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Choice of class mark

The class mark is the midpoint of a class interval and is used as the representative value of that class in grouped-data calculations.

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Student-friendly explanation

The class mark stands for the centre of a class interval. It is found by adding the lower and upper limits and dividing by 2. In mean calculations, it provides one value that can represent all observations inside the class.

How to write this in exams

  1. 1

    Start with the exact idea

    The class mark is the midpoint of a class interval and is used as the representative value of that class in grouped-data calculations.

  2. 2

    Then show how to use it

    1. Take the lower limit. 2. Take the upper limit. 3. Add them. 4. Divide the sum by 2. 5. Use the midpoint as the representative value.

  3. 3

    Add one concrete example

    For the class 20-30, the class mark is (20 + 30) / 2 = 25.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to use the width of the class interval instead of its midpoint.

Definition

The class mark is the midpoint of a class interval and is used as the representative value of that class in grouped-data calculations.

Example

For the class 20-30, the class mark is (20 + 30) / 2 = 25.

Rule to remember

Class mark = (lower limit + upper limit) / 2.

Memory hook

Middle of the interval, middle of the calculation.

Examples and method

Worked example

For the class interval 40-50, class mark = (40 + 50)/2 = 45. This value is then used in mean and other grouped-data methods.

Method to apply

1. Take the lower limit. 2. Take the upper limit. 3. Add them. 4. Divide the sum by 2. 5. Use the midpoint as the representative value.

Diagram support

A small number line or interval sketch can help show the midpoint of each class interval.

How CBSE asks it

Students may be asked to calculate class marks before finding mean, assumed mean, or step deviation values.

Avoid common mistakes

Common confusion

Students sometimes choose the upper limit or lower limit instead of the midpoint.

Common wrong answer

A common wrong answer is to use the width of the class interval instead of its midpoint.

Exam tip

If the class interval is written as a range, the midpoint is almost always the safest representative value.

Quick check

How is the class mark of an interval found?

The class mark is found by adding the lower limit and upper limit of the class interval and dividing by 2. It gives the midpoint of the class.

Answer writing and exam use

1-mark answer

The class mark is the midpoint of a class interval and is used as the representative value of that class in grouped-data calculations.

2-mark answer

The class mark is the midpoint of a class interval and is used as the representative value of that class in grouped-data calculations. Class mark = (lower limit + upper limit) / 2. For the class 20-30, the class mark is (20 + 30) / 2 = 25.

3-mark answer

The class mark stands for the centre of a class interval. It is found by adding the lower and upper limits and dividing by 2. In mean calculations, it provides one value that can represent all observations inside the class. Class mark = (lower limit + upper limit) / 2. For the class interval 40-50, class mark = (40 + 50)/2 = 45. This value is then used in mean and other grouped-data methods. Students may be asked to calculate class marks before finding mean, assumed mean, or step deviation values. A common wrong answer is to use the width of the class interval instead of its midpoint.
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