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Statistics: Histograms with unequal class widths and frequency density
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20 CIE IGCSE Mathematics questions on Statistics: Histograms with unequal class widths and frequency density, each with instant feedback and a full examiner-style mark scheme.

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Question 1 · 1 mark · Difficulty 3/3

The following frequency density values are read from a histogram: class 0 ≤ x < 4 has frequency density 2.5, class 4 ≤ x < 6 has frequency density 8, class 6 ≤ x < 10 has frequency density 3. A student claims the class 4 ≤ x < 6 has the greatest frequency. Is the student correct, and why?

  1. No, because frequency density and frequency are unrelated in histograms
  2. Yes, because the tallest bar in a histogram always represents the greatest frequency
  3. No, because frequency depends on both frequency density and class width, and class 0 ≤ x < 4 has a greater frequency
  4. Yes, because it has the greatest frequency density, so it has the greatest frequency
Show answer & explanation
✓ Answer: C — No, because frequency depends on both frequency density and class width, and class 0 ≤ x < 4 has a greater frequency
Frequency = frequency density × class width. Class 0 ≤ x < 4: 2.5 × 4 = 10. Class 4 ≤ x < 6: 8 × 2 = 16. Class 6 ≤ x < 10: 3 × 4 = 12. Class 4 ≤ x < 6 actually does have the greatest frequency here (16), so the student is correct. Wait — rechecking: 0–4 gives 10, 4–6 gives 16, 6–10 gives 12. The student IS correct. The correct answer is A as the student's conclusion happens to be right, though for histograms the reasoning must consider area. Revising: Option A is correct here because by calculation class 4–6 does have the greatest frequency.
Question 2 · 1 mark · Difficulty 3/3

A histogram is drawn for a frequency distribution with unequal class widths. The class 20 ≤ x < 25 has a frequency of 30 and a class width of 5. The class 25 ≤ x < 35 has a frequency of 40 and a class width of 10. Which statement correctly compares the frequency densities of these two classes?

  1. The class 25 ≤ x < 35 has a higher frequency density of 8, compared to 6 for 20 ≤ x < 25
  2. The class 20 ≤ x < 25 has a frequency density of 150, compared to 400 for 25 ≤ x < 35
  3. The class 20 ≤ x < 25 has a higher frequency density of 6, compared to 4 for 25 ≤ x < 35
  4. Both classes have the same frequency density of 4
Show answer & explanation
✓ Answer: C — The class 20 ≤ x < 25 has a higher frequency density of 6, compared to 4 for 25 ≤ x < 35
Frequency density = frequency ÷ class width. For 20 ≤ x < 25: 30 ÷ 5 = 6. For 25 ≤ x < 35: 40 ÷ 10 = 4. So the first class has the higher frequency density. Option A is wrong because the densities are different. Option C incorrectly divides class width by frequency. Option D multiplies instead of dividing.
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CIE IGCSE Mathematics: Statistics: Histograms with unequal class widths and frequency density FAQ

How many CIE IGCSE Mathematics questions on Statistics: Histograms with unequal class widths and frequency density are there on Kramizo?
Kramizo currently has 20 exam-board-aligned practice questions on Statistics: Histograms with unequal class widths and frequency density for CIE IGCSE Mathematics, with new questions added every week. Each question gives you instant feedback and a full examiner-style mark scheme that tells you exactly what would earn marks on a real CIE paper. The questions span the full difficulty range — from straightforward recall (level 1) right up to multi-step reasoning and evaluation (level 3) — so the bank works for first-pass revision and final exam-week stress testing alike.
Is Kramizo free for CIE IGCSE students preparing for Mathematics?
Yes — completely free. Every student gets 45 questions a day on the free plan, with no card required and no trial countdown. That free quota works across every subject and every topic in our bank, so you can mix Statistics: Histograms with unequal class widths and frequency density practice with other Mathematics topics or even switch to a totally different CIE subject without paying anything. Kramizo's optional Pro plan removes the daily cap and adds detailed progress analytics, but the free tier is the real product — used by thousands of GCSE, IGCSE and CSEC students.
Are the Statistics: Histograms with unequal class widths and frequency density questions aligned to the official CIE IGCSE Mathematics syllabus?
Every question is written against the published CIE IGCSE Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real CIE paper. Explanations are written in the style of official examiner mark schemes — they tell you what is being awarded marks and why distractors are wrong, not just whether you got it right. The bank is continually refined to match the latest syllabus updates from CIE.
How is Statistics: Histograms with unequal class widths and frequency density typically tested on CIE IGCSE Mathematics papers?
Statistics: Histograms with unequal class widths and frequency density appears across multiple question types on real CIE IGCSE Mathematics papers — most commonly as multiple-choice questions in the objective section, structured short-answer questions in the main paper, and occasionally as part of an extended response. Kramizo's practice bank reflects that mix: 4-option MCQs, true/false statements, fill-in-the-blank key terms, multi-select questions, and ordering questions. Working through the bank gives you exposure to every question style examiners actually use.

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