IB›IB Maths: Analysis and Approaches HL›Mind maps4.1 Populations, samples and data collectionIB Maths: Analysis and Approaches HL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsKey ideasPopulation: the whole group studiedSample: the part you collect data fromRandom: every member has an equal chanceDiscrete = counted, continuous = measuredAge is continuous, rounded downSampling methodsSimple random: number members, random generatorSystematic: every kkkth member, random startStratified: random sample from each groupQuota: set numbers per group, non-randomConvenience: easiest to reach, usually biasedStratified sizesstratumpopulation×sample size\frac{\text{stratum}}{\text{population}} \times \text{sample size}populationstratum×sample size330 and 270 students, sample 40330600×40=\frac{330}{600} \times 40 = 600330×40= 22Other stratum: 18Check total equals sample sizeSamplingdata collectionQ1Q_1Q1Q3Q_3Q3IQRBiasBiased: systematically over- or under-representsName who is left out and why it mattersSystematic sampling fails with a repeating patternStratified helps when groups differOutliers and gapsOutlier: below Q1−1.5 IQRQ_1 - 1.5\,\text{IQR}Q1−1.5IQROr above Q3+1.5 IQRQ_3 + 1.5\,\text{IQR}Q3+1.5IQRGenuine extremes are keptErrors are corrected or removedMissing data: exclude, never set to 0Exam tipsStratified is random within groups, quota is notNever remove an outlier without a reasonLink comments to context and variableSay which direction the estimate is pushed