Math

What is a discrete variable? A variable that can only take specific, countable values, usually whole numbers.

What is a continuous variable? A variable that can take any value within a range and is measured.

Question 7A: Reaction speed measured by the gap in milliseconds between a light turning green and pressing a button. Continuous — time is measured and can theoretically take any value, even though the equipment rounds it to the nearest 5 ms.

Question 7B: A researcher counts the number of bird calls during each 2-minute interval and records the volume of each call. The number of bird calls is discrete because calls are counted. The volume of each call is continuous because volume is measured.

Question 7C: A factory records the number of defects per batch and the weight of defective items. The number of defects is discrete because defects are counted. The weight is continuous because weight is measured.

What is stratified sampling? The population is divided into groups (strata), and random samples are taken from each group.

Question 8A: An IB coordinator selects 10 students from each Diploma subject group, with students randomly chosen within each group. Stratified sampling — the students are divided into subject groups and randomly selected from each group.

What is systematic sampling? Selecting members of a population using a fixed interval or pattern, such as every 12th person.

Question 8B: A theme park interviews every 12th person leaving the park. Systematic sampling — every 12th person is selected using a fixed interval.

Question 8C: A geographer divides a country into climate zones and randomly selects 5 weather stations per zone. Stratified sampling — the country is divided into groups and random samples are taken from each group.

What is convenience sampling? Selecting people who are easiest or most convenient to reach.

Question 8D: A student asks classmates they meet in the corridor during break to complete a survey. Convenience sampling — the students who are easiest to reach are selected.

What is quota sampling? Dividing the population into groups and selecting people from each group until a specific number (quota) is reached, without necessarily using random selection.

Question 8E: A company interviews 50 people aged 16–25, 50 aged 26–45, and 50 aged 46+, stopping when each group is filled. Quota sampling — specific numbers are required from each age group, and people are selected until each quota is filled.

Discrete Counted

Continuous Measured

Stratified Groups + random selection from each group

Systematic Every nth person

Convenience Easiest people to reach

Quota Groups + fixed number from each group