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.
| 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 |
Write down the modal class.
Calculate an estimate of the mean time.
Work out the percentage of students who exercised for more than hour.
students took a standardized test scored from to points. The frequency distribution of their scores is given below.
| Class Interval | Frequency (f) |
|---|---|
| 35 – 40 | 8 |
| 40 – 45 | 12 |
| 45 – 50 | 10 |
| 50 – 55 | 6 |
| 55 – 60 | 4 |
Calculate the mean score of the students.
Draw a histogram representing the frequency distribution of the test scores.
Explain what the mean score suggests about the class’s performance relative to the – test scale.
From the lowest two score intervals, students were removed from the class, and the average became . Determine how many students were removed from each interval.
A group of 51 students is playing hide and seek, with 1 student chosen as the seeker. The remaining 50 students hide up to 150 metres away. Their hiding distances are summarized in the table.
| Class Interval | Frequency (f) |
|---|---|
| 0 – 30 | 10 |
| 30 – 60 | 15 |
| 60 – 90 | 11 |
| 90 – 120 | 8 |
| 120 – 150 | 6 |
Calculate the mean distance of the hidden students.
The seeker must catch an equal number of students from every class interval. A student who is caught leaves the game. The seeker catches students from each interval so that the mean distance of the students remaining in the game is 57. Find .
Draw the histogram for the students who remain in the game after the seeker has caught students from each interval.
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 |
Calculate the mean completion time.
Draw a histogram representing the frequency distribution of the completion times.
Explain what the mean completion time suggests about the group’s performance relative to the – minute challenge limit.
From the lowest two time intervals, participants were removed from the data set, and the average became minutes. Determine how many participants were removed from each interval.
The data set of test scores ranging from to is .
Draw a histogram for the data using five equal-width class intervals: –, –, –, –, –.
What is the modal class of the histogram?
Calculate the mean of the data set.