Methods of Organization and Presentation of Data 3.

GRAPHICAL PRESENTATION
A graph is a very effective visual tool as it displays
Presentation of Data data at a glance, facilitates comparison, and can
1. TEXTUAL PRESENTATION reveal trends and relationships within the data such
All the data is presented in the form of text, phrase, as changes over time, and correlation or relative
or paragraphs. share of a whole.
It involves enumerating important characteristics,
emphasizing significant figures and identifying Different Kinds of Graphical Presentation
important features of data. 1. Bar Graph
is constructed by labeling each category of data on
2. TABULAR PRESENTATION either the horizontal or vertical axis and the
It is a systematic and logical arrangement of data in frequency or relative frequency of the category on
the form of Rows and Columns with respect to the the other axis.
characteristics of data. are useful when we want to compare the different
parts, not necessarily the parts to the whole.
Parts of the Tabular Presentation
1. Title Example of Bar Graph
the title must tell as simply as possible what is in the Simple Bar Graph
table. Multiple Bar Graph/Grouped Column Chart
it should answer the questions: Who? What are the Component Bar Graph/Subdivided Column Chart
data? Where are the data from? When?
2. Histogram
2. Boxhead is constructed by drawing rectangles for each class of
the boxhead contains the captions or column data.
headings. the height of each rectangle is the frequency or
the heading of each column should contain as few relative frequency of the class.
words as possible, yet explain exactly what the data the width of each rectangle is the same and the
in the columns represent. rectangles touch each other.

3. Stubs 3. Pie Chart

the row captions are known as the stub. is a circle divided into sectors.
items in the stub should be grouped to facilitate each sector represents a category of data.
interpretation of the data. the area of each sector is proportional to the
frequency of the category.
4. Footnotes are useful for showing the division of all possible
given at the foot of the table for explanation of any values of qualitative variable into its parts.
fact or information included in the table which needs
some explanation. 4. Line Graph
shows information that is connected in some way
5. Sources of Data (such as change over time).
the source of information from which data are very useful in identifying trends in the data over
taken. time.

Constructing of Data Tables Example of Line Graph

The title should be in accordance with the objective of Simple Line Graph
the study. Multiple Line Graph
Comparison
Alternative location of stubs
Headings
Footnote
Size of columns
Use of abbreviations
Units
 Guidelines for Determining the Lower Class Limit of the Measures of Central Tendency
First Class and Class Width 1. Mean
is the sum of the data values divided by the number
1. Choosing the Lower Class Limit of the First Class of data values.
Choose the smallest observation in the data set or a is also called the average.
convenient number slightly lower than the smallest is appropriate only for data under interval and ratio
observation in the data set. scale measurement.

2. Determining the Class Width Formula for Mean

Decide on the number of classes.
Generally, there should be between 5 and 20 classes. Sample Mean
The smaller the data set, the fewer classes you For Ungrouped Data
should have.
Determine the class width by computing:
cw = 𝑥𝑚𝑎𝑥 − 𝑥𝑚𝑖𝑛
𝑛𝑐
Where:
Organize Quantitative Variable in Table 𝑥𝑖 = 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠
Classes are categories into which data are grouped. 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
When a data set consists of a large number of
different discrete data values or when a data set For Grouped Data
consists of continuous data, we create classes by
using interval numbers.

Frequency Distribution
list each category of data and the number of Where:
occurrences for each category of data. 𝑥𝑖 = 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠
𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
Procedure in Constructing Frequency Table 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
1. Set an interval or range for your data. It is needed for
the “Bin Range”. Population Mean
2. Click “Data” on the menu bar and click “Data For Ungrouped Data
Analysis” on the tool bar.
3. The dialog box “Data Analysis” will appear and
choose “Histogram” on the dialog box then click “OK”.
4. Highlight your data for the “Input Range”.
5. Highlight your data for the “Bin Range”. Where:
6. Click the box of “Labels in First Row” then click 𝑥𝑖 = 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠
“OK”. N = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
7. The result will appear on the new worksheet of the
excel file. Get the percentage and tool. For Grouped Data

Grouped Data
is the type of data which is classified into groups
after collection.
Where:
Ungrouped Data 𝑥𝑖 = 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠
is also known as raw data that has not been placed 𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
in any group or category after collection. N = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
2. Median
is the middle observation when the data set is sorted
(in either increasing or decreasing order).
the median divides the distribution into two equal
parts.

Formula for Median

For Ungrouped Data
1. Arrange the data from lowest to highest (or highest to
lowest).
2. For an odd number of data, the median of a data set
is the middle observation. When the number of data is
even, the median is the average of the two middle scores.

For Grouped Data

Where:
LB = lower boundary of the median class
i = class width
n = no. of observation
< cf = less than the cumulative frequency of the class
preceding the median class.
f = frequency of the median class.

3. Mode
is the most frequently occurring value in a list of
data.
is sometimes called nominal average.
is an appropriate measures of average for data using
the nominal scale measurement.
is the only measure of central tendency used in both
quantitative and qualitative data.

Formula for Mode

For Ungrouped Data
1. Obtain a frequency distribution of the distinct values
of the data.
2. The mode is the most frequently occurring data (if
there is one).

For Grouped Data

Where:
LB = lower boundary of the median class
i = class width
𝑑1 = difference between the frequency of the modal class
and the class preceding it
𝑑2 = difference between the frequency of the modal class
and the class following it