Practice IB Mathematics Analysis and Approaches (AA) Topic SL 4.1—concepts, Reliability and Sampling Techniques with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.1—concepts, Reliability and Sampling Techniques and mirrors Paper 1, 2, 3 style where relevant.
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The table summarises the daily exercise times of students.
(a) Write down the modal class.
(b) an estimate of the mean time.
| Time (t minutes) | 0 < t ≤ 15 | 15 < t ≤ 30 | 30 < t ≤ 45 | 45 < t ≤ 60 | 60 < t ≤ 75 | 75 < t ≤ 90 |
|---|
| Frequency | 18 | 25 | 32 | 15 | 8 | 2 |
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.
A survey of 120 people recorded the greatest amount, in dollars, that each person would pay for a notebook (from to ). The data are summarized as follows: minimum value , first quartile , median , third quartile , and maximum value .
(a) a box plot to represent these data.
(b) the box plot in the context of the data.
51 students are playing hide and seek, where 1 is seeking. The other 50 go hide within 100 metres. The distribution of distances is given in the table.
| Class Interval | Frequency (f) |
|---|---|
| 0 – 20 | 10 |
| 20 – 40 | 15 |
| 40 – 60 | 15 |
| 60 – 80 | 5 |
| 80 – 100 | 5 |
(a) Estimate the mean distance of the students hiding.
(b) The seeker has to catch the same number of people from each class interval. If you get caught, you are out. The seeker caught people from each interval such that the estimated mean distance of those who are still in the game is 40. Find .
(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: –, –, –, –, –.
(c) the histogram for those who are still in the game after the seeker has caught people from each interval.
