Averages from Grouped Data

This lesson covers how to calculate averages and identify key features from grouped frequency tables — a topic that appears regularly on the AQA GCSE Mathematics exam. Because individual data values are lost in grouped data, you cannot find exact averages; instead, you estimate them. Understanding this distinction is crucial for full marks.

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Why Grouped Data Is Different

When data is presented in a grouped frequency table, you do not know the exact values — only that they fall within certain class intervals. This means:

• You can only calculate an estimated mean (not an exact mean).
• You can identify the modal class (not an exact mode).
• You can find the class containing the median (not an exact median).

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Estimated Mean from Grouped Data

To estimate the mean from a grouped frequency table:

1. Find the midpoint of each class interval.
2. Multiply each midpoint by its frequency.
3. Add up all the (midpoint x frequency) values.
4. Divide by the total frequency.

Estimated mean = sum of (midpoint x frequency) / total frequency

Worked Example