Scatter Diagram – Construction & Interpretation

A Scatter Diagram (or Scatter Plot) is the simplest and most powerful visual tool to show the relationship between two variables. It helps you instantly see whether variables have positive, negative, or zero correlation.

It is the first step before calculating Karl Pearson’s Correlation.

Meaning of Scatter Diagram

A scatter diagram is a graph that displays paired values of two variables (X and Y) as dots on a chart.

Each observation becomes a single point:

(X₁, Y₁), (X₂, Y₂), (X₃, Y₃)…

The pattern of these points indicates the type and strength of correlation.

Types of Patterns in Scatter Diagrams

A scatter diagram can show three main patterns:

1. Positive Correlation

As X increases, Y increases.

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    .
     .
      .

Interpretation: Higher advertising → higher sales.

2. Negative Correlation

As X increases, Y decreases.

      .
    .
  .
.

Interpretation: Higher price → lower demand.

3. Zero (No) Correlation

No clear upward or downward pattern.

.   .  .  .   .   .
   .    .   .

Interpretation: Shoe size vs intelligence.

Steps to Construct a Scatter Diagram

Follow these simple steps:

Step 1: Collect Paired Data

Example:

Step 2: Draw Axes

• Horizontal axis → X variable
• Vertical axis → Y variable

Step 3: Mark Scales for X and Y

Example:

• X-axis: 0 to 40
• Y-axis: 0 to 50

Step 4: Plot the Points

Plot each pair (X, Y).

Step 5: Observe the Pattern

If the dots rise together → positive correlation. If the dots fall → negative correlation. If scattered randomly → zero correlation.

Example – Interpretation from a Scatter Plot

Suppose the plotted points show a rising pattern like:

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       .
         .

Conclusion: Strong positive correlation.

This visual conclusion often matches the numerical value of Karl Pearson’s r.

Importance of Scatter Diagram

Scatter diagrams are widely used because they:

• Provide a quick visual understanding of correlation.
• Help detect outliers.
• Show whether the relationship is linear or non-linear.
• Indicate whether it’s meaningful to compute Pearson’s correlation.
• Assist in quality control and forecasting.

Important Notes

• Scatter diagrams cannot measure exact numerical strength; they only show trend.
• Outliers can distort the pattern.
• The diagram alone cannot prove causation.

Summary

• Scatter diagram = plot of paired data.
• Shows positive, negative, or zero correlation.
• Helps understand pattern before calculation.
• Useful in business, finance, economics, and research.

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