Knowledge Organiser: Frequency Tables
This topic summary covers Knowledge Organiser: Frequency Tables within Frequency Tables for GCSE Mathematics. Revise Frequency Tables in Statistics for GCSE Mathematics with 11 exam-style questions and 20 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 8 of 8
Practice
11 questions
Recall
20 flashcards
Knowledge Organiser: Frequency Tables
Key Terms
- Frequency: How many times a value appears in the data
- Tally marks: A counting method grouped in fives (||||| = 5)
- Modal class: The group or value with the highest frequency
- Class width: The size of each group interval
- Midpoint: Middle value of a class interval = (lower + upper) ÷ 2
- Σ (sigma): Means "sum of" — used in mean formula
Must-Know Facts
- Total frequency must equal the number of data values — always check this
- The modal class is a range, not a single value (for grouped data)
- Use "≤ x <" notation — the lower boundary is included, upper is not
- For ungrouped data: mean = Σ(f × x) ÷ Σf
- For grouped data: use the midpoint of each class to estimate the mean
- Median position = (n + 1) ÷ 2, located using cumulative frequency
Key Formulas
- Mean (frequency table) = Σ(f × x) ÷ Σf
- Estimated mean (grouped) = Σ(f × midpoint) ÷ Σf
- Midpoint = (lower boundary + upper boundary) ÷ 2
- Median position = (n + 1) ÷ 2
Common Mistakes
- Dividing by number of groups: Mean = Σ(f×x) ÷ Σf — divide by the total frequency, NOT the number of rows
- Forgetting to find midpoints for grouped data: Always use the midpoint of each class, not the boundary
- Modal class vs mode: Grouped data gives a modal class (the class with highest frequency), not a single mode value
- Median from frequency table: Use cumulative frequency to find which group contains the median position
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Practice Questions for Frequency Tables
The table below shows the number of books read by students in a month: | Books read | Frequency | |---|---| | 0 | 4 | | 1 | 7 | | 2 | 11 | | 3 | 6 | | 4 | 2 | What is the mode?
Explain why the mean calculated from a grouped frequency table is described as an 'estimate' rather than an exact value.
Quick Recall Flashcards
11 questions on Frequency Tables — practise free
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