Aims The main aim of this section is to discuss several ways of finding averages and to introduce you to the statistical facilities of your calculator.

A single number which is typical or representative of a collection (or batch - statistical term for a set of collected data.) of numbers is commonly referred to as an average. There are several different ways of defining such a number. Two are discussed briefly in Author(s): The Open University

The investigation so far illustrates just how difficult it can be to make a fair comparison of prices. In this subsection, the central question is still â€˜Are people getting better off?â€™ However, in order to make the task more straightforward, just look at the period from 1990 to 2004.

• How might you use the â€˜price of breadâ€™ measure as a way of investigating whether or not people got better off over this period?

In particular, t
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Cade: There shall be in England seven halfpenny loaves sold for a penny; the three-hooped pot shall have ten hoops; and I will make it felony to drink small beer.

(William Shakespeare, Henry VI, Part 2, written in 1594)

In this quotation, the character Cade anticipates the good times that are sure to follow after the revolution. The notion of the â€˜halfpenny loafâ€™ is interesting, as is t
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Aims The main aim of this section is to introduce some ideas about making valid comparisons and to focus on ways of extracting information from tables and graphs.

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Are we getting better off? Politicians and journalists often make sweeping claims about whether or not â€˜weâ€™ are getting better off.

• Who is this â€˜weâ€™ of whom they speak?

• On what do they base these claims?

• What does being better off mean to you?

• How would you go about assessing how well-off you are?

In attempting to resolve some of these questions, a number of important mathemat
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Pretend that you are the marker of another solution to the same problem. How would you mark Solution B?

## Example 16 Billions

You may think that you know what the word billion means but do you really have a feel for its size?

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First write out a full solution to the following problem.

## Example 16: Billions

You may think that you know what the word billion means but do you really have a feel for its size?

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The following table summarises some of the types of instructions you will encounter.

Write down â€¦ Determine â€¦ Show â€¦
What isâ€¦ Find â€¦ Prove â€¦
Calculate â€¦
A simple answer will do but generally g
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In this type of question you are given the answer! All the marks are allocated for correct reasoning and justification.

## Example 15

Suppose you now decide to place your new bath (length 1.7 m, height 0.8 m) against this wall as shown in the diagram below.

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## Example 14

Suppose you have decided to tile the wall using square tiles of side 10 cm. You are proposing to use the tiles across the full 5 metre width of the wall up to a height of 1.8 m.

Find the number of boxes of tiles that you will require to cover the wall if the tiles are sold in boxes o
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Before you can attempt a question, you must read and understand it. This may sound obvious but you will need to know, before you start, what is expected by way of an answer. In particular, you will need to know the meaning of the instructions contained in the question. This section contains a discussion of the precise meanings attached to words like â€˜findâ€™, â€˜showâ€™, â€˜write downâ€™ and â€˜determineâ€™ in mathematics questions. The different types of instruction are illustrated by posi
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By the end of this unit you should be able to:

• lay out and, where appropriate, label simple mathematical arguments;

• understand the precise mathematical meaning of certain common English words;

• understand and use common mathematical symbols;

• write clear, unambiguous mathematical solutions using appropriate notation;

• identify and modify some sources of ambiguity or inappropriate use of notation in a mathematical solution;
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Do you want to improve your ability to subtract one number from another, especially if decimals are involved, without having to rely on a calculator? This unit will help you get to grips with subtraction and give you some practice in doing it.

You can start with some practice in subtracting small numbers in your head if you want to. Then we will show you how to subtract bigger numbers on paper. Finally we look at how to subtract decimal numbers.

You donâ€™t need to complete the
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The example of 25546 divided by 53 is suitable for long division. First write the calculation down on paper in the same way you did before.

<
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When you divide by a number up to 10, the steps are as follows:

1. Take each digit of the number under the line in turn, starting from the left.
2. Work out how many times the dividing number goes into it.
3. Write the answer to the division above the line
4. If there is a remainder, carry it by putting it in front of the next digit on the right.
5. Work out how many times the dividing number goes into the next digit, including any car
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1. Data in the form of counts of individual entities (for example, people, animals, power stations) in a small set of discrete categories can be presented in bar charts or pie charts. For most purposes, bar charts are preferable. Pie charts draw particular attention to the proportions in which the entities are split between the different categories. However, they do so by representing the proportions by angles, and even when the main interest lies in the propo
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For the six ordered data items 1, 3, 3, 6, 7, 7, the lower quartile is given by

In other words, the lower quartile qL is given by the number three-quarters of the way between x (1)=1 and x (2)=3. The difference betwe
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Figure 19 shows a histogram of chest measurements (in inches) of a sample of 5732 Scottish soldiers.

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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 2.2Â 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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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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