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 & 2 are derived from the array. The answer to questions 3, 4 & 5 are derived from the frequency table.
Aed1222 lesson 5
Introduction to Statistics for Built
Course Code: AED 1222
DEPARTMENT OF ARCHITECTURE AND ENVIRONMENTAL DESIGN (AED)
CENTRE FOR FOUNDATION STUDIES (CFS)
INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
Summarizing Quantitative Data 1
Summarizing Quantitative Data:
The data array
Relative Frequency Distribution
Cumulative Frequency Distribution
TabularTabular GraphicalGraphical TabularTabular GraphicalGraphical
Bar GraphBar Graph
Pie ChartPie Chart
An overview of common data presentation:
Raw data (sometimes called source data or atomic data) is data
that has not been processed for use. A distinction is sometimes
made between data and information to the effect that
information is the end product of data processing.
The simplest way of systematically organizing raw data is the
Although raw data has the potential to become "information," it
requires selective extraction, organization, and sometimes
analysis and formatting for presentation.
The data array
The data array is an arrangement of data items in either an
ascending (from lowest to highest value), or descending (from
highest to lowest value).
The advantages of the data array:
• Identifying the range of data, which is the difference
between the largest and smallest numbers in the data set.
• Identifying the upper and lower halves of the data.
• An array can show the presence of large concentrations of
items at particular values.
In spite of these advantages, the array is an awkward data
organization tool, especially when the number of data items is
Therefore, there is a need to arrange the data into a more
compact form for analysis and communication purposes.
The data array cont.
Constructing a frequency table
To construct a frequency distribution table, it is necessary to
determine the following:
1.The range of the collected data
2.The number of classes that will be used to group the data.
3.The width of these classes.
4.Determine the class boundaries.
5.Count the frequency of each class (based on the data
Determining the number of classes
Fewer classes with a very large width can result in the
loss of important detail.
Many classes with small width can be used for
preliminary analysis, but may contain too much detail to
be used in a formal data presentation.
How to determine Number of Classes?
The number of classes depends on the number of
observations being grouped, the purpose of the
distribution, and the preference of the researcher.
In formal presentations, the number of classes used to group the
data generally varies from 5 to 20.
Determining the number of classes cont.
The key is to use classes that give you a good view of the data
pattern and enable you to gain insights into the information
that is there.
• Therefore, the researcher had to determine the suitable
number of classes that suits best to its study.
Determining class interval
Class Interval must satisfy two conditions:
1. All data items from the smallest to the largest must be
2. Each item must be assigned to only one class, i.e. no gaps or
overlapping among classes.
The width of each class (the class interval) should be equal.
To determine the interval of each class, divide the range (the
difference between the highest and lowest items in the data
set) by the desired number of classes, and then round up.
How to determine Class Interval?
Class Interval & Boundary
Table: Number of respondents by age and gender.
Table: Heights of 100 male students at XYZ University.
Includes all measurements
from 62.5in. – 65.5in.
62.5= lower class boundary
65.5= upper class boundary
Size of class interval
Upper class boundary - Lower class boundary
65.5 – 62.5 = 3
68.5 – 65.5 = 3
Class interval & boundary cont.
Why use Frequency Distribution?
• Frequency distribution tables provide insights about
the data that cannot be quickly obtained by looking
only at the original data (raw data).
• In addition, it is a method of organizing data items
into a compact form without obscuring (covering)
• This purpose is achieved by grouping the data into a
relatively small number of classes.
• Therefore, a frequency distribution (for quantitative
data) groups data items into classes and then
records the number of items that appear in each
Why use Relative Frequency?
• The relative frequency of a class is the fraction or
proportion of the total number of data items
belonging to the class.
• A relative frequency distribution is a tabular summary
of a set of data showing the relative frequency for
• Relative frequencies can be written as fractions,
percents, or decimals.
What is a Cumulative frequency?
• Cumulative frequency analysis is the analysis of the
frequency of occurrence of values of a phenomenon
less than a reference value.
• i.e. It tells how often the value of the random variable
is less than or equal to a particular reference value.
No. of students
300-399 14 14 + 0 = 14 14/400 = 0.035 3.5
400-499 46 14 + 46 = 60 46/400 = 0.115 11.5
500-599 58 60 + 58 = 118 58/400 = 0.145 14.5
600-699 76 118 + 76 = 194 76/400 = 0.19 19.0
700-799 68 194 + 68 = 262 68/400 = 0.17 17.0
800-899 62 262 + 62 = 324 62/400 = 0.155 15.5
900-999 48 324 + 48 = 372 48/400 = 0.12 12.0
1000-1099 22 372 + 22 = 394 22/400 = 0.055 5.5
1100-1199 6 394 + 6 = 400 6/400 = 0.015 1.5
Cumulative frequency cont.
From the table below,
118 students surfed internet for up to 599 minutes (i.e. 599 minutes or less)
324 students surfed internet for up to 899 minutes (i.e. 899 minutes or less)
We can state that:
Time taken by students to surfed internet .
Conduct a survey of the number of siblings (brothers and
sisters) 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 frequency column.