medium difficulty5 min

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.

In one line: Middle of the interval, middle of the calculation.

Practice This Concept

Understand it

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.

Example

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

Formula and rule

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

See it worked out

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

Worked example

1For the class interval 40-50, class mark = (40 + 50)/2 = 45.
2This value is then used in mean and other grouped-data methods.

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

How is the class mark of an interval found?

Think first, then show answer

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.

Common wrong answer

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

Don't mix this up

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

Exam tip

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

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 calculate class marks before finding mean, assumed mean, or step deviation values.

1
Enough for 1 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.
2
Add for 2 marks
It is found by adding the lower and upper limits and dividing by 2.
3
Add for 3 marks
In mean calculations, it provides one value that can represent all observations inside the class.

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