CAIE A-Level · Mathematics 9709 · Representation of Data

Representing Data and Choosing a Diagram (PS1 – 5.1)

10 min readSyllabus 5.1PreviewBy Uzair Khan

Syllabus objective

Select a suitable way of presenting raw statistical data, and discuss advantages and/or disadvantages that particular representations may have.

Introduction

Raw statistical data — an unorganised collection of values — must be presented in a clear, informative way before it can be interpreted. In the 9709 examination, you are expected to select an appropriate diagram for a given data set and articulate why that choice is (or is not) suitable. Questions often ask you to "state one advantage" or "give a reason why [diagram X] would not be appropriate", so understanding the strengths and weaknesses of each representation is just as important as knowing how to draw one.


Core Concept

Different diagrams suit different types and structures of data. The key questions to ask when choosing a representation are:

  1. Is the data quantitative (numerical) or qualitative (categorical)?
  2. Is the quantitative data discrete or continuous?
  3. Is the focus on distribution shape, spread, individual values, or comparison between groups?
  4. How many data points are there? (Stem-and-leaf is impractical for very large data sets, for example.)

The table below summarises the main representations in 9709 PS1 and the data type each suits.

DiagramBest suited toKey feature
Stem-and-leaf diagramSmall/medium discrete or continuous dataRetains raw values; easy to find median/quartiles
Back-to-back stem-and-leafComparing two small/medium data setsSide-by-side comparison of two distributions
Box-and-whisker plotContinuous (or discrete) data; comparisonShows five-number summary; highlights outliers
HistogramContinuous grouped data (unequal or equal class widths)Area ∝ frequency; frequency density on yy-axis
Frequency diagram (bar chart for grouped)Continuous grouped data with equal class widthsHeight ∝ frequency when widths are equal
Bar chartDiscrete or qualitative dataGaps between bars; height = frequency
Pie chartQualitative or discrete data; proportionsAngle ∝ relative frequency
Cumulative frequency graph (ogive)Continuous grouped dataEstimates median, quartiles, percentiles
Dot plot / frequency tableVery small discrete data setsSimple; shows every value

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