Unit 4: Statistics and Probability
Topic 4.3: Central Tendency and Spread Questions
Practice 20 exam-style questions for IB Math AA SL Topic 4.3. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Find2 marks
2026• Aimnova practice — 4.3.3
A data set has minimum 4, Q₁ = 11, median 16, Q₃ = 23, maximum 35. Find the range and the interquartile range.
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2026• Aimnova practice — 4.3.4
A data set has mean 30 and standard deviation 5. Every value is increased by 8. Write down the new mean and standard deviation.
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2026• Aimnova practice — 4.3.3
A data set has IQR 14 and lower quartile 23. Find the upper quartile.
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2026• Aimnova practice — 4.3.1
Find the mean, median and mode of 5, 8, 8, 11, 14, 14, 14.
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2026• Aimnova practice — 4.3.1
The number of goals in 25 matches: 0 → 6, 1 → 9, 2 → 7, 3 → 3. Find the mean number of goals.
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2026• Aimnova practice — 4.3.4
A data set has variance 49. State its standard deviation.
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2026• Aimnova practice — 4.3.4
Find the mean and standard deviation of 3, 5, 6, 8, 8, 12 using a calculator.
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2026• Aimnova practice — 4.3.4
Daily temperatures (°C) over a week are 17, 19, 18, 22, 24, 20, 20.
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2026• Aimnova practice — 4.3.2
Heights are grouped: 140–150 → 4, 150–160 → 9, 160–170 → 14, 170–180 → 8, 180–190 → 5 (40 people). State the modal class.
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2026• Aimnova practice — 4.3.1
The mean of 4, 9, x, 12, 16 is 10. Find x.
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2026• Aimnova practice — 4.3.2
Lengths (cm) are grouped: 10–20 → 7, 20–30 → 15, 30–40 → 18, 40–50 → 10 (50 items). Using a calculator, estimate the mean.
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2026• Aimnova practice — 4.3.3
Find the median, Q₁, Q₃ and IQR of 3, 5, 5, 8, 9, 11, 12, 16.
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2026• Aimnova practice — 4.3.4
A frequency table has values 1, 2, 3, 4 with frequencies 6, 9, 8, 7. Find the mean and standard deviation.
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2026• Aimnova practice — 4.3.3
The 1-Var Stats output for a class test gives Q₁ = 48, Med = 61, Q₃ = 72. Find the interquartile range, and state what it represents.
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2026• Aimnova practice — 4.3.3
Find the median, lower quartile and upper quartile of 6, 9, 11, 14, 15, 18, 21, 25, 30.
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2026• Aimnova practice — 4.3.4
A data set has mean 12 and standard deviation 3. Every value is multiplied by 4. Find the new mean and standard deviation.
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2026• Aimnova practice — 4.3.4
Two data sets have the same mean. Set P has σ = 2.1; Set Q has σ = 6.8. State which set is more spread out, and what that tells you.
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2026• Aimnova practice — 4.3.1
A frequency table of test marks (out of 5) has frequencies 4, 6, 10, 5, 3, 2 for marks 0–5. Find the mean mark.
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2026• Aimnova practice — 4.3.3
Find the median and interquartile range of 14, 9, 21, 7, 16, 11, 19, 13 (unordered).
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2026• Aimnova practice — 4.3.2
Times (seconds) are grouped: 0–5 → 8, 5–10 → 14, 10–15 → 12, 15–20 → 6 (40 runners). Estimate the mean time.
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