C
CraftExam
medium difficulty5 min

Ogive interpretation

An ogive is a cumulative frequency graph used to interpret grouped data and locate values such as the median.

In one line: Ogive means cumulative curve, not frequency bars.

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Understand it

An ogive is drawn from cumulative frequencies, usually less-than cumulative frequencies. Its shape helps us read positions like median and compare the spread of data. When the curve is drawn carefully, it gives a clear visual summary of the distribution.

Example

If the cumulative frequencies rise steadily and then flatten, the ogive shows how the data is distributed across classes.

Formula and rule

Ogive points are formed by plotting cumulative frequency against upper class boundaries for less-than ogive.

See it worked out

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

Worked example

If the less-than cumulative frequencies are 4, 10, 15, and 20 against upper boundaries 10, 20, 30, and 40, the ogive is formed by plotting these points and joining them smoothly.

Method you can reuse

  1. 1Prepare the cumulative frequency table.
  2. 2Mark boundaries on the x-axis.
  3. 3Mark cumulative frequencies on the y-axis.
  4. 4Plot the points.
  5. 5Join them smoothly and read required values.

Sketch it in your answer

Draw axes with class boundaries on the x-axis and cumulative frequency on the y-axis, then join the plotted points smoothly.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What kind of values are plotted on an ogive?

Think first, then show answer
Cumulative frequencies are plotted on an ogive, usually against class boundaries. The graph is then used to read median and other position-based values from the distribution.

Common wrong answer

A common wrong answer is to join points with straight bars like a histogram instead of drawing a smooth cumulative curve.

Don't mix this up

Students often plot ordinary frequencies on an ogive instead of cumulative frequencies.

Exam tip

For an ogive, always plot cumulative frequency against class boundary, not class mark.

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 often ask students to interpret an ogive, locate the median, or compare two data sets from their curves.
  1. 1

    Enough for 1 mark

    An ogive is a cumulative frequency graph used to interpret grouped data and locate values such as the median.

  2. 2

    Add for 2 marks

    Example: If the cumulative frequencies rise steadily and then flatten, the ogive shows how the data is distributed across classes.

  3. 3

    Add for 3 marks

    An ogive is drawn from cumulative frequencies, usually less-than cumulative frequencies.

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