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Mode of grouped data

The mode of grouped data is the value that occurs most frequently, estimated using the modal class and a standard formula.

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Student-friendly explanation

For grouped data, the exact most frequent value is not directly visible, so we estimate mode from the modal class. The formula uses the lower boundary of the modal class, the frequency of the modal class, and the frequencies of the class just before and just after it. This gives a practical estimate of the most common value.

How to write this in exams

  1. 1

    Start with the exact idea

    The mode of grouped data is the value that occurs most frequently, estimated using the modal class and a standard formula.

  2. 2

    Then show how to use it

    1. Identify the modal class. 2. Note l, h, f1, f0, and f2. 3. Substitute into the formula. 4. Simplify the fraction carefully. 5. Write the final value with units if needed.

  3. 3

    Add one concrete example

    If the modal class is 20-30, the mode lies near that class and is calculated using the grouped-data mode formula.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to use the class with the highest frequency but stop there, instead of applying the formula.

Definition

The mode of grouped data is the value that occurs most frequently, estimated using the modal class and a standard formula.

Example

If the modal class is 20-30, the mode lies near that class and is calculated using the grouped-data mode formula.

Rule to remember

Mode = l + [(f1 - f0) / (2f1 - f0 - f2)] x h, where l is lower boundary of modal class, f1 is modal class frequency, f0 is preceding frequency, f2 is succeeding frequency, and h is class width.

Memory hook

Mode lives near the tallest class, but the formula finds the exact estimate.

Examples and method

Worked example

If modal class is 20-30 with l = 20, h = 10, f1 = 12, f0 = 8, and f2 = 5, then mode = 20 + [(12 - 8)/(24 - 8 - 5)] x 10 = 20 + (4/11)x10 = 23.64 approximately.

Method to apply

1. Identify the modal class. 2. Note l, h, f1, f0, and f2. 3. Substitute into the formula. 4. Simplify the fraction carefully. 5. Write the final value with units if needed.

Diagram support

Use a frequency table and mark the modal class along with the preceding and succeeding frequencies before applying the formula.

How CBSE asks it

Board questions often ask for the mode of grouped data after giving a frequency table and may require identifying the modal class first.

Avoid common mistakes

Common confusion

Students often use the frequency of the modal class as the mode itself, which is not correct for grouped data.

Common wrong answer

A common wrong answer is to use the class with the highest frequency but stop there, instead of applying the formula.

Exam tip

Always identify the modal class first, then use the three frequencies around it carefully in the formula.

Quick check

Why is the mode of grouped data only an estimate?

It is only an estimate because grouped data does not show every original value separately. We know the interval with the highest frequency, so we calculate a value that best represents the most common observation.

Answer writing and exam use

1-mark answer

The mode of grouped data is the value that occurs most frequently, estimated using the modal class and a standard formula.

2-mark answer

The mode of grouped data is the value that occurs most frequently, estimated using the modal class and a standard formula. Mode = l + [(f1 - f0) / (2f1 - f0 - f2)] x h, where l is lower boundary of modal class, f1 is modal class frequency, f0 is preceding frequency, f2 is succeeding frequency, and h is class width. If the modal class is 20-30, the mode lies near that class and is calculated using the grouped-data mode formula.

3-mark answer

For grouped data, the exact most frequent value is not directly visible, so we estimate mode from the modal class. The formula uses the lower boundary of the modal class, the frequency of the modal class, and the frequencies of the class just before and just after it. This gives a practical estimate of the most common value. Mode = l + [(f1 - f0) / (2f1 - f0 - f2)] x h, where l is lower boundary of modal class, f1 is modal class frequency, f0 is preceding frequency, f2 is succeeding frequency, and h is class width. If modal class is 20-30 with l = 20, h = 10, f1 = 12, f0 = 8, and f2 = 5, then mode = 20 + [(12 - 8)/(24 - 8 - 5)] x 10 = 20 + (4/11)x10 = 23.64 approximately. Board questions often ask for the mode of grouped data after giving a frequency table and may require identifying the modal class first. A common wrong answer is to use the class with the highest frequency but stop there, instead of applying the formula.
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