Practice IB Mathematics Analysis and Approaches (AA) Topic SL 4.2—histograms, CF Graphs, Box Plots with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.2—histograms, CF Graphs, Box Plots and mirrors Paper 1, 2, 3 style where relevant.
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The histogram shows the heights, in centimetres, of plants in a greenhouse.
(a) Write down the modal class.
(b) Find the number of plants with a height of at least cm.
The box-and-whisker diagrams show the scores of two classes, Class A and Class B, on the same test.
(a) Write down the median score for each class.
(b) Find the interquartile range for each class.
(c) the two classes by referring to the median and the interquartile range.
36 participants attempted a timed puzzle, with a maximum allowed time of 30 minutes. The grouped distribution of their completion times is given below.
| Time (minutes) | Frequency (f) |
|---|---|
| 8–12 | 4 |
| 12–16 | 8 |
| 16–20 | 12 |
| 20–24 | 8 |
| 24–28 | 4 |
(a) the mean completion time.
(b) a histogram representing the frequency distribution of the completion times.
The data set of test scores ranging from to is .
(b) What is the modal class of the histogram?
(c) the mean of the data set.
An analyst defines a new measure, known as the Market Influence Index (MII), to assess how much impact particular firms have in a market. The results are displayed in the box-and-whisker diagram below.
(a) It is known that the median (), the upper quartile () and the maximum value () satisfy . If the range is , find the values of and .
(b) Suppose the names of every firm are written on separate slips of paper and placed in a container. One slip is chosen at random. What is the probability that the firm has an MII below or above ?
(c) A firm is chosen at random with replacement three times. Find the probability that an MII score above occurs at least once?
(c) what the mean completion time suggests about the group’s performance relative to the – minute challenge limit.
(d) From the lowest two time intervals, participants were removed from the data set, and the average became minutes. how many participants were removed from each interval.
(a) a histogram for the data using five equal-width class intervals: –, –, –, –, –.
