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2.14 Samples and populations

It is no accident that the examples used to illustrate the statistics for repeated measurements of individual quantities were drawn from chemistry and physics. Experiments involving repeated measurements of some quantity are typical of the physical sciences. There are, however, many other types of scientific work in which a typical procedure is to collect data by measuring or counting the members of a sub-set of things which form part of a larger group, and
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2.10.1 Mean and standard deviation for repeated measurements

In everyday terms, everybody is familiar with the word ‘average’, but in science and statistics there are actually several different kinds of average used for different purposes. In the kind of situation exemplified by Table 2, the sort to use is the mean (or more strictly the ‘arithmetic mean’) For a set of measurements, this is de
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2.5 Expressing probability

According to Equation 1, probability is defined as a fraction. However a fraction such as may also be expressed as a decimal number or as a percentage:

 
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1.4 How precise are the measurements?

Scientists are always trying to get better and more reliable data. One way of getting a more precise measurement might be to switch to an instrument with a more finely divided scale. Figure 4 shows parts of two thermometers placed side by side to record the air temperature in a room.

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1.2 Units of measurement

In the UK, two systems of units are in common use. We still use old imperial measures for some things: milk is sold in pints and signposts indicate distances in miles. But for many other everyday measurements metric units have been adopted: we buy petrol in litres and sugar in kilogram bags. A great advantage of metric units is that we no longer have to convert laboriously from imperial units, such as gallons, feet and inches, in order to trade with continental Europe. Also, calculations are
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An introduction to complex numbers
This unit looks at complex numbers. You will learn how they are defined, examine their geometric representation and then move on to looking at the methods for finding the nth roots of complex numbers and the solutions to simple polynominal equations. First published on Mon, 13 Jun 2011 as Author(s): Creator not set

Complex numbers
You may have met complex numbers before, but not had experience in manipulating them. This unit gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The unit includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry.Author(s): Creator not set

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Exploring data: Graphs and numerical summaries
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.
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Interpreting data: Boxplots and tables
This unit is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the boxplot. A boxplot is a fairly simple graphic, which displays certain summary statistics of a set of data. Boxplots are particularly useful for assessing quickly the location, dispersion, and symmetry or skewness of a set of data, and for making comparisons of these features in two or more data sets. Boxplots can also be useful for drawing attention to possible outliers in a dat
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Surfaces
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the classification theorem of compact surfaces. First published on Thu, 18 Aug 2011 as <
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Acknowledgements

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Modelling heat transfer

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

Click 'View document' to open the workbook (PDF, 0.4 MB).

Introduction

In the OpenLearn unit on Developing modelling skills (MSXR209_3), the idea of revising a model was introduced. In this unit you will be taken through the whole modelling process in detail, from creating a first simple model, through evaluating it, to the subsequent revision of the model by changing one of the assumptions. The new aspect here is the emphasis on a revised model, which comes in Section 2. The problem that will be examined is one based on heat transfer.

This unit, the four
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1 Developing modelling skills

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

Click 'View document' to open the workbook (PDF, 0.2 MB).

Introduction

This unit provides an overview of the processes involved in developing models. It starts by explaining how to specify the purpose of the model and moves on to look at aspects involved in creating models, such as simplifying problems, choosing variables and parameters, formulating relationships and finding solutions. You will also look at interpreting results and evaluating models.

This unit, the third in a series of five, builds on the ideas introduced and developed in Modelling poll
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Unit Image

Wade_In_Tulsa, photos

All other materials included in thi
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1 Analysing skid marks

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

Click 'View document' to open the workbook (PDF, 0.2 MB).

Acknowledgements

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

All materials included in this unit are derived from content originated at the Open University.


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Introduction

This unit explores a real-world system – the Great Lakes – where mathematical modelling has been used to understand what is happening and to predict what will happen if changes are made. The system concerned is extremely complex but, by keeping things as simple as possible, sufficient information will be extracted to allow a mathematical model of the system to be obtained.

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