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Mean of grouped data

The mean of grouped data is the average value found by using class marks and frequencies of the grouped table.

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Student-friendly explanation

For grouped data, we do not use every original value separately. We first take the class mark of each class interval, multiply it by the frequency, add all such products, and divide by total frequency. This gives a single representative average for the whole data set.

How to write this in exams

  1. 1

    Start with the exact idea

    The mean of grouped data is the average value found by using class marks and frequencies of the grouped table.

  2. 2

    Then show how to use it

    1. Find the class mark of each class. 2. Multiply each class mark by its frequency. 3. Add all products. 4. Add all frequencies. 5. Divide total of products by total frequency.

  3. 3

    Add one concrete example

    If class marks are 10, 20, and 30 with frequencies 2, 3, and 5, then mean = (2x10 + 3x20 + 5x30) / 10 = 23.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to average the class intervals themselves, which ignores the frequency distribution and the representative value of each class.

Definition

The mean of grouped data is the average value found by using class marks and frequencies of the grouped table.

Example

If class marks are 10, 20, and 30 with frequencies 2, 3, and 5, then mean = (2x10 + 3x20 + 5x30) / 10 = 23.

Rule to remember

Mean = Σ(f_i x_i) / Σf_i, where x_i is the class mark and f_i is the frequency.

Memory hook

Think: class mark first, frequency next, then divide at the end.

Examples and method

Worked example

For classes 0-10, 10-20, 20-30 with frequencies 4, 3, 5, class marks are 5, 15, 25. Then Σf_i x_i = 4x5 + 3x15 + 5x25 = 20 + 45 + 125 = 190 and Σf_i = 12. So mean = 190/12 = 15.83 approximately.

Method to apply

1. Find the class mark of each class. 2. Multiply each class mark by its frequency. 3. Add all products. 4. Add all frequencies. 5. Divide total of products by total frequency.

Diagram support

Use a frequency table with class intervals, class marks, f_i x_i, and totals written neatly in columns.

How CBSE asks it

Board questions usually give a grouped table and ask for the mean, sometimes asking for a comparison after calculation.

Avoid common mistakes

Common confusion

Students often use class intervals directly instead of class marks, which gives an incorrect mean.

Common wrong answer

A common wrong answer is to average the class intervals themselves, which ignores the frequency distribution and the representative value of each class.

Exam tip

Always write the class mark first, then multiply by frequency, and keep the total frequency in the denominator.

Quick check

Why do we use class marks while finding the mean of grouped data?

We use class marks because the actual values inside each class interval are not listed separately. The class mark acts as one representative value for that class and helps us calculate the average correctly.

Answer writing and exam use

1-mark answer

The mean of grouped data is the average value found by using class marks and frequencies of the grouped table.

2-mark answer

The mean of grouped data is the average value found by using class marks and frequencies of the grouped table. Mean = Σ(f_i x_i) / Σf_i, where x_i is the class mark and f_i is the frequency. If class marks are 10, 20, and 30 with frequencies 2, 3, and 5, then mean = (2x10 + 3x20 + 5x30) / 10 = 23.

3-mark answer

For grouped data, we do not use every original value separately. We first take the class mark of each class interval, multiply it by the frequency, add all such products, and divide by total frequency. This gives a single representative average for the whole data set. Mean = Σ(f_i x_i) / Σf_i, where x_i is the class mark and f_i is the frequency. For classes 0-10, 10-20, 20-30 with frequencies 4, 3, 5, class marks are 5, 15, 25. Then Σf_i x_i = 4x5 + 3x15 + 5x25 = 20 + 45 + 125 = 190 and Σf_i = 12. So mean = 190/12 = 15.83 approximately. Board questions usually give a grouped table and ask for the mean, sometimes asking for a comparison after calculation. A common wrong answer is to average the class intervals themselves, which ignores the frequency distribution and the representative value of each class.
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