Graphs of Frequency Distribution – Histogram, Frequency Polygon & Ogive 📊📉

Frequency data can be displayed visually using:

✔ Histogram
✔ Frequency Polygon
✔ Ogive (Cumulative Frequency Curve)

These are essential tools for analyzing distribution shapes, spread, skewness, and central tendency.

1. Histogram 🟥📦

A histogram is a set of adjacent rectangles representing class intervals (X-axis) and frequencies (Y-axis).

Features:

• No gaps between bars
• Used for continuous data
• Area of bars ∝ frequency (height shows frequency)
• Shows shape of distribution (normal, skewed, bimodal)

Example:

Marks distribution (class intervals & frequencies):

Histogram: Rectangles from 0–10, 10–20, etc., with heights 5, 9, 12, 8.

2. Frequency Polygon 🔺📈

A frequency polygon is drawn by:

• Plotting mid-points of each class
• Connecting them with straight lines
• Starting and ending at zero frequency

Often drawn over the histogram for clarity.

Why use a polygon?

✔ Shows shape more clearly than histogram
✔ Useful for comparing two distributions
✔ Less cluttered

Example Midpoints

Class 0–10 → midpoint = 5
Class 10–20 → midpoint = 15

Plot (5,5), (15,9), (25,12), (35,8)

3. Ogive (Cumulative Frequency Curve) 🌙📉

Used for:

• Median
• Quartiles
• Percentiles

There are two types:

A. Less Than Ogive

Plot:

Less than 10 → 5
Less than 20 → 14
Less than 30 → 26
Less than 40 → 34

Join points with a smooth curve.

Shows how many observations fall below a certain value.

B. More Than Ogive

Plot:

More than 0 → 34
More than 10 → 29
More than 20 → 20
More than 30 → 8

Intersection of Less Than & More Than Ogive = Median

This is a common exam question.

ASCII Diagram — Frequency Graphs Flow

Histogram
↓
Frequency Polygon
↓
Ogive (Less Than / More Than)

Summary ✨

• Histogram → continuous data, no gaps
• Polygon → midpoints connected
• Ogive → cumulative frequencies used for median, quartiles

Quiz Time! 🎯