Diagrammatic & Graphic Presentation

Diagrammatic & Graphic Presentation

Introduction

·        Diagrammatic and graphic presentation are visual methods of presenting statistical data for quick and easy understanding.

·        They help in simplifying complex data, revealing trends, and making comparisons clearer.

Difference between Diagrams & Graphs:

Diagrams	Graphs
More attractive and artistic	More precise and mathematical
Usually qualitative or approximate	Usually quantitative and exact
Used for popular presentation	Used for statistical/technical analysis

Graphical Location of Median

• Median: The middle value when data is arranged in order.
• Graphical Method (Using Ogive):
1. Prepare a Cumulative Frequency Table.
2. Plot Cumulative Frequency Curve (Ogive) on graph paper:
• Less than Ogive: X-axis → class boundaries; Y-axis → cumulative frequency.
3. Locate N/2 on Y-axis (N = total frequency).
4. Draw a horizontal line from this point to the ogive, then drop a vertical line to X-axis.
• This X-value is the Median.

• Sometimes both less than and more than ogives are drawn; their intersection gives the median.

Graphical Location of Quartiles

• Quartiles: Divide the data into four equal parts.
• Q1Q_1 → value below which 25% of observations lie.
• Q3Q_3 → value below which 75% of observations lie.
• Graphical Method:

1.               Use the Less than Ogive.

2.               Locate N/4N/4 for Q1Q_1 and 3N/43N/4 for Q3Q_3 on Y-axis.

3.               Draw horizontal lines from these points to the ogive, then verticals to X-axis.

4.               The corresponding X-values are Q1Q_1 and Q3Q_3.

Graphical Location of Mode

• Mode: The value occurring most frequently.
• Graphical Method (Histogram method):
1. Draw a Histogram for the frequency distribution.
2. Identify the modal class (highest rectangle).
3. Join the top left corner of the modal class rectangle to the top right corner of the previous rectangle.
4. Join the top right corner of the modal class rectangle to the top left corner of the next rectangle.
5. The intersection point inside the modal class, when dropped vertically to X-axis, gives the Mode.

One-Dimensional Diagrams

• Represent data through length only.
• Types:
1. Simple Bar Diagram
• Equal width, length proportional to value.
• Used to compare one variable across categories.
2. Multiple Bar Diagram
• Grouped bars for comparing more than one variable.
3. Sub-divided Bar Diagram (Component Bar)
• Single bar divided into components showing parts of a whole.
4. Percentage Bar Diagram
• Similar to sub-divided bar but components expressed in percentages.
5. Broken Bar Diagram
• Used when values are very large; break is shown for saving space.

Two-Dimensional Diagrams

• Represent data through area (length × breadth).
• Types:
1. Rectangular Diagrams
• Area proportional to data values; rectangles may represent different categories.
2. Square Diagrams
• Side length proportional to √(value).
3. Circular or Pie Diagrams
• Circle divided into sectors; each sector’s angle proportional to value.
  Formula:
  Angle=Value of itemTotal value×360∘\text{Angle} = \frac{\text{Value of item}}{\text{Total value}} \times 360^\circ
4. Pictograms
• Pictures or symbols represent quantities; each symbol represents a fixed value.
5. Cartograms
• Map-based diagrams showing data geographically.

Advantages of Diagrammatic & Graphic Presentation

• Quick understanding of complex data.
• Easier to remember.
• Attracts attention.
• Helpful for comparisons.
• Reveals patterns and trends.

Limitations

• Less accurate than tabular form.
• Can mislead if not drawn to scale.
• Not suitable for very large and complex data analysis.

Video Description

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