ST9: Tables & Tabulation
Learn how to construct and interpret tally charts, frequency tables, grouped frequency tables, and two-way tables for GCSE Statistics.
Tables & Tabulation
Learn how to construct and interpret tally charts, frequency tables, grouped frequency tables, and two-way tables for GCSE Statistics.
Key Fact: A tally chart uses strokes to record data count, with every fifth stroke crossing the previous four for easy counting.
Key Fact: A frequency table lists each data value or class alongside its frequency (count of occurrences).
Key Fact: Grouped frequency tables organise continuous data into class intervals; each interval has a lower and upper boundary.
Key Fact: Class width is the difference between the upper and lower class boundaries; all classes in a table may have equal or unequal widths.
Key Fact: When using grouped frequency tables, the class interval should be written clearly, e.g. 10 ≤ x < 20, so there is no ambiguity about where a value belongs.
Key Fact: The midpoint of a class interval is calculated as (lower boundary + upper boundary) ÷ 2 and is used for estimating the mean.
Key Fact: Two-way tables (contingency tables) display data classified by two different variables, one in rows and one in columns.
Key Fact: In a two-way table, row totals and column totals allow you to analyse the relationship between the two variables.
Key Fact: Discrete data can be listed as individual values in a frequency table; continuous data must be grouped into class intervals.
Key Fact: When constructing a grouped frequency table, there should be no gaps or overlaps between class intervals.
Key Fact: Frequency density = frequency ÷ class width; this is used when drawing histograms with unequal class widths.
Key Fact: Relative frequency = frequency ÷ total frequency; it can be expressed as a decimal, fraction, or percentage.
📋 Key Vocabulary and Concepts
For Tables & Tabulation, you must know:
- Tally chart: A table that records data using tally marks, grouping every fifth mark as a diagonal stroke across four previous marks.
- Frequency: The number of times a particular value or class interval occurs in a set of data.
- Grouped frequency table: A table that shows the frequency of data values falling within each class interval.
- Two-way table: A table that displays data classified by two variables, with one variable in rows and the other in columns.
- Class interval: A range of values into which data is grouped, defined by a lower and upper boundary.
- Midpoint: The value halfway between the lower and upper boundaries of a class interval, found by averaging them.
❓ Practice Questions
Q: What is the advantage of using a tally chart when collecting data?
Q: Data is recorded in the grouped frequency table with class intervals 0–9, 10–19, 20–29. What is the class width of each interval?
Q: In a two-way table, 40 students study Biology, 30 study Chemistry, and 15 study both. How many study at least one subject?
Q: A grouped frequency table has class intervals 5 ≤ x < 15 and 15 ≤ x < 25. What is the midpoint of the second class?
Q: The total frequency is 200 and the frequency of the class 10 ≤ x < 20 is 50. What is the relative frequency of this class?
✅ Answers
- A tally chart allows data to be recorded quickly and efficiently as it is collected, and the grouped tally marks (every five) make counting easy.
- Each class interval has a width of 10. For the interval 0–9, the boundaries are –0.5 and 9.5, giving a width of 10.
- Using the addition rule: 40 + 30 – 15 = 55 students study at least one subject.
- The midpoint is (15 + 25) ÷ 2 = 20.
- Relative frequency = 50 ÷ 200 = 0.25 or 25%.
🎯 Exam Tips
- Always check whether class intervals are written using ≤ and < (e.g. 10 ≤ x < 20) so you know exactly which class a boundary value belongs to.
- In two-way table questions, always calculate row and column totals first — they help you find missing values and check your working.
- When asked to estimate the mean from a grouped frequency table, use midpoints of each class interval, not the upper or lower boundaries.
- If a question asks for the most common class interval, look for the highest frequency — not the widest class.
- When drawing up a grouped frequency table, choose class widths so that no class has a frequency of zero unless the data genuinely has a gap.
📝 Exam Technique
GCSE Statistics Exam Tips — Tables & Tabulation:
1. For Tables & Tabulation questions, show every step of your working clearly — method marks count even if the final answer is wrong
2. Check your answer makes sense in context (estimation, units, reasonableness)
3. Use correct mathematical notation and state formulae before substituting values
4. If a Tables & Tabulation question asks you to 'prove' or 'show', write a logical chain of reasoning with a conclusion line
5. For problem-solving, identify the topic first, then recall the relevant method
1. For Tables & Tabulation questions, show every step of your working clearly — method marks count even if the final answer is wrong
2. Check your answer makes sense in context (estimation, units, reasonableness)
3. Use correct mathematical notation and state formulae before substituting values
4. If a Tables & Tabulation question asks you to 'prove' or 'show', write a logical chain of reasoning with a conclusion line
5. For problem-solving, identify the topic first, then recall the relevant method
⚠️ Common Errors
✗ Writing class intervals as 0–10, 10–20 so that 10 appears in two intervals ✓ Use inequality notation such as 0 ≤ x < 10, 10 ≤ x < 20 so each value belongs to exactly one class.
✗ Using the upper class boundary as the midpoint ✓ The midpoint is the average of the lower and upper class boundaries: (lower + upper) ÷ 2.
✗ Forgetting to subtract the overlap when combining two categories in a two-way table ✓ When two categories overlap (e.g. both Biology and Chemistry), subtract the intersection once to avoid double-counting.
✗ Confusing frequency with frequency density ✓ Frequency is the raw count; frequency density is frequency ÷ class width, used specifically for histograms with unequal class widths.
✍️ Model Answer
Full-Mark Response
A survey of 60 households recorded the number of pets owned. The results are shown in the grouped frequency table below. Estimate the mean number of pets. Class intervals: 0–2 (f=22), 2–4 (f=18), 4–6 (f=12), 6–8 (f=8)
Class interval | Midpoint (m) | Frequency (f) | f x m 0 ≤ x < 2 | 1 | 22 | 22 2 ≤ x < 4 | 3 | 18 | 54 4 ≤ x < 6 | 5 | 12 | 60 6 ≤ x < 8 | 7 | 8 | 56 Total | | 60 | 192 Estimated mean = Σ(fm) ÷ Σf = 192 ÷ 60 = 3.2 pets. The mean is estimated because we use midpoints rather than the actual data values within each class.
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Knowledge & Understanding): Demonstrate knowledge and understanding of tables & tabulation, including data collection, presentation and calculation techniques relevant to Edexcel 1ST0 & AQA 8382.
AO2 (Application): Apply knowledge and understanding of tables & tabulation to interpret data, reason statistically and draw conclusions in context.
AO3 (Evaluation): Evaluate statistical methods and conclusions, assessing appropriateness, reliability, validity and bias through the statistical enquiry cycle.
📝 Exam Questions by Topic
- AQA Past Papers - Topic Questions -- AQA
- Edexcel Past Papers - Topic Questions -- Edexcel
- CCEA Past Papers - Topic Questions -- CCEA
🎬 Video Resources
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