A population is the complete group being studied; a sample is the group actually observed. Define both in context before interpreting a result. A discrete variable has countable possible values; a continuous variable measures quantities over an interval. **Decision** | **What to check** Random selection | Use a random mechanism so the intended population can be represented. A larger biased sample remains biased. Reliability | Check who collected the data, when, how and for which population. Missing or erroneous values | Investigate missing responses, units and recording errors; document corrections rather than silently deleting observations. Outliers | Flag values below Q_1-1.5IQR or above Q_3+1.5IQR. A flagged value may be genuine. Example: surveying only early arrivals to estimate all students’ travel times excludes later arrivals. Increasing the number surveyed at the same early time does not remove this bias.

A population is the complete group being studied; a sample is the group actually observed. Define both in context before interpreting a result. A discrete variable has countable possible values; a continuous variable measures quantities over an interval.

Example: surveying only early arrivals to estimate all students’ travel times excludes later arrivals. Increasing the number surveyed at the same early time does not remove this bias.

Sampling

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Populations, Samples and Data Quality

Populations, Samples and Data Quality

Decision	What to check
Random selection	Use a random mechanism so the intended population can be represented. A larger biased sample remains biased.
Reliability	Check who collected the data, when, how and for which population.
Missing or erroneous values	Investigate missing responses, units and recording errors; document corrections rather than silently deleting observations.
Outliers	Flag values below \(Q_1-1.5\operatorname{IQR}\) or above \(Q_3+1.5\operatorname{IQR}\). A flagged value may be genuine.