Chapter 1: Representation of Data

Stem-and-leaf diagrams are presented as an effective method for representing small discrete datasets while preserving individual data values, using a structure where the last digit forms the leaf and preceding digits create the stem, with back-to-back configurations enabling direct comparison between two related datasets. Histograms are introduced as the primary tool for displaying continuous data, with emphasis on the area principle whereby column area represents frequency rather than height alone, requiring the use of frequency density (calculated as class frequency divided by class width) on the vertical axis and class boundaries rather than rounded values on the horizontal axis to eliminate misleading gaps. Cumulative frequency graphs, plotted using upper class boundaries and accumulated frequencies, serve as visualization tools for estimating proportions and identifying central tendency measures like medians and quartiles through either polygonal line segments or smooth curves. The chapter concludes with practical guidance on selecting appropriate representations based on data characteristics, explaining that qualitative and ungrouped discrete data suit pictograms and bar charts, small discrete datasets benefit from stem-and-leaf preservation of raw values, and large grouped datasets require histograms and cumulative frequency graphs to reveal overall distribution patterns while accommodating varying class widths. Throughout the chapter, the emphasis remains on matching representation method to data type and analytical purpose.