative (category) data. •The height of bar/rectangle or the size of pie slice : -shows the frequency or percentage for each category. Bar Graph and Pie ChartGraphical Graphical
20. 20. Bar Graph Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. What is a Bar Graph/Bar Chart? • A bar graph is a graphical device for depicting qualitative data that has been summarized in a frequency, or relative frequency distribution. • Using a bar/rectangle of fixed width drawn above each class label, we extend the height appropriately. • A frequency, or relative frequency scale can be used for the vertical axis. • On the horizontal axis we specify the labels that are used for each of the classes. Graphical Graphical
21. 21. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Procedure to construct a Bar Graph. • First draw a vertical and horizontal axis; then label the axis using the categories or frequency to differentiate the axis into frequency that correspond to the category for each bar. • Construct a bar/rectangle over each category with the height of the rectangle equal to the frequency in that category. • The base should be of the same width and are separated to emphasize the fact that each class is a separate category. Bar Graph cont. Graphical Graphical
22. 22. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. 0 10 20 30 40 50 0 1 2 3 4 5 6 7 Freuency Number of days newspaper is read per week Newspaper readership per week Number of days read Frequency 0 44 1 24 2 18 3 16 4 20 5 22 6 26 7 30 Total 200 Example of Bar Graph: Category Category Frequenc y Bar Graph cont. Graphical Graphical
23. 23. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. 0 10 20 30 40 50 Stocks Bonds CD Savings Amount in \$1000's Investor's Portfolio (Note that bar charts/graphs can also be displayed with horizontal bars) Example of Bar Graph: Category Category Frequenc Bar Graph cont. Graphical Graphical
24. 24. Comparing Investors 0 10 20 30 40 50 60 S tocks B onds CD S avings Investor A Investor B Investor C Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. (Note that bar charts/graphs can also be tabulating and Graphing Multivariate Categorical Data) Example of Bar Graph: Category Category Frequenc y • Side by side charts Bar Graph cont. Graphical Graphical
25. 25. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Sales by quarter for three sales territories. 0 10 20 30 40 50 60 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr East West North 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr East 20.4 27.4 59 20.4 West 30.6 38.6 34.6 31.6 North 45.9 46.9 45 43.9 • Side by side charts Bar Graph cont. Graphical Graphical
26. 26. Pie Chart Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. What is a Pie Chart? • The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data. • It consist of one or more circles that are divided into sectors. (shows the number of objects or percentage of each group of category) • The angle/degree in the sector is proportional to the number or percentage of elements in that category. Graphical Graphical
27. 27. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Procedure to construct a Pie Chart • First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class. • Since there are only 360 degrees in a circle, a class with a relative frequency of 42% would consume 42% x 360 = 151 deg. of the circle, 15% x 360 = 54 deg... and so on (refer next example) Pie Charts cont. Graphical Graphical
28. 28. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Percentages are rounded to the nearest percent Current Investment Portfolio Savings 15% CD 14% Bonds 29% Stocks 42% Investment Amount Percentage Type (in thousands) Stocks 46.5 42.27 Bonds 32.0 29.09 CD 15.5 14.09 Savings 16.0 14.55 Total 11 100 (Variables are Qualitative) Example of Pie Chart: Category Category Frequenc y Category Category Frequenc y151 deg Pie Charts cont. Graphical Graphical Current Investment Portfolio
29. 29. Example of Pie Chart: AED 1016 Graphic Communication 1 Ex 1 6% Ex 2 6% Ex 3 6% Ex 4 10% Ex 5 10% Ex 6 10% Ex 7 10% Ex 8 10% Sketch Task 16% Sketchbook 4% Portfolio 10% LEGEND Pie Charts cont. Graphical Graphical Breakdown of marks
30. 30. Business Statistics: A Decision- Making Approach, 7e © 2008 Prentice-Hall, Inc. Why use Bar Graph / Pie Chart? • Data in raw form are usually not easy to use for decision making -- Some type of organization is needed: • The sectoral condenses the raw data into a graphical form, • and also allows for a quick visual interpretation of the data. Bar Graph and Pie ChartGraphical Graphical
31. 31. Try this exercise! Conduct a survey of the number of siblings for each student in your group has. 1. What is the range of the data? 2. Identify the upper and lower halves of the data. 3. What percentage of the students have from 2 to 3 siblings? 4. What percentage of the students have fewer than 4 siblings? 5. How many students had up to 5 siblings? Answer the following questions: 1. Arrange the obtained raw data in an ascending array. 2. Group the data and create a frequency table. 3. Add to it a cumulative frequency column, a relative frequency column and a cumulative relative frequency column.