Selecting & Interpreting Data Representations (Edexcel GCSE Statistics)

Selecting Data Representations

What should be considered when choosing a data representation?

• Representing data in tables, graphs, charts, diagrams, etc. can make it easier to understand the data and spot patterns in it

  • Such representations of data may be referred to as visualisations (i.e., ways of 'seeing' or visualising the data)

  • Statistical software and spreadsheets can create these sorts of representations from data entered into them

• When choosing a representation, a number of factors should be considered:

  • The target audience

    • For an audience not especially familiar with statistics, a simple visualisation would be more appropriate

      • e.g. bar chart, pictogram or pie chart

    • Whereas for an audience of experienced statisticians, a more technical visualisation could be used

      • e.g. box plot, cumulative frequency diagram or histogram

  • The nature of the data

    • Some representations are or are not appropriate for certain types of data

      • e.g. bar charts are good for discrete data but should not be used for continuous data

      • Scatter diagrams are appropriate for bivariate data

      • Histograms are appropriate for grouped data

  • The particular strengths (and weaknesses) of different representations

    • Different representations can highlight or obscure different features in the data

      • e.g. bar charts and line graphs make patterns in the data clear and data values can often be read off the scale

      • Tables contain exact values but do not clearly show patterns or trends in the data

      • Pie charts show proportions clearly but do not show exact data values

• On the exam you may be asked to:

  • Choose a representation that should be used for a set of data and justify your choice

  • Comment on or criticise a representation that has been used

  • Compare data sets that have been presented in different formats

    • and comment on the strengths and weaknesses of each format for the data shown

Misrepresentations in Statistical Diagrams

What sort of misrepresentations can appear in statistical diagrams?

• If a data representation gives a misleading or incorrect impression about the data, this is known as a misrepresentation

  • Sometimes this may be the result of a mistake

  • But sometimes it may be done intentionally in order to be misleading

• If scales in diagrams do not go up in equal steps, or if parts of them are missed out

  • this will distort the sizes and shapes of things plotted against them

• If scales in diagrams do not start at zero

  • this can give a misleading sense of the true size of bars, etc., plotted against them

    • Note that scales don't have to start at zero

    • But not starting at zero can change the impression given about the data

• If axes on a graph are not labelled

  • then there is no way to know for sure what the data represents

• If a graph or chart doesn't have a key

  • then it may be impossible to interpret what it is meant to show

• If a diagram uses bright colours

  • it can make some parts of a diagram stand out more than others

• If lines on a graph are drawn too thick

  • it can make it difficult to read the graph precisely

• If frequency densities for histograms are calculated incorrectly, or if the class widths are plotted incorrectly on the horizontal axis

  • the bars on the histogram will not represent the data accurately

What are possible problems with 3D representations?

• 3D representations can look nice and be quite 'eye-catching'

  • but they can also distort the data or be misleading

• For example, in a 3D pie chart

  • the angles of the different sections are distorted

  • parts at the front can seem bigger or more prominent

  • parts at the back can seem smaller or be hidden behind parts at the front

  • a section that is pulled out of the 'pie' can be hard to compare with the rest of the sections

• Or in a 3D bar chart

  • it can be hard to compare the true heights of the different bars with each other

  • it can be hard to read the heights of the bars accurately against the scale

  • bars at the back can be hidden behind bars in the front