Cumulative Frequency Diagrams

 

What Is a Cumulative Frequency Diagram?

A cumulative frequency diagram is a graph that shows how the data builds up over time or across class intervals.

It helps us understand how many values fall below a certain point in a grouped dataset.

These diagrams are perfect for estimating:

• The median
• Quartiles
• Percentiles
• And for spotting how the data is spread

 

How Do I Draw One?

Let’s go step by step using a fresh example.

Example: Quiz Scores

A teacher records the scores of 60 students in a quiz and groups them like this:

 

Score (x/100)	Frequency
$20 \leq x \lt 30$	5
$30 \leq x \lt 40$	8
$40 \leq x \lt 50$	16
$50 \leq x \lt 60$	17
$60 \leq x \lt 70$	9
$70 \leq x \lt 80$	5

 

Step 1: Add the Cumulative Frequency Column

 

Score (x/100)	Frequency	Cumulative Frequency
$20 \leq x \lt 30$	5	5
$30 \leq x \lt 40$	8	5 + 8 = 13
$40 \leq x \lt 50$	16	13 + 16 = 29
$50 \leq x \lt 60$	17	29 + 17 = 46
$60 \leq x \lt 70$	9	46 + 9 = 55
$70 \leq x \lt 80$	5	55 + 5 = 60

 

Step 2: Plot the Cumulative Frequency

 

On graph paper or digital software, use the following coordinate pairs:

• (30, 5)
• (40, 13)
• (50, 29)
• (60, 46)
• (70, 55)
• (80, 60)

📌 Don’t forget:

Add a starting point at the beginning of the lowest group:

→ (20, 0)

 

Step 3: Draw the Curve

 

• Plot all the points carefully
• Connect them with a smooth curved line — not straight segments!
• You should see an “S-shaped” curve that never goes backwards