Loe raamatut: «Numbers: B2+»
Collins
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First edition 2013
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You can trust Collins COBUILD
The 4.5-billion-word Collins Corpus is the world’s largest database of the English language. It is updated every month and has been at the heart of Collins COBUILD publishing for over 20 years. All definitions provided in the glossary boxes in this book have been taken from the Collins COBUILD Advanced Dictionary.
Source ISBN: 9780007507153
Ebook Edition © April 2014 ISBN 9780008101848
Version: 2014-07-01
Contents
Title Page
Copyright
Introduction
Chapter 1 Getting started
look at numbers in everyday life
understand the purpose and use of statistics
learn key terms for working with numbers
learn the basics about spreadsheets
practice referring to and labelling graphics in writing
Chapter 2 Starting primary research
practise formulating research questions
understand the principles of sampling
learn how to formulate a hypothesis
Chapter 3 Research methods
understand some common research methods
understand when to use interviews, questionnaires and focus groups
understand the advantages and disadvantages of common research methods
Chapter 4 Questionnaires
understand how to write a questionnaire
practise forming polite question forms
understand different sampling techniques
understand the pros and cons of distribution methods
Chapter 5 Interviews
understand how to ask good interview questions
learn how to structure different questions
learn about the interviewer effect
learn how to use reported speech
Chapter 6 Percentages and fractions
learn how to work with percentages
learn how to understand fractions
compare fractions and percentages
use verbs and nouns and dependent prepositions
Chapter 7 Averages
learn why we use averages
learn about different types of averages
learn when to use frequency tables to find averages
learn how to choose the right average to use
Chapter 8 Presenting your data
understand the use of different visual information
use the present simple, past simple and present perfect to describe graphics
use the active and passive voice to describe graphics
Chapter 9 Describing change
represent change visually
use verbs of change
use adverbs describing change
use adjective and noun combinations to describe change
Chapter 10 Making comparisons
use graphics to compare information
use comparative structures
use superlative structures and cautious language
Chapter 11 Making connections
understand correlation
understand the effect of sample size
express links and connections
describe facts and data
Chapter 12 Working with collected data
learn how to present survey results
avoid producing misleading results from diagrams
describe cause and effect
express generalizations and specifics
use language of argumentation
use evaluative language
learn how to write conclusions
Further reading
The grammar of fractions
Glossary 
Answer key
About the Author
About the Publisher
Introduction
Collins Academic Skills Series: Numbers will give you the skills you need for doing research, collecting data, presenting it, using numbers and appropriate language to describe it, and working with the collected data.
Designed to be used on a self-study basis to support English for Academic Purposes or study skills courses, it is intended for students on pre-sessional or foundation courses as well as for first-year undergraduate students.
The book has twelve chapters covering the key stages of the research process from start to finish. You will learn how to:
choose the right research methods
use basic maths skills
present your data
analyse your data
At the back of the book there is:
a list of useful books in Further reading
helpful information in The grammar of fractions
a Glossary of key terms
a comprehensive Answer key
Chapter structure
Each chapter includes:
Aims – These set out the skills covered in the chapter.
A self-evaluation quiz – By doing this you are able identify what you already know on the subject of the chapter and what you need to learn.
Information on academic guidelines on how to develop academic skills – These sections will help you understand university practices and expectations so you know what is required.
Practical exercises – These help you to develop the skills to succeed at university. You can check your answers at the back of the book.
Tips – Key points are highlighted for easy reference and provide useful revision summaries for the busy student.
Glossary – Difficult words are glossed in boxes next to where the word appears in the chapter. There is also a comprehensive Glossary at the back of the book.
Remember sections – This is a summary of key points for revision and easy reference.
Glossary boxes
Where we feel that a word or phrase is difficult to understand, we have glossed this word/phrase. All definitions provided in the glossary boxes have been taken from the COBUILD Advanced Dictionary. At the end of the book there is a full alphabetical list of the most difficult words from the book for your reference.
Using Numbers
You can either work through the chapters from Chapter 1 to Chapter 12 or you can choose the chapters and topics that are most useful to you. The Contents page will help in your selection.
Study tips
Each chapter will take between one and three hours. Take regular breaks and do not try to study for too long. Thirty to sixty minutes is a sensible study period.
Regular study is better than occasional intensive study.
Read the chapter through first to get an overview without doing any exercises. This will help you see what you want to focus on.
Try the exercises before checking the Answer key.
After doing the exercises in the book, try them again using your own research topic and reading materials. If possible, ask a more experienced colleague or friend to give you feedback on your work.
All university departments are different. Use the information in the book as a guide to investigating your own university department.
Write questions you can ask to find out how your department expects you to do research and collect and present data.
There is no one correct way of doing research and working with collected data. Use your experience of doing the exercises to learn what works best for you. Adapt the suggestions in this book to suit your learning style and context.
Learning to do research and work with data is an on-going process, which means you need to practise the same skills many times. Revise regularly.
Other titles
Also available in the Collins Academic Skills Series: Writing, Lectures, Research, Presenting, and Group Work.
1 
Getting Started
Aims
look at numbers in everyday life
understand the purpose and use of statistics
learn key terms for working with numbers
learn the basics about spreadsheets
practise referring to and labelling graphics in writing
Quiz
Self-evaluation
Read the statements below. Circle the answers that are true for you.
| 1 I understand what statistics is and the language to describe it. | agree | disagree | not sure |
| 2 I know a number of basic terms and phrases to describe numbers in English. | agree | disagree | not sure |
| 3 I know how to use a spreadsheet. | agree | disagree | not sure |
| 4 I know how to refer to and label graphics such as bar charts and line graphs in writing. | agree | disagree | not sure |
Numbers and mathematics are very important in our everyday lives because we use them frequently when we manage our finances, go shopping, make travel plans, convert currency, follow instructions for a recipe or take measurements when we are building and creating things. If we carry out an academic study or investigation, then we need to use a branch of mathematics known as statistics which involves collecting and organizing data, making sense of our information and presenting findings.
Glossary
data You can refer to information as data, especially when it is in the form of facts or statistics that you can analyse. In American English, data is usually a plural noun. In technical or formal British English, data is sometimes a plural noun, but at other times, it is an uncountable noun.
This chapter begins by reminding us of the calculations and vocabulary that are used when we are working with money and taking measurements. It then provides an introduction to statistics, explaining where data is used in different subject areas and describing different categories of data. With a more technical focus, the chapter then describes how to use a computer program known as a spreadsheet which can help with storing and presenting data. Finally, an explanation is given of the use of graphics in academic writing, highlighting ways to refer to graphics in your text so that you can comment on your data and findings effectively.
Numbers in everyday life
In this section, we will explore some of the ways in which numbers are used in everyday situations. We will investigate taking measurements and working with money.
Money
It is important to know how to work with money so that you can:
Recognize the value of amounts of money
Estimate your expenditure
Often money calculations will involve the use of percentages and fractions. You will learn about these in Chapter 6.
Glossary
estimate If you estimate a quantity or value, you make an approximate judgement or calculation of it.
expenditure Expenditure is the spending of money on something, or the money that is spent on something.
value In mathematics, the value of a symbol or letter is the amount represented by it.
The value of a digit in a number depends on its position in the number. In the following amounts of money, the digit 4 has a different meaning:
| 14p or £0.14 | four pence |
| 45¢ or 0.45¢ | forty cents |
| £14.27 | four pounds |
| $49.99 | forty dollars |
| £458.60 | four hundred pounds |
| €4,700 | four thousand euros |
| $46,500 | forty thousand dollars |
A place value diagram may help to remind you how to recognize the value of amounts of money. The highest number in the group is the maximum and the lowest is the minimum.
| $10,000 | €1,000 | £100 | $10 | £1 | . | ¢1/10 | 1/100p |
| ten thousand dollars | one thousand euros | one hundred pounds | ten dollars | one pound | . | ten cents | one pence |
Estimating can be a useful skill when you are calculating your monthly expenditure because you can work out approximately how much your total bill will be without adding up all of the individual values. Estimating involves rounding prices up or down to the nearest ten pounds, dollars or euros so that you can work out the total more easily.
This list shows the actual expenditure with the estimated value for each cost:
| Monthly Expenditure | ||
| Actual cost | Estimated cost | |
| Accommodation | £512.40 | £510 |
| Food and drink | £148.60 | £150 |
| Travel | £31.52 | £30 |
| Clothes | £56.80 | £60 |
| Entertainment | £86.53 | £90 |
So, when we add up the actual prices the aggregate total price for our shopping is £835.85 and the estimated cost is £840.
Glossary
round up/down If you round an amount up or down, you change it to the nearest whole number or the nearest multiple of 10, 100, 1,000, and so on.
aggregate An aggregate amount or score is made up of several smaller amounts or scores added together.
Measurements
Taking measurements is about finding a number that shows the amount or size of something. We are most often interested in measuring temperature, length, speed, time, capacity and mass. To make an accurate measurement, you would need to choose an appropriate measuring device and use the correct type of units on a scale. Here are some examples:
Glossary
capacity The capacity of a container is its volume, or the amount of liquid it can hold, measured in units such as litres or gallons.
mass In physics, the mass of an object is the amount of physical matter that it has.
| Measurement | Measuring device | Units |
| temperature | thermometer | degrees Celsius (°C) or degrees Fahrenheit (°F) |
| length | ruler or tape measure | centimetres (cm), metres (m) or kilometres (km) |
| speed | speedometer | metres per second (m/s) or kilometres per hour (km/h) |
| time | clock or stopwatch | seconds (sec), minutes (min) or hours (hr) |
| capacity | measuring jug | millilitres (ml) or litres (l) |
| mass | weighing scales | grams (g) or kilograms (kg) |
Exercise 1
Match the correct unit of measurement with each item to be measured.
| Unit of measurement | Item being measured |
| degrees Celsius (°C ) | distance between London and Paris |
| kilometres (km) | weight of a pencil |
| kilometres per hour (km/h) | time taken to count to ten |
| seconds (sec) | temperature of a cup of coffee |
| millilitres (ml) | amount of orange juice in a glass |
| grams (g) | speed of a train |
There are a number of key terms that are useful to learn when working with numbers and data. Test your knowledge of these by completing the following exercises.
Exercise 2
Use the words in the box to complete these sentences. You might need to change the form of the word.
accurate calculation fraction measurement
aggregate / total capacity mass percentage
approximately estimated maximum / minimum round up / down
1 The ________of 9, 10, 24, 6, 8, 5 is 62. It is also known as the ________.
2 The ________of the lecture theatre is 200 people.
3 Economic forecasters have ________that the economy will grow by 0.5% next year.
4 There are ________300,000 international students studying in the UK.
5 The spreadsheet automatically ________or ________to the nearest whole number.
6 The ________loan available is £5,000 and the ________loan available is £500.
7 The ________of a bowling ball is 7.25 kilograms.
8 ________measurements are essential in many scientific experiments.
Exercise 3
Use another word in the box in Exercise 2 to describe each item below.
1 1/3 ________
2 245 × 6 ________
3 98% ________
4 100 ml ________
Exercise 4
Put the word in brackets into the correct form in each of these sentences.
1 The closest ________was 2 years 4 months. (estimate)
2 There are a number of different ways to ________an average. (calculate)
3 There are ________1.3 billion people in China. (approximate)
4 The ________of another variable completely changed the outcome of the experiment. (add)
5 The values were ________and then used to find the average. (total)
6 The answers were cross-checked to ________predict the outcome. (accurate)
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