Cumulative Frequency

 

What Does “Cumulative” Mean?

“Cumulative” means adding up as you go — like a running total.

]In statistics, cumulative frequency tells us how many data points are less than or equal to a certain value.

It’s super useful when:

• You want to understand how data builds up over time
• You’re preparing to draw a cumulative frequency graph
• You want to find the median, quartiles, or percentiles

 

How Do I Create a Cumulative Frequency Table?

Let’s say a group of students were timed running a 100m sprint. Their times were grouped into a table like this:

 

Time (s)	Frequency
$10 \leq t \lt 12$	4
$12 \leq t \lt 14$	6
$14 \leq t \lt 16$	9
$16 \leq t \lt 18$	5
$18 \leq t \lt 20$	2

 

To make a cumulative frequency table, we add a third column:

 

Time (s)	Frequency	Cumulative Frequency
$10 \leq t \lt 12$	4	4
$12 \leq t \lt 14$	6	4 + 6 = 10
$14 \leq t \lt 16$	9	10 + 9 = 19
$16 \leq t \lt 18$	5	19 + 5 = 24
$18 \leq t \lt 20$	2	24 + 2 = 26

 

Final cumulative frequency = total number of students = 26

 

Alternative Format

Sometimes, cumulative tables show only the upper boundary of each class:

 

Time (t < x)	Cumulative Frequency
t < 12	4
t < 14	10
t < 16	19
t < 18	24
t < 20	26

 

From this version, we can subtract to get the individual class frequencies:

• 10 - 4 = 6 $\to$ frequency of $12 \leq t \lt 14$
• 19 - 10 = 9 $\to$ frequency of $14 \leq t \lt 16$
• etc.