Advanced Measurements in Statistics — Quartiles and their graphic representation

About this lesson

This unit teaches students how to calculate quartiles (lower, middle, and upper) for data presented in various forms: ungrouped (single) data, frequency tables, and stem-and-leaf plots. It covers two cases for ungrouped data: when (n+1) is divisible by 4, quartiles are directly data values; otherwise, a formula involving interpolation between neighboring values is used. For frequency tables, students learn to use ascending cumulative frequency and a specific formula to find quartile values. The unit also explains how to find quartiles graphically using the ascending cumulative frequency curve. Finally, it introduces the box plot (box-and-whisker plot) as a visual representation using the minimum, lower quartile, median, upper quartile, and maximum. Examples include student test scores, ages of library visitors, working hours of workers, temperatures, hemoglobin levels, and car fuel consumption. By the end, students should be able to compute quartiles algebraically and graphically from different data formats and draw and interpret box plots.