Aed1222 lesson 4

Introduction to Statistics for Built Environment

Course Code: AED 1222

Compiled byDEPARTMENT OF ARCHITECTURE AND ENVIRONMENTAL DESIGN (AED)

CENTRE FOR FOUNDATION STUDIES (CFS)INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

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.

The need for summarizing data

●Summarizing dataData 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

DATA

Qualitative Quantitative

TabularTabular GraphicalGraphical TabularTabular GraphicalGraphical

Frequency DistributionFrequency

Distribution

Rel. Freq. Distribution


Bar GraphBar Graph

Pie ChartPie Chart

Frequency DistributionFrequency

Distribution



Cumulative Freq. Dist.

Cumulative Freq. Dist.

Histograms & Polygons

Histograms & Polygons

Stem and Leaf PlotStem and Leaf Plot

An overview

OgivesOgives

An overview of common data presentation:

Contingency Table

Contingency Table

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

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.


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:

Frequency Tables

Category CategoryFrequency

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.


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 CategoryFrequency

Example 3 : An advertiser asks 200 customers how many days per week they read the daily newspaper.


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

Relative Frequency TablesTabular

Tabular

.20100

20

20% of the respondent is Strongly Agree with the sample report.

Relative Frequency: What proportion is in each category?


Tabular

.464097

45

46.4% of the Academic Staff is respondent in the sample report.

Relative Frequency: What proportion is in each category?


Relative Frequency: What is the proportion of each category?

Number of days read

FrequencyRelative

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

.220200

44

22% of the people in the sample report that they read the newspaper 0 days per week


Tabular



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

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

●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:

●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).


●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.



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?


●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

Bar Graph


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


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.Graphica

l

Graphical


0

10

20

30

40

50

0 1 2 3 4 5 6 7

Freu

ency

Number of days newspaper is read per week

Newspaper readership per weekNumber 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

CategoryFrequency


l

Graphical


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

CategoryFrequency


l

Graphical

Comparing Investors

0 10 20 30 40 50 60

S toc k s

B onds

CD

S avings

Inves tor A Inves tor B Inves tor C


(Note that bar charts/graphs can also be tabulating and Graphing Multivariate Categorical Data)

Example of Bar Graph:

Category

CategoryFrequency

• Side by side charts


l

Graphical


Sales by quarter for three sales territories.

0

10

20

30

40

50

60

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

EastWestNorth

1st Qtr 2nd Qtr 3rd Qtr 4th QtrEast 20.4 27.4 59 20.4West 30.6 38.6 34.6 31.6North 45.9 46.9 45 43.9

• Side by side charts


l

Graphical

Pie Chart


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


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.Graphica

l

Graphical


Percentages are rounded to the nearest percent

Current Investment Portfolio Savings 15%

CD 14%

Bonds 29%

Stocks42%

Investment Amount PercentageType (in thousands)

Stocks 46.5 42.27Bonds 32.0 29.09CD 15.5 14.09Savings 16.0 14.55

Total 11 100

(Variables are Qualitative)

Example of Pie Chart:

Category

CategoryFrequency

Category

CategoryFrequency

151 deg


l

Graphical

Current Investment Portfolio

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


l

Graphical

Breakdown of marks


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

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.

Date post:	14-May-2015
Category:	Technology
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Aed1222 lesson 4

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