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Less-than cumulative frequency table

A less-than cumulative frequency table lists the number of observations less than each upper class boundary.

In one line: Less-than means count up to the upper boundary.

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Understand it

In this table, we keep adding frequencies and write totals against the upper limits of the classes. It is very useful for finding the median and for drawing ogives. The data becomes easier to interpret because the totals increase smoothly from top to bottom.

Example

For classes 0-10, 10-20, 20-30 with frequencies 4, 6, 5, the less-than cumulative frequencies are 4, 10, 15.

Formula and rule

Less-than cumulative frequency = running total of frequencies written against upper class boundaries.

See it worked out

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

Worked example

  1. 1If the classes are 0-5, 5-10, 10-15 and frequencies are 2, 4, 3, the less-than cumulative frequencies are 2, 6, 9.
  2. 2These are written against 5, 10, and 15 respectively.

Method you can reuse

  1. 1Write the class intervals in order.
  2. 2Add frequencies step by step.
  3. 3Attach each running total to the upper boundary.
  4. 4Check that the last total equals total frequency.
  5. 5Use the table for graphing or median work.

Sketch it in your answer

Make a table with class interval, frequency, and less-than cumulative frequency against upper boundaries.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is the less-than cumulative frequency table helpful in Statistics?

Think first, then show answer
It is helpful because it turns grouped data into a running total that is easy to read and graph. It is also used directly for finding the median and for drawing an ogive.

Common wrong answer

A common wrong answer is to write the totals beside lower boundaries, which breaks the pattern used for an ogive.

Don't mix this up

Students sometimes attach the cumulative total to the lower boundary instead of the upper boundary.

Exam tip

Write the upper class boundary carefully; the graph and median position depend on it.

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

Students may be asked to complete a less-than cumulative frequency table before plotting an ogive or finding the median.
  1. 1

    Enough for 1 mark

    A less-than cumulative frequency table lists the number of observations less than each upper class boundary.

  2. 2

    Add for 2 marks

    Example: For classes 0-10, 10-20, 20-30 with frequencies 4, 6, 5, the less-than cumulative frequencies are 4, 10, 15.

  3. 3

    Add for 3 marks

    In this table, we keep adding frequencies and write totals against the upper limits of the classes.

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