Practice IB Mathematics Applications & Interpretation (AI) Topic SL 4.1—introduction to Statistics with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.1—introduction to Statistics and mirrors Paper 1, 2, 3 style where relevant.
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The table below shows the distribution of parcels delivered per day by a group of bicycle couriers surveyed during a festival week in Amsterdam.
| Parcels | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|
| Frequency | 3 | 6 | 10 | 14 | 23 | 21 | 13 | 7 | 3 |
A courier is chosen at random from the group of couriers.
A second courier is chosen at random from the group of couriers.
The time taken by the couriers to complete a standard route was normally distributed with a mean of minutes and a standard deviation of minutes.
The couriers were selected for the survey by randomly choosing names from the full company list using a computer generator.
Find the mean number of parcels delivered by the couriers.
Find the standard deviation of the number of parcels delivered.
Find the median number of parcels delivered by the couriers.
Find the interquartile range.
Find the probability that this courier delivered or more parcels.
Given that the first courier chosen at random delivered or more parcels, find the probability that both couriers delivered exactly parcels.
Calculate the probability that a courier chosen at random took at least minutes to complete the route.
Calculate the expected number of couriers whose route took at least minutes.
Identify the sampling technique used in this sampling method.
A city youth orchestra has 900 members distributed across 5 instrument sections. The distribution of members by section is shown in the table below.
| Section | Strings | Woodwind | Brass | Percussion | Keyboard |
|---|---|---|---|---|---|
| Number of members | 108 | 153 | 189 | 216 | 234 |
The manager intends to form a sample of 25 members. The goal is to ensure the representation of each section within the sample matches, as closely as possible, the distribution across the whole orchestra.
Determine the appropriate number of Brass members to be included in this sample.
The manager decides how many members are needed from each section, then uses a random number generator to select the required number from each section list. Identify the two sampling techniques from the list below that best classify the approach taken. Stratified, Quota, Convenience, Systematic, Simple random
The table below shows the distribution of parcels delivered per shift by a group of couriers surveyed on a working day in Dublin.
| Parcels | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|
| Frequency | 4 | 6 | 12 | 18 | 25 | 17 | 10 | 5 | 3 |
Find the mean number of parcels delivered by the couriers.
Find the standard deviation of the number of parcels delivered.
Find the median number of parcels delivered by the couriers.
Find the interquartile range.
Find the probability that a courier chosen at random delivered or more parcels.
Given that the first courier chosen at random delivered or more parcels, find the probability that both couriers delivered exactly parcels.
The time spent on route-planning training by a courier is modelled by . Calculate the probability that a courier chosen at random spent at least hours on training.
Calculate the expected number of couriers that spent at least hours on training.
The survey was carried out by selecting every th name from an alphabetical staff list. Identify the sampling technique used in this sampling method.
A language college has 780 students distributed across 5 course levels. The distribution of students by level is shown in the table below.
| Level | Foundation | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|---|
| Number of students | 96 | 132 | 156 | 180 | 216 |
The coordinator intends to form a sample of 24 students. The goal is to ensure the representation of each level within the sample matches, as closely as possible, the distribution across the whole college.
Determine the appropriate number of Level 2 students to be included in this sample.
The coordinator fills each level's places by asking students from the after-school chess club in that level to join, and continues until the required number from each level is reached. Identify the two sampling techniques from the list below that best classify the approach taken. Stratified, Quota, Convenience, Systematic, Simple random
The table below shows the distribution of parcels delivered per day by a group of bicycle couriers surveyed during a busy week in Copenhagen.
| Parcels | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|
| Frequency | 3 | 6 | 10 | 14 | 23 | 20 | 13 | 8 | 3 |
A courier is chosen at random from the group of couriers.
A second courier is chosen at random from the group of couriers.
The delivery times of the couriers were normally distributed with a mean of minutes and a standard deviation of minutes.
The couriers were selected for the survey by randomly choosing names from the full staff list using a computer generator.
Find the mean number of parcels delivered by the couriers.
Find the standard deviation of the number of parcels delivered.
Find the median number of parcels delivered by the couriers.
Find the interquartile range.
Find the probability that this courier delivered or more parcels.
Given that the first courier chosen at random delivered or more parcels, find the probability that both couriers delivered exactly parcels.
Calculate the probability that a courier chosen at random had a delivery time lasting at least minutes.
Calculate the expected number of couriers whose delivery time lasted at least minutes.
Identify the sampling technique used in this sampling method.