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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. ●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. ●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. ●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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.