What is a Cumulative Frequency Table?

S3-SA3-0022

Grade Level:

Class 8

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A Cumulative Frequency Table shows the running total of frequencies. It helps us quickly see how many data points fall below a certain value, by adding up the frequencies as we go along.

Simple Example

Quick Example

Imagine you're counting how many students scored marks in different ranges on a math test. A regular frequency table tells you how many scored between 0-20, 21-40, etc. A cumulative frequency table would tell you how many students scored *up to* 20, *up to* 40, *up to* 60, and so on.

Worked Example

Step-by-Step

Let's make a cumulative frequency table for the number of mobile phones owned by families in a small colony.

Original Data:
Number of Phones | Number of Families (Frequency)
-----------------|--------------------------------
0 | 2
1 | 5
2 | 8
3 | 3
4 | 2

Step 1: Start with the first frequency. The cumulative frequency for 0 phones is 2.

Step 2: Add the next frequency to the previous cumulative frequency. For 1 phone, it's 2 (from 0 phones) + 5 (for 1 phone) = 7.

Step 3: Continue this process. For 2 phones, it's 7 (cumulative for 1 phone) + 8 (for 2 phones) = 15.

Step 4: For 3 phones, it's 15 (cumulative for 2 phones) + 3 (for 3 phones) = 18.

Step 5: For 4 phones, it's 18 (cumulative for 3 phones) + 2 (for 4 phones) = 20.

Answer: The Cumulative Frequency Table is:
Number of Phones | Frequency | Cumulative Frequency
-----------------|-----------|----------------------
0 | 2 | 2
1 | 5 | 7
2 | 8 | 15
3 | 3 | 18
4 | 2 | 20

Why It Matters

Understanding cumulative frequency is super useful in fields like Data Science and AI/ML, where you often need to analyze large datasets. It helps economists understand income distribution and engineers analyze failure rates. You could be the next data scientist at an e-commerce giant!

Common Mistakes

MISTAKE: Not adding the frequencies correctly, or starting the cumulative frequency from 0. | CORRECTION: Always start the first cumulative frequency with the first actual frequency. Each subsequent cumulative frequency is the sum of the *current* frequency and the *previous* cumulative frequency.

MISTAKE: Confusing cumulative frequency with just frequency. | CORRECTION: Frequency is for a specific interval or value, while cumulative frequency is the *total up to that point*.

MISTAKE: Thinking the last cumulative frequency is always 100. | CORRECTION: The last cumulative frequency should always be equal to the *total number of data points* (the sum of all frequencies), not necessarily 100 unless the frequencies are percentages.

Practice Questions

Try It Yourself

QUESTION: A class recorded the number of books read in a month by students:
Books Read | Students (Frequency)
-----------|---------------------
0 | 3
1 | 7
2 | 5
3 | 2
What is the cumulative frequency for students who read 'up to 1' book? | ANSWER: 10

QUESTION: A survey asked people about their daily chai consumption:
Chai Cups | People (Frequency)
----------|-------------------
0-1 | 10
2-3 | 15
4-5 | 8
6+ | 2
What is the cumulative frequency for people who drink 'up to 5' cups of chai? | ANSWER: 33

QUESTION: The marks obtained by 25 students in a test are given:
Marks Range | Number of Students
------------|--------------------
0-20 | 5
21-40 | 9
41-60 | 7
61-80 | 4
Construct a complete cumulative frequency table for this data. | ANSWER:
Marks Range | Frequency | Cumulative Frequency
------------|-----------|---------------------
0-20 | 5 | 5
21-40 | 9 | 14
41-60 | 7 | 21
61-80 | 4 | 25

MCQ

Quick Quiz

If the frequency for a certain class interval is 12, and the cumulative frequency of the *previous* interval was 30, what is the cumulative frequency for the *current* interval?

The Correct Answer Is:

Cumulative frequency is found by adding the current frequency to the previous cumulative frequency. So, 30 + 12 = 42.

Real World Connection

In the Real World

In India, companies like Flipkart or Amazon use cumulative frequency to understand customer buying patterns. For example, they might look at how many customers spent 'up to Rs. 500', 'up to Rs. 1000', etc., to plan sales and offers. Even cricket analysts use it to see how many runs a batsman has scored 'up to' a certain number of matches.

Key Vocabulary

Key Terms

FREQUENCY: How often a particular value or range appears in a dataset. | CUMULATIVE: Building up or increasing by successive additions. | DATASET: A collection of related data. | RUNNING TOTAL: A total that is continuously updated as new numbers are added.

What's Next

What to Learn Next

Now that you understand cumulative frequency, you're ready to learn about 'Cumulative Frequency Curves' (also called Ogives). This will show you how to visually represent this data and quickly find important values like the median.