EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
📊
Statistics & Probability · Foundation & Higher

Frequency tables

Frequency tables organise data by listing values (or groups) and how often each occurs. You use them to find averages and draw charts.

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) / Σf

x = value, f = frequency

✍️

Worked examples

Example 1

The table shows scores: Score 1(f=3), 2(f=5), 3(f=4), 4(f=2), 5(f=1). Find the mean.

Working

  1. Σ(x × f) = 1×3 + 2×5 + 3×4 + 4×2 + 5×1 = 3 + 10 + 12 + 8 + 5 = 38
  2. Σf = 3 + 5 + 4 + 2 + 1 = 15
  3. Mean = 38 ÷ 15 = 2.53 (2 d.p.)
AnswerMean ≈ 2.53
Example 2

From the same table, find the median.

Working

  1. Total frequency = 15, so median is the 8th value
  2. Cumulative frequencies: 3, 8, 12, 14, 15
  3. The 8th value falls in the score 2 group (cumulative reaches 8)
  4. 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 →
← All topicsDashboard

▶️ Watch on YouTube

Free video lessons

Click a topic to search

frequency tables GCSE mathsmean from frequency table GCSEmedian frequency table GCSEfrequency table averages GCSE

Opens YouTube — pick any free GCSE video.