Grouped Frequency Tables
Revise Grouped Frequency Tables for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Grouped frequency tables sort continuous data into class intervals.
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Topic overview
When data has many different values, it is grouped into class intervals so the pattern can be seen. A grouped frequency table shows how many values fall into each interval.
Intervals should be of equal width where possible, and there should usually be between five and ten of them. Too few hides the pattern; too many leaves the table as sparse as the raw data.
The cost of grouping is that individual values are lost. Once data is grouped you can no longer tell what the individual values were, so the mean can only be estimated using midpoints, and the exact median cannot be found. This trade-off between clarity and precision is examined directly.
Revision notes
Choosing intervals
Intervals should be of equal width where possible, and there should usually be between five and ten.
Too few intervals hides the pattern in the data. Too many leaves the table almost as sparse as the raw values. For continuous data use inequalities so there are no gaps.
What grouping costs
Individual values are lost once data is grouped.
You can see that four values fall between 150 and 160 cm, but not what those four values were. This is why the mean of grouped data can only be estimated.
Modal class
The modal class is the interval with the highest frequency.
Note it is a class, not a single value — you cannot identify the mode exactly from grouped data. Writing a single number as the answer loses the mark.
Key points
- Grouping puts data into class intervals.
- Intervals should usually be of equal width.
- Five to ten intervals is normally suitable.
- Individual values are lost when grouping.
- The mean can only be estimated from grouped data.
- The modal class is the interval with highest frequency.
Worked examples
Example 1
A grouped frequency table has classes with frequencies 6, 11, 9 and 4. State the modal class frequency. [1 mark]
Working
Example 2
Explain why the exact mean cannot be calculated from a grouped frequency table. [2 marks]
Working
Example 3
A student uses 25 class intervals for 30 data values. Give one criticism. [1 mark]
Working
Common mistakes
Giving a single value as the modal class.
The answer is the interval, not one number.
Saying the mean from grouped data is exact.
It is an estimate, because midpoints replace the actual values.
Using unequal intervals without reason.
Equal widths make comparison straightforward.
Leaving gaps between continuous intervals.
Use inequalities so every value has an interval.
Exam tips
- State the modal class as an interval, not a number.
- Always say estimate for the mean of grouped data.
- Aim for five to ten equal intervals.
- Explain the loss of individual values when asked why.
Key terms
- Class interval
- A group into which data values are placed.
- Grouped frequency table
- A table showing frequencies for class intervals.
- Modal class
- The interval with the highest frequency.
- Midpoint
- The middle value of a class, used to estimate the mean.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.