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Cumulative frequency

Cumulative frequency is the running total of frequencies up to a class interval.

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Student-friendly explanation

Cumulative frequency helps us see how many observations are counted up to a certain class. It is built by adding frequencies step by step. This is very useful for median, ogive, and data interpretation questions.

How to write this in exams

  1. 1

    Start with the exact idea

    Cumulative frequency is the running total of frequencies up to a class interval.

  2. 2

    Then show how to use it

    1. Write the first frequency as it is. 2. Add the second frequency to the first total. 3. Continue adding each next frequency to the previous cumulative total. 4. Verify the final total with the sum of all frequencies.

  3. 3

    Add one concrete example

    If frequencies are 4, 3, and 5, then cumulative frequencies are 4, 7, and 12.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to confuse frequency with cumulative frequency and repeat the same numbers down the table.

Definition

Cumulative frequency is the running total of frequencies up to a class interval.

Example

If frequencies are 4, 3, and 5, then cumulative frequencies are 4, 7, and 12.

Rule to remember

Cumulative frequency of a class = sum of its frequency and all previous frequencies.

Memory hook

Cumulative means keep adding, not starting again.

Examples and method

Worked example

If the frequencies are 2, 6, 4, and 3, then the cumulative frequencies are 2, 8, 12, and 15. Each new value is obtained by adding the current frequency to the previous total.

Method to apply

1. Write the first frequency as it is. 2. Add the second frequency to the first total. 3. Continue adding each next frequency to the previous cumulative total. 4. Verify the final total with the sum of all frequencies.

Diagram support

Prepare a two-column table with frequency and cumulative frequency side by side.

How CBSE asks it

Questions may ask students to complete a cumulative frequency table before finding the median or drawing an ogive.

Avoid common mistakes

Common confusion

Students sometimes write each class frequency again instead of adding them cumulatively.

Common wrong answer

A common wrong answer is to confuse frequency with cumulative frequency and repeat the same numbers down the table.

Exam tip

Check the running total after every row; one wrong addition can affect the full table and the median.

Quick check

What does cumulative frequency show in a grouped table?

Cumulative frequency shows the running total of observations up to each class interval. It tells us how many data values have been counted by the time we reach that class.

Answer writing and exam use

1-mark answer

Cumulative frequency is the running total of frequencies up to a class interval.

2-mark answer

Cumulative frequency is the running total of frequencies up to a class interval. Cumulative frequency of a class = sum of its frequency and all previous frequencies. If frequencies are 4, 3, and 5, then cumulative frequencies are 4, 7, and 12.

3-mark answer

Cumulative frequency helps us see how many observations are counted up to a certain class. It is built by adding frequencies step by step. This is very useful for median, ogive, and data interpretation questions. Cumulative frequency of a class = sum of its frequency and all previous frequencies. If the frequencies are 2, 6, 4, and 3, then the cumulative frequencies are 2, 8, 12, and 15. Each new value is obtained by adding the current frequency to the previous total. Questions may ask students to complete a cumulative frequency table before finding the median or drawing an ogive. A common wrong answer is to confuse frequency with cumulative frequency and repeat the same numbers down the table.
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