This Unit looks at a wide variety of ways of comparing prices and the construction of a price index. You will look at the Retail Price Index (RPI) and the Consumer Price Index (CPI), indices used by the UK Government to calculate the percentage by which prices in general have risen over any given period. You will also look at the important statistical and mathematical ideas that contribute to the construction of a price index.

In order to complete this Unit you will need to have obta
Author(s): The Open University

Introduction

This unit has two aims: firstly, to help you read and interpret information in the form of diagrams, charts and graphs, and secondly, to give you practice in producing such diagrams yourself.

To start you will deal with interpreting and drawing diagrams to a particular scale. You will then learn to extract information from tables and charts. Finally you will learn to draw graphs using coordinate axes, which is a very important mathematical technique.

This unit is from our archive
Author(s): The Open University

8 Get some practice

Now that youâ€™ve learned how to do subtraction on paper, you might want to practice your new skills.

To practice subtracting whole numbers, including borrowing where necessary, go to the Practice Subtracting section of the Numbers website and click on Get sum. Then follow the instructions.

To practise subtracting decimals, go to
Author(s): The Open University

8 Dealing with remainders

How do you deal with divisions where there is a remainder and there are no more digits you can carry to? In most cases you will need to express your answer as a decimal number rather than as a whole number plus a remainder.

Take the example of 518 divided by 8.

Author(s): The Open University

1.4.5.1 Chest measurements of Scottish soldiers

Figure 19 shows a histogram of chest measurements (in inches) of a sample of 5732 Scottish soldiers.

Author(s): The Open University

1.1.7 Body weights and brain weights for animals

The next data set comprises average body and brain weights for 28 kinds of animal, some of them extinct. The data are given in Table 6.

1.1.3: USA workforce

The data set in Table 2 comprises the figures published by the US Labor Department for the composition of its workforce in 1986. It shows the average numbers over the year of male and female workers in the various different employment categories and is typical of the kind of data publ
Author(s): The Open University

Introduction

This unit will introduce you to a number of ways of representing data graphically and of summarising data numerically. You will learn the uses for pie charts, bar charts, histograms and scatterplots. You will also be introduced to various ways of summarising data and methods for assessing location and dispersion.

This study unit is an adapted extract from the Open University course M248 Author(s): The Open University

6.1 How a question is marked

When you tackle a mathematical question, it is often helpful to think about how it would be marked.

To give yourself some practice at this, in this section you will:

• read and criticise sample solutions;

• see if any of the tutor's comments are applicable to your own solutions.

Author(s): The Open University

A lot of people use the equals sign wrongly in places where another word or phrase might actually make the meaning clearer. Sometimes a link word or phrase is useful at the beginning of a mathematical sentence: examples include â€˜Soâ€™, â€˜This impliesâ€™ or â€˜It follows thatâ€™ or â€˜Henceâ€™.

## Example 3

Author(s): The Open University

4 OpenMark quiz

Now try the quiz and see if there are any areas you need to work on.

Author(s): The Open University

3.5 Does the answer make sense in the real world?

Many mathematical problems include units of measurement. The measurement may be of length, weight, time, temperature or currency. The UK uses both metric and imperial units.

The table below gives the units of length that are in everyday use in the UK, but you may know some others.

MetricAuthor(s): The Open University

Once you have done a calculation, with or without the aid of a calculator, it is important that you pause for a moment to check your calculation.

You need to ask yourself some questions.

1. Have I done the right calculation in the right order?

2. Have I given due consideration to units of measurement?

4. Did I make a rough estimate to act as a check?

Author(s): The Open University

## Activity 9

Round 2098Â 765

• (a) to 1 s.f.

• (b) to 2 s.f.

• (c) to 3 s.f.

• (d) to 4 s.f.

Author(s): The Open University

## Activity 1

Round the numbers below:

• (a) to the nearest 10.

• (b) to the nearest 100.

• (c) to the nearest 1000.

Â Â
Author(s): The Open University

You will probably think to yourself that the coat shown costs about Â£300. Â£290 is considerably closer to Â£300 than it is to Â£200, so Â£300 is a reasonable approximation. In this case, 290 has been rounded up to 300. Similarly, 208 would be rounded down to 200 because it is closer to 200 than it is to 300. Both numbers have been rounded to the nearest hundred pounds.

When rounding to the nearest hundred, anything below fifty rounds down. So 248 rounds to 200. Anything o
Author(s): The Open University

Our aim is to show that the object that we produce when we identify some or all the edges of a polygon is a surface. Therefore, by the definition of a surface given in Section 2.5, we must show how it can be given the structure of a topological space, and that this space is Hausdorff. Furthermore, we must show that every point has
Author(s): The Open University

We can use a similar technique to find the Euler characteristic of a 2-fold torus. If we cut the surface into two, as shown in Figure 95, and separate the pieces, we obtain two copies of a 1-fold torus with 1 hole, each with Euler characteristic âˆ’1.

Author(s): The Open University

Using this result, we can obtain the Euler characteristic of a surface with any number of holes by successively inserting the holes one at a time. For example, since a closed disc has Euler characteristic 1, it follows that a closed disc with 1 hole has Euler characteristic 0, a disc with 2 holes has Euler characteristic âˆ’1, and so on.