Frequency Polygon & Curve – Construction

"Connecting the dots!" 📉

1. Frequency Polygon

[!NOTE] Definition: A many-sided closed figure formed by joining the mid-points of the top of histogram bars with straight lines.

Construction Methods:

Method A: Using Histogram

1. Draw a Histogram.
2. Mark the mid-point of the top of each rectangle.
3. Join these points with straight lines.
4. Join the ends to the X-axis (at mid-points of empty classes at both ends) to close the polygon.

Method B: Without Histogram

1. Calculate Mid-points of all classes.
2. Plot points (Mid-point, Frequency).
3. Join points with straight lines.
4. Close the polygon at both ends.

2. Frequency Curve

[!NOTE] Definition: A smooth freehand curve drawn through the points of a frequency polygon.

Difference from Polygon:

• Polygon: Joined by straight lines (Scale/Ruler). Sharp corners.
• Curve: Joined by freehand. Smooth turns. No sharp corners.
• Purpose: To show the general trend of distribution, ignoring minor fluctuations.

Types of Frequency Curves 🌊

1. Normal Curve (Bell-shaped): Symmetrical. Mean = Median = Mode. Most common in nature (Height, IQ).
2. Positively Skewed: Tail to the Right. (Income distribution - few rich people).
3. Negatively Skewed: Tail to the Left. (Age at death - most people die old).
4. U-shaped: High at ends, low in middle.
5. J-shaped: Rising or falling continuously.

Summary

• Frequency Polygon: Line graph joining mid-points. Closed figure.
• Frequency Curve: Smooth freehand version of polygon.
• Normal Curve: Bell-shaped, symmetrical.
• Skewed Curve: Asymmetrical (Tail to one side).

The Bottom Line: Polygon is precise; Curve is a smooth trend! 📉