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
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. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. 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.
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.