Diagrammatic & Graphical Presentation of Data

1. Why Use Visual Presentations?

A manager presented with 10 pages of raw spreadsheets cannot quickly identify trends. Visual representations convert cold figures into compelling stories:

Attractive and Eye-Catching: Captures executive attention immediately.
Simplifies Complex Facts: Highlights patterns, spikes, and declines.
Facilitates Instant Comparison: Compares performance across years or competitors.
Universal Appeal: Understandable even to non-mathematical audiences.

2. Diagrammatic vs. Graphical Presentation

Feature	Diagrams (Geometric Figures)	Graphs (Plotted on Coordinate Axes)
Medium	Drawn on plain paper or presentation slides.	Plotted precisely on ruled graph paper (X and Y axes).
Data Nature	Best for categorical or discrete data (e.g., Sales by country).	Best for continuous frequency distributions and time series.
Purpose	Visual comparison and public display.	Mathematical analysis and determining values (Median, Mode).
Examples	Simple Bar, Multiple Bar, Pie Chart.	Histogram, Frequency Polygon, Ogives.

3. Major Types of Business Diagrams

5 Standard Business Diagrams

1. Simple Bar Diagram

Rectangular bars of uniform width and equal spacing, where height represents magnitude.

2. Multiple Bar Diagram

Two or more adjacent bars grouped together to compare related variables (e.g., Import vs. Export).

3. Sub-Divided (Component) Bar

Total bar is segmented into internal components (e.g., Total cost split into Material, Labor & Overhead).

4. Percentage Bar Diagram

All bars are drawn to a uniform 100% height, showing relative percentage shares.

5. Pie Chart (Circular Diagram)

A circle divided into angular sectors proportional to component values.

How to Construct a Pie Chart:

Calculate the total sum of all components (Total = ΣX).
Convert each component value into degrees of a circle (total circle = 360°):
Angle of Sector = (Component Value ÷ Total Value) × 360°
Draw a circle using a compass, measure angles with a protractor, and use distinct colors or shading for each segment.

4. Graphs of Frequency Distributions

For continuous grouped data, four primary graphs are used in business statistics:

A. Histogram (Finding Mode Graphically)

Structure: A series of adjacent vertical rectangles with no gaps between them.
- Class intervals are placed on the X-axis.
- Frequencies are plotted on the Y-axis.
- Area of each rectangle is directly proportional to its frequency.
Finding Mode from Histogram:
1. Identify the tallest bar (modal class).
2. Join the top-left corner of the modal rectangle to the top-left corner of the next rectangle.
3. Join the top-right corner of the modal rectangle to the top-right corner of the preceding rectangle.
4. From the intersection point of these two diagonal lines, drop a perpendicular to the X-axis.
5. The value on the X-axis is the Mode!

B. Frequency Polygon & Frequency Curve

Frequency Polygon: Formed by plotting mid-points of each class interval against frequency and connecting them with straight line segments.
Frequency Curve: Formed by smoothing the sharp jagged corners of a polygon into a gentle, continuous curve with a freehand stroke.

C. Ogives (Cumulative Frequency Curves & Finding Median)

An Ogive (pronounced Oh-jive) is a graph of cumulative frequencies. There are two types:

“Less Than” Ogive: Rises upward from left to right (S-shaped curve). Plotted against upper class limits.
“More Than” Ogive: Falls downward from left to right. Plotted against lower class limits.

How to Determine the Median Graphically Using Ogives

Step 1

Plot Both Ogives

Plot 'Less than' & 'More than' curves on the same graph

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Step 2

Intersection Point (E)

Locate point where both curves cross each other

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Step 3

Drop Perpendicular

Draw a vertical straight line down to the X-axis

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Result

Exact Median (M)

The reading on the X-axis is exactly equal to the Median!

Cumulative Frequency (cf)
  ^
N | \             /  <-- "Less Than" Ogive
  |  \           /
N/2|----\-------* E (Intersection Point)
  |      \     /|
  |       \   / |
  |        \ /  |
  0 +-------*---|-------------> Variable X (Marks / Wages)
            0   Median (M)

(Note: The point where the two Ogives intersect corresponds exactly to N ÷ 2 on the vertical Y-axis and the Median on the horizontal X-axis!)

Diagrammatic & Graphical Presentation of Data | BBA Notes