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1.1 A shared understanding

All representations (including graphical ones) rely on shared understandings of symbols and styles to convey meaning. Like maps, graphical representations stress some features and ignore others. As you work through this Unit, bear in mind that graphs are selective representations of information. When you come across different graphs ask yourself what is being stressed and what is being ignored.

In the newspapers, you are likely to find graphs used to present all sorts of information: ho
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Learning outcomes

After studying this Unit you should be able to:

  • Explain in English and by using examples, the conventions and language used in graph drawing to someone not studying the course

  • Use the following terms accurately, and be able to explain them to someone else: ‘time-series graph’, ‘conversion graph’, ‘directly proportional relationship’, ‘“straight-line” relationship’, ‘gradient’, ‘intercept’, ‘x-coordinate’, ‘y-coordinate’, ‘coor
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Introduction

Graphs are a common way of presenting information. However, like any other type of representation, graphs rely on shared understandings of symbols and styles to convey meaning. Also, graphs are normally drawn specifically with the intention of presenting information in a particularly favourable or unfavourable light, to convince you of an argument or to influence your decisions.

This unit is from our archive and is an adapted extract from Open mathematics (MU120) which is no longer
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9 Subtracting small numbers

If you want to subtract without using a calculator, you need to know off by heart what you get if you subtract any number up to 10 from any bigger number up to 20. All the possible combinations are shown in the table below.

Figure 15
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4.3 Decimals

A decimal number is a different way of representing numbers smaller than one. You put them after a full stop (the decimal point), for instance 0.5. The first digit after the decimal point represents tenths. If you sliced a cake into 10 slices, each slice would be a tenth of the cake. So 0.5 is the same as saying 5 tenths, and can be written
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1.3.6 Summary of Section 3

In this section, you have learned about appropriate ways of interpreting data in tables. By working through examples, you have seen how it can be useful to calculate appropriate proportions and ratios, and to present some of the data in graphical form. Guidelines for the choice of graphics have been given. When the data in a table are in the form of counts, you have seen that it can be useful to calculate the counts in a particular row or column as proportions (usually in the form of percenta
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1.3.2 Health care personnel in Thailand: activities

Activity 3.1: Health care personnel in Thailand: calculating percentages

Would it be helpful, in considering possible changes in the way health care personnel are divided into the five categories listed, to recalculate the numbers in t
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1.2.6 Summary of Section 2

In this section you have been introduced to some guidelines for presenting data in tables. These guidelines apply particularly when the data in a table are being used to illustrate a particular point or to show up clearly a particular pattern.

You have seen that, in some circumstances, following the second of these guidelines leads to some pooling together of rows. (In other cases, it could be columns or individual cells that are pooled.) However, care is needed when, by making such sim
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1.2.4 Including the results of useful calculation

Can Table 2.4 be simplified further by pooling more rows or columns? Perhaps it might be, but there may well be a risk of losing some important or relevant information. So, before considering any further simplification, we shall look at adding information to the table, in the form of the
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1.2.1 Data sets in different tabular forms

In much of your statistical work, you will begin with data set, often presented in the form of a table, and use the information in the table to produce diagrams and/or summary statistics that help in the interpretation of the data set. However, in practice, much interpretation of data sets can be done directly from an appropriate table of data, or by re-presenting the data in a rather different tabular form. Dealing with data in tables is the subject of this section and the next. By the time
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1.1.4: Infants with SIRDS

The data in Table 3 are the recorded birth weights of 50 infants who displayed severe idiopathic respiratory distress syndrome (SIRDS). This is a serious condition which can result in death.

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5.2 Doing and undoing

Now try the following.

Think of a number. Add 4. If my answer is 11, can you work out what number I was thinking of?

You might have said ‘What number do I have to add on to 4 to get 11?’ or perhaps ‘If I take away 4 from 11 what number do I get?’ In both cases you should have arrived at the answer 7.

In the second method ‘subtracting 4’ undoes the ‘adding 4’ in the original instructions.

This process can be illustrated by a ‘doing–undoing diagram’
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3.3 Maths in healthcare

The body mass index (BMI) is sometimes used to help determine whether an adult is under- or overweight. It is calculated as follows:

Although care needs to be taken in interpreting the results (for example, the formula isn't appropriate for children, old people or those w
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3.2 Maths in cookery

The time taken to cook a fresh chicken depends on its mass, as given by the following formula:

Roughly how long will a chicken with a mass of 2.2 kg take to cook?

To use the formula, you need to substitute the mass of the chicken into the right-hand side of the equ
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3.1 Introduction

In the last section, we considered how a formula could be built up and then how it could be used. This section considers some more complicated formulas, which have already been developed and are used in a variety of different situations – cookery, healthcare, business and archaeology. We hope that these examples illustrate some of the very broad applications of maths and how mathematical relationships can be used in making decisions. As you work through these examples, you may like to consi
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1 Exploring patterns and processes

Suppose you are tiling a bathroom or kitchen and the last row of square tiles is to be a frieze made up of blank tiles and patterned tiles as shown below.

Figure 1
F
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Learning outcomes

After completing this unit you should be able to:

  • visualise problems using pictures and diagrams;

  • recognise patterns in a variety of different situations;

  • use a word formula to help solve a problem;

  • derive simple word formulas of your own, for example for use in a spreadsheet;

  • use doing and undoing diagrams to change formulas round;

  • solve problems involving direct and inverse proportion;

  • in
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Introduction

Patterns occur everywhere in art, nature, science and especially mathematics. Being able to recognise, describe and use these patterns is an important skill that helps you to tackle a wide variety of different problems. This unit explores some of these patterns ranging from ancient number patterns to the latest mathematical research. It also looks at some useful practical applications. You will see how to describe some patterns mathematically as formulas and how these can be used to solve pro
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