Revising frequency tables the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Frequency tables GCSE” on the site for the complete guide.
🔑
Key facts to remember
- 1Frequency = how many times a value occurs.
- 2A tally chart groups frequencies as data is collected.
- 3To find the mean from a frequency table: sum of (value × frequency) ÷ total frequency.
- 4The mode is the value with the highest frequency.
- 5The median is found by locating the middle value using cumulative frequency.
- 6Grouped frequency tables use class intervals (e.g. 10 ≤ x < 20).
📐
Formulas
Mean from frequency table
Mean = Σ(x × f) / Σfx = value, f = frequency
✍️
Worked examples
Example 1The table shows scores: Score 1(f=3), 2(f=5), 3(f=4), 4(f=2), 5(f=1). Find the mean.
Working
- Σ(x × f) = 1×3 + 2×5 + 3×4 + 4×2 + 5×1 = 3 + 10 + 12 + 8 + 5 = 38
- Σf = 3 + 5 + 4 + 2 + 1 = 15
- Mean = 38 ÷ 15 = 2.53 (2 d.p.)
AnswerMean ≈ 2.53
Example 2From the same table, find the median.
Working
- Total frequency = 15, so median is the 8th value
- Cumulative frequencies: 3, 8, 12, 14, 15
- The 8th value falls in the score 2 group (cumulative reaches 8)
- Median = 2
AnswerMedian = 2
⚠️
Common mistakes
✗Finding the mean by averaging the values without weighting by frequency.
✗Reading the modal class instead of the modal value in a frequency table.
✗Miscounting cumulative frequency when finding the median position.
🎯
Exam tips
✓Add a "x × f" column to the table — it makes the mean calculation much less error-prone.
✓For the median, find the position (n+1)/2 first, then locate which group that falls in.
Ready to test yourself on Frequency tables?
Get AI-marked practice questions on exactly this subtopic.
Practice this topic →