A LITTLE PRACTICE, EVERY DAY·GCSE MATHS
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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.

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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.

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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).
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Formulas

Mean from frequency table
Mean = Σ(x × f) / Σf

x = value, f = frequency

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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
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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.
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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.

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