C
CraftExam
medium difficulty5 min

Cumulative frequency

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

In one line: Cumulative means keep adding, not starting again.

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Understand it

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.

Example

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

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1If the frequencies are 2, 6, 4, and 3, then the cumulative frequencies are 2, 8, 12, and 15.
  2. 2Each new value is obtained by adding the current frequency to the previous total.

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What does cumulative frequency show in a grouped table?

Think first, then show answer
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.

Common wrong answer

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

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions may ask students to complete a cumulative frequency table before finding the median or drawing an ogive.
  1. 1

    Enough for 1 mark

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

  2. 2

    Add for 2 marks

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

  3. 3

    Add for 3 marks

    Cumulative frequency helps us see how many observations are counted up to a certain class.

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