Unit 4: Statistics and Probability
Topic 4.3: Measures of Spread and Outliers Questions
Practice 20 exam-style questions for IB Math AI SL Topic 4.3. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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True or false: the mode is the only average that can have multiple values for one dataset.
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State whether the standard deviation can be negative. Justify.
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Find the median of: 5, 12, 8, 14, 9, 17, 3, 11.
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The mean of 5 numbers is 18. Four of them are 12, 15, 20, 22. Find the fifth number.
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Frequency table: [0,5): 4, [5,10): 9, [10,15): 14, [15,20): 11, [20,25): 7. Identify the modal class and the estimated modal value (midpoint).
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State one limitation of the mode as a measure of central tendency.
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In a school survey, students were asked their preferred sport. Football: 42, Basketball: 38, Tennis: 25, Swimming: 18, Other: 12. State the mode and explain why mean/median don''t apply.
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For the frequency table: x = 1, 2, 3, 4, 5 with frequencies 2, 5, 8, 4, 1. Find the mean.
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The lengths (in minutes) of 42 podcast episodes are grouped as: [0,5): 7, [5,10): 19, [10,15): 11, [15,20): 5.
(a) Write down the modal class.
(b) Estimate the modal length using the midpoint of that class.
(a) Write down the modal class.
(b) Estimate the modal length using the midpoint of that class.
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A frequency table records weekly hours of study: 2 hours: 5 students; 3 hours: 8 students; 4 hours: 10 students; 5 hours: 4 students; 6 hours: 3 students. Calculate the mean hours of study.
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A data set has mean 50. If 12 is added to every value, find the new mean.
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A teacher adds 5 marks to every student''s test score. If the original mean was 64, find the new mean.
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A shoe shop records the sizes sold one afternoon: 7, 8, 8, 9, 9, 9, 10, 10, 11, 9, 8. Find the modal shoe size and state why the mode is the most useful average for a shop ordering stock.
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A dataset has mean 70 and σ 5. Identify whether the value 85 is an outlier using the mean ± 2σ rule.
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Find the mean of: 12, 15, 18, 22, 25, 28, 30.
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A dataset has mean 20 with n = 8. Find the new mean if the value 30 is REMOVED.
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Test scores in a small class: 65, 72, 65, 80, 65, 72, 80, 65, 88, 72. Find the mode.
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For the dataset 5, 5, 5, 5, 5, find the standard deviation.
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