Histogram – Construction & Interpretation

Histogram is the "Bar Diagram" for Continuous Data! 📊

What is a Histogram?

[!NOTE] Definition: A graph of a frequency distribution in which class intervals are plotted on the X-axis and frequencies on the Y-axis.

• It consists of adjacent rectangles (no gaps).
• Area of rectangle represents frequency.

Difference: Histogram vs Bar Diagram

Construction Rules 🛠️

1. Equal Class Intervals

• Draw rectangles with Height = Frequency.
• Width = Class Interval.
• Example:
  • Class: 0-10, 10-20
  • Freq: 5, 10
  • Draw bar from 0 to 10 with height 5.
  • Draw bar from 10 to 20 with height 10.

2. Unequal Class Intervals

• If class widths are different (e.g., 0-10, 10-30), we must adjust frequency.
• Frequency Density = Frequency / Class Width.
• Plot Frequency Density on Y-axis.

3. Inclusive Series

• Convert to Exclusive Series first.
• (0-9, 10-19) → (-0.5 to 9.5, 9.5 to 19.5).
• Histogram must have continuous boundaries.

Uses of Histogram 🌟

1. To Find Mode:

   • The highest bar represents the Modal Class.
   • Join the top corners of the highest bar to the adjacent bars.
   • The intersection point gives the Mode on X-axis.

2. Visualizing Distribution:

   • Is it symmetric? (Bell curve)
   • Is it skewed? (Tail to left or right)

Summary

• Histogram = Adjacent rectangles for continuous data.
• No Gaps between bars.
• Area represents frequency.
• Used to find Mode graphically.
• For unequal classes, use Frequency Density.

The Bottom Line: If data is continuous (like height, weight), use a Histogram, not a Bar Chart! 📏