SL 4.2—Data presentation

Use a frequency table for discrete or grouped continuous data, an equal-class-width histogram for grouped continuous data, and a cumulative-frequency graph to read median, quartiles and percentiles. Frequency density histograms are not required at SL.

A box plot shows minimum, $Q_1$, median, $Q_3$ and maximum, with outliers marked separately by crosses. Compare two distributions using median, IQR, range and symmetry; a roughly symmetric box and whiskers can support, but not prove, possible normality.

Example

If a cumulative-frequency graph for 80 observations gives $Q_1=18$, median $=25$ and $Q_3=31$, then $IQR=13$. The outlier fences are $18-1.5(13)=-1.5$ and $31+1.5(13)=50.5$, so a value of 54 is plotted as an outlier cross.

Do not use bar gaps for continuous histogram classes or confuse cumulative frequency with class frequency. State units, preserve inequality class boundaries and compare both centre and spread.