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medium difficulty8 min

Mean of grouped data

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

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

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Understand it

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.

Example

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

Formula and rule

Mean = Σ(fi xi) / Σfi, where xi is the class mark and fi is the frequency.

See it worked out

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

Worked example

For classes 0-10, 10-20, 20-30 with frequencies 4, 3, 5, class marks are 5, 15, 25.

  1. 1Then Σfi xi = 4x5 + 3x15 + 5x25 = 20 + 45 + 125 = 190 and Σfi = 12.
  2. 2So mean = 190/12 = 15.83 approximately.

Method you can reuse

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

Sketch it in your answer

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer
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.

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.

Don't mix this up

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

Exam tip

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

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

Board questions usually give a grouped table and ask for the mean, sometimes asking for a comparison after calculation.
  1. 1

    Enough for 1 mark

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

  2. 2

    Add for 2 marks

    For grouped data, we do not use every original value separately.

  3. 3

    Add for 3 marks

    This gives a single representative average for the whole data set.

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