65 exam-style questions on Data presentation: frequency tables, histograms, cumulative frequency, box plots — topic 4.2 of Statistics and Probability in the IB Mathematics: Applications and Interpretation syllabus — with answers and explanations. Samples below; the full set is free with an account.
A cumulative frequency graph for the test scores of 80 students shows a cumulative frequency of 20 at a score of 45 and a cumulative frequency of 60 at a score of 72. Determine the estimated interquartile range.
Answer: 27
For 80 students, Q1 is at cf = 20 (score 45) and Q3 is at cf = 60 (score 72), so IQR = 72 − 45 = 27.
The five-number summary of a data set is minimum 12, Q1 = 18, median 25, Q3 = 30, maximum 46. Using the 1.5 × IQR rule, determine whether the maximum value 46 is an outlier.
Answer: No, because 46 ≤ 48
IQR = 30 − 18 = 12, so the upper fence is Q3 + 1.5×IQR = 30 + 18 = 48. Since 46 ≤ 48, it is not an outlier.
A frequency table records the number of pets owned by families: 0 pets (frequency 8), 1 pet (frequency 15), 2 pets (frequency 12), 3 pets (frequency 5). State the total number of families surveyed.
Answer: 40
The total number of families is the sum of the frequencies: 8 + 15 + 12 + 5 = 40.
A histogram uses unequal class widths. One class spans 10 ≤ x < 30 and contains a frequency of 40. Calculate the frequency density for this class.
Answer: 2
Frequency density = frequency ÷ class width = 40 ÷ (30 − 10) = 40 ÷ 20 = 2.
On a box-and-whisker plot the box extends from 34 to 52 with a line at 41. State what the value 41 represents.
Answer: The median
On a box plot the line inside the box marks the median; the box edges are Q1 and Q3.
From a cumulative frequency curve for 200 people, the cumulative frequency at a waiting time of 15 minutes is 150. Determine the estimated number of people who waited longer than 15 minutes.
Answer: 50
Cumulative frequency counts values up to 15 min (150 people), so those waiting longer = 200 − 150 = 50.
That was 6 of 65 Data presentation: frequency tables, histograms, cumulative frequency, box plots questions.
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65 Data presentation: frequency tables, histograms, cumulative frequency, box plots questions — free with an account. Spaced repetition, streaks and full exam simulations included.
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