Processing and Graphical Representation of the data
UNIT II Processing and Graphical Representation of the data
1. Data Collection
This is the first and most crucial step. It refers to the
process of gathering information from various sources to answer a specific
research question or test a hypothesis.
- Primary
Data: Collected firsthand by the researcher specifically for the
study (e.g., surveys, interviews, experiments, observations).
- Secondary
Data: Data that has already been collected and published by
someone else (e.g., government census reports, company annual reports,
journals, online databases).
2. Data Editing
Once data is collected, it is usually "raw" and
contains errors. Editing is the process of detecting and correcting these
errors to ensure accuracy, consistency, and completeness before analysis.
- Field
Editing: Preliminary editing done at the time of data collection
to catch obvious errors immediately (e.g., illegible handwriting, missing
answers).
- Central
Editing: Rigorous editing done at a central office. It involves:
- Scrutiny: Checking
for omissions, inconsistencies, and irrelevant answers.
- Correction: Adjusting
obvious errors. If a correction is uncertain, the data is flagged or
discarded.
Coding is the process of assigning numerical or alphabetical
symbols (codes) to raw responses so they can be easily entered into a computer
and statistically analyzed.
- Purpose: To
condense vast amounts of narrative/qualitative information into
manageable, countable categories.
- Example: For
the question, "What is your highest level of education?" you
might assign: 1 = High School, 2 = Bachelor's, 3 = Master's, 4 = PhD.
- Rule
of Thumb: Codes must be mutually exclusive (a
response fits into only one code) and exhaustive (every
possible response has a code, such as "99 = Other").
4. Classification of Data
Classification is the process of arranging data into
homogeneous (similar) groups or classes according to common characteristics.
Types of Classification:
A. External Classification
This classification is based on external attributes—characteristics
that are visible, tangible, or temporal in nature.
- Alphabetical: Arranging
data by letters (e.g., sorting employee names from A to Z).
- Chronological: Arranging
data by time (e.g., sales data by year: 2020, 2021, 2022).
- Geographical/Spatial: Arranging
data by location (e.g., population figures by country, state, or city).
B. Internal Classification
This classification is based on the inherent attributes or
qualities of the data itself. These attributes cannot be seen physically but
are conceptual.
- Qualitative
(Attribute-based): Grouping based on non-numeric characteristics
or attributes (e.g., gender, religion, marital status, occupation). These
can be:
- Simple
(Dichotomy): Divided into two categories (e.g., Male/Female,
Pass/Fail).
- Manifold: Divided
into more than two categories (e.g., Religion:
Hindu/Muslim/Christian/Sikh).
- Quantitative
(Variable-based): Grouping based on numeric characteristics that
can be measured (e.g., age, income, weight, height).
5. Preparation of Frequency Distribution
A Frequency Distribution is a tabular summary of data
showing the number (frequency) of observations in each of several
non-overlapping categories or classes.
- For
Qualitative Data: You simply list each category and count how
many times it occurs.
- For
Quantitative Data: You group the numeric data into classes (intervals).
Steps for preparing a Quantitative Frequency
Distribution:
- Find
the Range (R): Subtract the smallest value (minimum) from the
largest value (maximum). R = Maximum - Minimum.
- Determine
the Number of Classes (K): Use Sturges' Rule: K = 1 + 3.322
* log10(N), where N is the total number of observations. (Round to a whole
number).
- Determine
the Class Width (i): Divide the Range by the Number of
Classes. i = R / K. Always round up to the nearest
convenient number for simplicity.
- Establish
Class Limits: Decide the lower limit of the first class (usually
the minimum value or a rounded-down number below it). Add the class width
successively to create the subsequent classes.
- Tally
the Observations: Go through the raw data and place a tally mark
in the appropriate class.
- Count
the Frequencies: Convert tally marks into numerical frequencies
and sum them to ensure they equal N.
Example of a Final Frequency Distribution Table (External
& Internal)
Let’s say we collected the test scores (out of 100) of 50
students.
- External
Classification: We arrange the data chronologically (by
the date the test was taken) or geographically (by the
student's homeroom class).
- Internal
Classification: We arrange the data quantitatively based
on the score itself into a frequency table (as shown below):
|
Class Interval (Scores) |
Tally |
Frequency (f) |
|
0 – 10 |
II |
2 |
|
11 – 20 |
IIII |
4 |
|
21 – 30 |
IIII I |
6 |
|
31 – 40 |
IIII IIII |
9 |
|
41 – 50 |
IIII IIII I |
11 |
|
51 – 60 |
IIII III |
8 |
|
61 – 70 |
IIII |
5 |
|
71 – 80 |
III |
3 |
|
81 – 90 |
I |
1 |
|
91 – 100 |
I |
1 |
|
Total |
N = 50 |
Important Terms Used in Frequency Distribution (Internal
Preparation)
- Class
Limits: The highest and lowest values that can belong to a class
(e.g., 0 and 10).
- Class
Boundaries: The exact points where one class ends and another
begins (e.g., -0.5 to 10.5). Used to eliminate gaps between classes.
- Class
Midpoint (Mark): The average of the upper and lower limits (e.g.,
(0+10)/2 = 5). Used as the representative value of the class for further
calculations.
- Class
Frequency: The number of observations falling within a particular
class.
- Cumulative
Frequency: The running total of frequencies (adding each class's
frequency to the sum of the previous classes). Useful for finding medians
and percentiles.
Diagrammatic Presentation
of Data
Introduction
Diagrammatic presentation of
data is the graphical representation of numerical information using diagrams.
It simplifies complex statistical data, making it easier to understand,
compare, analyze, and interpret. Diagrams are widely used in education, research,
business, administration, and social sciences to communicate information
effectively.
Rules for Preparing
Diagrams
A good diagram should follow
certain principles to ensure clarity and effectiveness.
1. Appropriate Title
- Give a clear, brief, and meaningful title.
- It should indicate what the diagram represents.
2. Simplicity
- Keep the diagram simple and easy to understand.
- Avoid unnecessary decorations.
3. Accuracy
- Represent data accurately.
- Maintain correct proportions and scale.
4. Proper Scale
- Use a suitable and uniform scale.
- Mention the scale clearly whenever required.
5. Neatness
- The diagram should be clean, attractive, and
professionally presented.
6. Proper Labels
- Label axes, categories, and sections clearly.
- Include units of measurement.
7. Legend (Key)
- Use a legend whenever different colours,
patterns, or symbols are used.
8. Uniform Width
- Bars should have equal width.
- Equal spacing should be maintained between bars.
9. Source of Data
- Mention the source below the diagram whenever
applicable.
10. Suitability
- Choose the diagram according to the nature of the
data and the purpose of presentation.
Takeaway: A well-prepared diagram is simple, accurate,
attractive, and easy to interpret.
Types of Diagrams
Diagrams are broadly
classified into:
- One-Dimensional (Bar) Diagrams
- Two-Dimensional Diagrams
- Three-Dimensional Diagrams
- Pictograms
- Cartograms
This unit mainly focuses on One-Dimensional
Bar Diagrams, Pie Diagram, Structure Diagram, Organisational
Chart, and Flow Chart.
One-Dimensional Bar
Diagrams
A one-dimensional bar diagram
represents data using bars of equal width, where only the height (length)
varies according to the data values.
Characteristics
- Equal width
- Equal spacing
- Height proportional to values
- Easy comparison
1. Simple Bar Diagram
Definition
A simple bar diagram
represents only one variable using separate bars.
Example
|
Department |
Students |
|
Science |
80 |
|
Commerce |
65 |
|
Arts |
50 |
Uses
- Comparison of one characteristic.
- Showing frequencies or totals.
Advantages
- Easy to construct.
- Easy to interpret.
- Suitable for beginners.
Limitations
- Represents only one variable.
Takeaway: A simple bar diagram compares one set of values
across categories.
2. Multiple Bar Diagram
Definition
A multiple bar diagram
compares two or more related variables for the same categories.
Example
|
Department |
Boys |
Girls |
|
Science |
45 |
35 |
|
Commerce |
30 |
35 |
|
Arts |
20 |
30 |
Each category contains two or
more bars placed side by side.
Uses
- Comparing different groups.
- Comparing yearly performance.
- Educational achievement studies.
Advantages
- Easy comparison between variables.
- Attractive presentation.
Limitations
- Becomes crowded with many variables.
Takeaway: Multiple bar diagrams compare two or more related
datasets simultaneously.
3. Subdivided
(Component/Stacked) Bar Diagram
Definition
A subdivided bar diagram
divides one bar into several parts to show the composition of a total.
Example
|
School |
Boys |
Girls |
Total |
|
A |
40 |
60 |
100 |
|
B |
50 |
50 |
100 |
Each bar represents the total
and is divided into components.
Uses
- Showing composition of totals.
- Budget allocation.
- Population distribution.
- Examination results.
Advantages
- Displays both total and components.
- Easy comparison of composition.
Limitations
- Difficult when many subdivisions exist.
Takeaway: Subdivided bar diagrams show how a total is
divided into different parts.
Pie Diagram (Pie Chart)
Definition
A pie diagram is a circular
diagram divided into sectors representing the proportion of each category.
The entire circle represents 100%
or 360°.
Formula
Angle of Sector = (Value /
Total) × 360°
Example
|
Subject |
Marks |
|
English |
80 |
|
Tamil |
70 |
|
Maths |
90 |
|
Science |
60 |
Each subject is represented
by a sector whose angle is proportional to its marks.
Uses
- Percentage distribution.
- Budget analysis.
- Market share.
- Population composition.
Advantages
- Attractive.
- Easy to understand.
- Best for percentage data.
Limitations
- Not suitable for many categories.
- Difficult to compare small differences.
Takeaway: Pie charts effectively display the proportion of
parts within a whole.
Structure Diagram
Definition
A structure diagram visually
represents the relationship between different parts of a system or concept.
Example
Uses
- Educational concepts
- Classification
- Research framework
- System representation
Advantages
- Clear hierarchical arrangement.
- Easy visualization.
Takeaway: Structure diagrams show how components are
organized within a system.
Definition
An organisational chart
illustrates the hierarchy, authority, and reporting relationships within an
organisation.
Example
Uses
- Schools
- Colleges
- Universities
- Government offices
- Business organisations
Advantages
- Shows chain of command.
- Clarifies responsibilities.
- Facilitates communication.
Takeaway: Organisational charts display the hierarchy and
reporting structure of an institution.
Flow Chart
Definition
A flow chart is a diagram
that shows the sequence of steps in a process using standard symbols connected
by arrows.
Common Symbols
|
Symbol |
Meaning |
|
Oval |
Start/End |
|
Rectangle |
Process |
|
Diamond |
Decision |
|
Parallelogram |
Input/Output |
|
Arrow |
Direction of flow |
Example
Uses
- Research methodology
- Teaching-learning process
- Computer programming
- Decision-making
- Administrative procedures
Advantages
- Easy to understand.
- Shows sequence clearly.
- Improves communication.
Summary
|
Diagram Type |
Purpose |
|
Simple Bar Diagram |
Compare one variable |
|
Multiple Bar Diagram |
Compare two or more related variables |
|
Subdivided Bar Diagram |
Show composition of a total |
|
Pie Diagram |
Show percentage or proportional distribution |
|
Structure Diagram |
Show relationships among components |
|
Organisational Chart |
Show hierarchy and authority |
|
Flow Chart |
Show sequential steps in a process |
Conclusion
Diagrammatic
presentation is an essential tool in statistics and educational research.
Different types of diagrams serve different purposes, from comparing values
(bar diagrams) and showing proportions (pie diagrams) to illustrating
structures (organisational and structure diagrams) and processes (flow charts).
Selecting the appropriate diagram enhances understanding, interpretation, and
effective communication of data.
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