IB›IB Maths: Analysis and Approaches SL›Mind maps4.2 Presentation of dataIB Maths: Analysis and Approaches SL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsFrequency tablesClasses as inequalities: 10≤L<1510 \le L < 1510≤L<15No gaps or overlaps between classesGrouped tables give estimates onlyHistogramsEqual widths: bar height is the frequencyBars touch because data is continuousShows clusters, skew and gapsCumulative frequencyMedian at position n2\frac{n}{2}2nQ1Q_1Q1 at n4\frac{n}{4}4n, Q3Q_3Q3 at 3n4\frac{3n}{4}43npppth percentile at p100×n\frac{p}{100} \times n100p×nIQR =Q3−Q1= Q_3 - Q_1=Q3−Q1Plot at the upper class boundaryData displaytables, graphs, quartilesQ1Q_1Q1Q3Q_3Q3IQRInterpolationEstimate =a+rf×w= a + \dfrac{r}{f} \times w=a+fr×w200 apples, 90 below 140 g, 60 in the next classMedian is the 100th, so r=10r = 10r=10140+1060×20=140 + \frac{10}{60} \times 20 = 140+6010×20= 143.3 gBox and whiskerFive numbers: min, Q1Q_1Q1, median, Q3Q_3Q3, maxOutliers are 1.5 × IQR beyond a quartileQ1=95Q_1 = 95Q1=95, Q3=145Q_3 = 145Q3=145: boundaries 20 and 220So 230 is an outlierComparingCompare one centre and one spread, in contextMedian near Q1Q_1Q1: positively skewedMedian near Q3Q_3Q3: negatively skewedSkewed data is not well modelled as normalWith outliers, use IQR not range