Unit 4: Statistics and Probability
Topic 4.2: Measures of Central Tendency Questions
Practice 20 exam-style questions for IB Math AI SL Topic 4.2. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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A dataset has Q1 = 12, Q3 = 28. State BOTH outlier fences.
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For raw data 12, 14, 16, 18, 20, 22, 24, 14, 16, 18, 22, 24, 26, 18, 20, build an ungrouped frequency table and find the modal value.
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From a box plot of test scores: Q1 = 55, Q3 = 78. How many of the 80 students scored between Q1 and Q3?
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A data set has five-number summary: Min = 12, Q1 = 18, Median = 24, Q3 = 33, Max = 41. Find the range and the interquartile range.
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A histogram has unequal class widths. Class [0,10) has frequency 30; class [10,30) has frequency 40. Find the frequency density of each.
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Calculate the lower outlier fence for Q1 = 24, Q3 = 40.
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Find the five-number summary for the dataset: 3, 6, 7, 8, 9, 11, 12, 15, 18.
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Find the median for: 12, 14, 16, 18, 20, 22.
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A box plot has Q1 = 25, median = 35, Q3 = 45. Comment on symmetry.
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State the percentage of data that lies BELOW Q1.
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In a grouped table with class width 20, the third class is [40,60). State its lower boundary, upper boundary, and midpoint.
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Why must class intervals in a grouped table be non-overlapping?
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A frequency table has total n = 50. Relative frequencies of three classes are 0.20, 0.30, 0.10. Find the actual frequency of each.
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State two differences between a histogram and a bar chart.
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A class has width 5 and frequency 20. Find the frequency density.
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State what is plotted on the y-axis of a histogram when class widths are unequal.
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State the steps to construct a box plot from a five-number summary.
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Construct cumulative frequency values from class frequencies 7, 13, 22, 15, 8.
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A frequency table has class [10,20) with f = 8 and total n = 40. Find the relative frequency for this class.
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A class records the number of pets each student has: 0, 1, 1, 2, 0, 3, 1, 2, 0, 1, 2, 4, 1, 0. Construct an ungrouped frequency table.
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