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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.

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

Assume, deviate, multiply, correct, and finish.

Examples and method

Worked example

Take class marks 15, 25, 35 with frequencies 2, 3, 5 and choose A = 25. Then deviations are -10, 0, 10. So Σf_i d_i = 2(-10) + 3(0) + 5(10) = 30. Mean = 25 + 30/10 = 28.

Method to apply

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

Diagram support

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

How CBSE asks it

Questions often ask students to find mean using the assumed mean method for a grouped frequency table.

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

Why is the assumed mean method useful in grouped data?

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.

Answer writing and exam use

1-mark answer

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

2-mark answer

The assumed mean method is a shortcut for finding the mean of grouped data by taking one convenient central value as a reference. Mean = A + [Σf_i d_i / Σf_i], where A is assumed mean and d_i = x_i - A. If 20 is chosen as the assumed mean, then deviations are found from 20 and used to compute the mean quickly.

3-mark answer

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. Mean = A + [Σf_i d_i / Σf_i], where A is assumed mean and d_i = x_i - A. Take class marks 15, 25, 35 with frequencies 2, 3, 5 and choose A = 25. Then deviations are -10, 0, 10. So Σf_i d_i = 2(-10) + 3(0) + 5(10) = 30. Mean = 25 + 30/10 = 28. Questions often ask students to find mean using the assumed mean method for a grouped frequency table. A common wrong answer is to treat the assumed mean as the final mean without adding the correction term from deviations.
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