This final subsection is an overview of the various modes of mathematical communication used so far, like words, tables and graphs, and diagrams. You may have a preference for one over the others as a way of presenting ideas and of receiving information. However, they can all aid your understanding and communication of different mathematical ideas. So you need to develop your skills in using and interpreting all of them.
Look back at Figure 2, which shows the structure of the RPI. Notice how the slices of the central circle show by their size how large each group is compared with the others. For example, you can see at a glance that the slice representing ‘Food and catering? is roughly twice the size of the slice representing the group ‘Alcohol and tobacco?. Other features are equally easy to pick out; for example, ‘Housing and household expenditure? is visually the largest slice and ‘Personal expenditure? the smallest. None of these features would be immediately apparent from the numbers alone. (If you are not convinced of this, turn to the weights in Table 19 and see if these patterns leap out from the numbers as powerfully as they do from the graphical representation in Figure 2.)
Look back through the notes which you have made about diagrams and tables (starting with Activity 6). Think about at least one example each where information has been communicated:
(a) in words:
(b) in a table:
(c) in a graph or diagram:
(d) in symbols.
Note down at least one strength and one weakness of each approach. Give an example when it would be helpful to use a table, and when a graph. Try to use more than one of these modes of communication in your notes.
Use the printed response sheet that you used first in Activity 6.
Words are usually familiar and comfortable. They can be good for communicating subtlety and shades of meaning in aspects of description which are difficult to quantify. For example, describing someone's mood is not something which can easily be expressed in numbers; words alone or together with images seem best.
Tables emphasise information which exists in the form of numbers and categories. The individual slots generally hold the numbers and the row and column headings show the categories. Tables are good at providing detail (exact values), but not so good at showing an overview (which value is largest, smallest, and so on).
Graphs and diagrams, like tables, operate on categories and numerical information. However, they are complementary to tables in that they emphasise overall patterns and trends at the expense of providing detail in the form of exact values. Graphs use size or position to represent numbers whereas diagrams tend to be used to represent relationships. This means that the making of relative comparisons is easy. For example:
♦ one bar looks roughly two-thirds the height of another;
♦ one bar is the tallest/shortest;
♦ there is a wide spread/narrow spread of values, etc.
Symbols are good for generalising techniques, in particular formulas. The formulas for the mean and weighted mean are much clearer and more concise when written using symbols.
These ideas are summarized in the diagram overleaf.
After studying this section, you should:
♦ understand the distinction between relative and absolute comparisons (Activities 30 and 31);
♦ understand the terms ratio, proportion and similar, and be able to use them appropriately (Activities 32, 33, 34, 35);
♦ be able to identify the strengths and weaknesses of using words, tables, graphs, diagrams and symbols to present information (Activity 36).
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