Practice IB Mathematics Applications & Interpretation (AI) Topic SL 4.3—mean, Median, and Mode with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.3—mean, Median, and Mode and mirrors Paper 1, 2, 3 style where relevant.
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The table below shows the distribution of calls handled per shift by a group of call centre agents surveyed on a working day in Manila.
| Calls | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 |
|---|---|---|---|---|---|---|---|---|---|
| Frequency | 1 | 3 | 9 | 14 | 23 | 24 | 15 | 8 | 3 |
A agent is chosen at random from the group of agents.
A second agent is chosen at random from the group of agents.
The length of breaks taken by the agents was normally distributed with a mean of minutes and a standard deviation of minutes.
The agents were selected for the survey by dividing the full workforce into three shift groups and randomly choosing a fixed number from each shift group.
Find the mean number of calls handled by the agents.
Find the standard deviation of the number of calls handled.
Find the median number of calls handled by the agents.
Find the interquartile range.
Find the probability that this agent handled or more calls.
Given that the first agent chosen at random handled or more calls, find the probability that both agents handled exactly calls.
Calculate the probability that an agent chosen at random took a break of at least minutes.
Calculate the expected number of agents that took a break of at least minutes.
Identify the sampling technique used in this sampling method.
Trays at a warehouse each contain five ceramic mugs. Each mug is either intact or cracked. It is hypothesized that the number of cracked mugs in a tray follows a binomial distribution. A sample of 120 trays was inspected with the following results.
| Number of cracked mugs per tray | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Frequency | 22 | 43 | 34 | 16 | 4 | 1 |
Find the arithmetic mean number of cracked mugs per tray.
Thus, determine an estimate for , the success probability of choosing a cracked mug.
Using a goodness of fit test, evaluate at the 5% significance level if the binomial model is an appropriate fit for this dataset.
The table below shows the distribution of patients attended per shift by a group of nurses surveyed on a working day in Dublin.
| Patients | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
|---|---|---|---|---|---|---|---|---|---|
| Frequency | 2 | 4 | 9 | 12 | 25 | 22 | 16 | 8 | 2 |
A nurse is chosen at random from the group of nurses.
A second nurse is chosen at random from the group of nurses.
The time spent with each patient by the nurses was normally distributed with a mean of minutes and a standard deviation of minutes.
The nurses were selected for the survey by ensuring nurses from each of the hospital's departments were chosen at random.
Find the mean number of patients attended by the nurses.
Find the standard deviation of the number of patients attended.
Find the median number of patients attended by the nurses.
Find the interquartile range.
Find the probability that this nurse attended or more patients.
Given that the first nurse chosen at random attended or more patients, find the probability that both nurses attended exactly patients.
Calculate the probability that a nurse chosen at random spent at least minutes with a patient.
Calculate the expected number of nurses that spent at least minutes with a patient.
Identify the sampling technique used in this sampling method.
The recorded masses, in grams, of eight parcels are shown below.
| Parcel mass (g) | 7 | 7 | 7 | 7 | 13 | 13 | 13 | 13 |
|---|
If 4 grams are added to each recorded mass, determine the updated value for the standard deviation.
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.