medium difficulty8 min

Assumed mean method

The assumed mean method is a shortcut for finding the mean of grouped data by taking one convenient central value as a reference.

In one line: Assume, deviate, multiply, correct, and finish.

Practice This Concept

Understand it

When numbers are large, direct multiplication can be lengthy. In the assumed mean method, we choose a class mark as an assumed mean, find deviations from it, multiply deviations by frequencies, and use the formula for mean. It saves time and reduces calculation load.

Example

If 20 is chosen as the assumed mean, then deviations are found from 20 and used to compute the mean quickly.

Formula and rule

Mean = A + [Σf_i d_i / Σf_i], where A is assumed mean and d_i = x_i - A.

See it worked out

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

Worked example

Take class marks 15, 25, 35 with frequencies 2, 3, 5 and choose A = 25.

1Then deviations are -10, 0, 10.
2So Σf_i d_i = 2(-10) + 3(0) + 5(10) = 30.
3Mean = 25 + 30/10 = 28.

Method you can reuse

1Choose a suitable assumed mean.
2Find deviations of class marks from it.
3Multiply each deviation by frequency.
4Add the products.
5Apply the formula and add the assumed mean at the end.

Sketch it in your answer

Make a table with class mark, assumed mean, deviation, frequency, and f_i d_i columns.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is the assumed mean method useful in grouped data?

Think first, then show answer

It is useful because it reduces long multiplication and makes the arithmetic easier. We work with small deviations from a chosen value, so the mean can be found faster and with fewer calculation errors.

Common wrong answer

A common wrong answer is to treat the assumed mean as the final mean without adding the correction term from deviations.

Don't mix this up

Students forget to add the assumed mean back at the final stage, so the answer becomes incomplete.

Exam tip

Choose a class mark near the center of the data to keep deviations small and calculations simple.

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 find mean using the assumed mean method for a grouped frequency table.

1
Enough for 1 mark
The assumed mean method is a shortcut for finding the mean of grouped data by taking one convenient central value as a reference.
2
Add for 2 marks
Example: If 20 is chosen as the assumed mean, then deviations are found from 20 and used to compute the mean quickly.
3
Add for 3 marks
When numbers are large, direct multiplication can be lengthy.

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