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7 Beliefs and theories

‘Authorities’ – critics, historians, philosophers and so forth – of course argue from their interpretations of what a work of art, an event or an idea means. And their judgements are based on certain beliefs – about the nature of the objects they study and about what they themselves do as readers and interpreters of them. From our discussion of ‘Meeting at Night’ you have seen what my beliefs are: that people can reach some understanding of a text through the proce
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1.1 Analysis, interpretation and evaluation

When you study a painting, for example, you take it apart to see how it ‘works’ as a painting. You analyse it ‘as it is in itself’, because this gives you many clues to what it might mean. But that analysis is complicated by the fact that the way we understand a painting itself changes over time. For instance, what a religious painting might have meant to the artist and his contemporaries in sixteenth-century Italy cannot be the same as it means to us now. We do n
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Learning outcomes

After studying this course, you should be able to:

  • understand aspects of human culture, past and present

  • analyse various ‘objects’, interpret their meaning and evaluate them.


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4 Supply and demand: Kiran's story

The first six months have just flown by. I've really enjoyed working with the two or three schools that I chose following my conversation with my friend who is a student. I feel that I have established a good reputation for reliability as well as keeping the classes moving forward in their work. My family
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7.2.1 Mean, median and mode

The mean, median and mode are all types of average and are typical of the data they represent. Each has advantages and disadvantages, and can be used in different situations, but they all give us an idea of the general size of the values involved. Here we provide brief definitions, and some idea of when each should be used.

The following set of data is the number of miles (to the nearest mile) walked in a week by a group of students. You are going to look at how to calculate the mean, m
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7.1 Introduction

Charts, graphs and tables are all very helpful ways of representing a set of data. However, they are not the only ways of passing on information about data. This section looks at how you can analyse a set of data to summarise the given information as briefly and simply as possible.

Essentially, there are two features of a set of data that enable summarising: the average and the spread. This section starts by looking at what is meant by ‘average’. If you have already studied Worki
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5.2.1 Discrete variables

The charts about different modes of transport and that on attendance figures at a range of cultural events all use what might be called ‘word categories’. Each category (e.g. bus, rail, cycle, and walk) is quite distinct from any other in the set of categories. Such distinct categories are known in mathematics as ‘discrete variables’.

Word categories are not the only type of variable that is discrete; numbers can also be discrete. For example, at the beginning of this section, w
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4.1.1 When are line graphs used?

A line graph shows a relationship between two variables. In other words, it shows how one thing varies by comparison to another. For example, a distance-time graph shows distance varying against the time of day, or the start time of a journey. The distance increases when a vehicle is moving but remains the same when the vehicle is stationary.


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4.1 What is a line graph?

This section covers line graphs. We define the format, give some ideas about when it should be used, and draw some graphs. You can have a go at drawing a line graph in Activity 6, based on data that we supply.

A line graph, at its simplest, is a diagram that shows a line joining several points, or a line that shows the best possible relationship between the points. Sometimes the line will go through all of the points, and sometimes it will show the best possible fit. The line does not h
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3.1.2 When is a table not a good format to use?

There are very few cases where a table will be the worst format to use. However, when you have a huge amount of data, you may wish to present some of it in a different format. Other formats for presenting data are explained in Sections 4–6.


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1 Getting the most from charts, graphs and tables

Do you sometimes feel confused about how to create a chart, graph or table?

Are you not always sure which of these to choose to illustrate your set of data?

Why do we produce charts, graphs and tables anyway?

Spend a few minutes writing down what you think are the reasons why we choose to present data in this way before you read on.

One student has said:

If an exam or assessment question ask
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Learning outcomes

After studying this course, you should be able to:

  • reflect on the reasons for needing to improve skills in using charts, graphs and tables

  • understand the following mathematical concepts and how to use them, through instruction, worked examples and practice activities: reflecting on mathematics; tables; line graphs; bar charts and histograms; pie charts; analysis

  • draw on a technical glossary, plus a a list of references to further reading and sources
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Learning direct

This is a telephone line that was set up in the middle of 1998, to help adults to find out about local provision. The number is 0800 100 900. Lines are open 08.00. to 22.00 everyday. Calls are free and you can ring as many times as you like. There is also a comprehensive website at www.learndirect.co.uk.


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5.1 Difficulties in interpretation

Graphs and charts are often used to illustrate information that is discussed in course materials or a newspaper article, so it is important to be able to interpret them correctly. Often, the authors of an article will attempt to emphasise the point they are trying to make by presenting the facts and figures in such a way as to confirm their argument. This is a commonly used journalistic approach, which means that it is essential to examine graphs and charts used to support arguments very care
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4.8.2 Median

The median is the middle value of a set of numbers arranged in ascending (or descending) order. If the set has an even number of values then the median is the mean of the two middle numbers. For example:

1, 1, 2, 5, 8, 10, 12, 15, 24This set of nine values is arranged in ascending order and the median is 8.
32, 25
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4.7 Proportion

We can use a number of different ways to indicate change – fractions, decimals, and percentages tend to be the ones with which many of us are familiar.

Activity 11

Which of these represents the greater proporti
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4.6 Line graphs

These are probably the graphs that you will be most used to seeing on an everyday basis. Line graphs are most suitable when you are just comparing one value as it changes with another value. They are less suitable when you want to look at several things at once; for example to study changes in oil prices and supermarket profits on petrol sales, the scales on the left-hand and right-hand sides of a graph would have to be different, and this can be very misleading (there is an example of this i
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4.5 Histograms

Histograms are a special form of bar chart in which the bars usually touch each other because histograms always show data collected into ‘groups’ along a continuous scale. They tend to be used when it's hard to see patterns in data, for example when there are only a few variables, or the actual amounts are spread over a wide range. For example, suppose you manufactured biscuits; it is important to manufacture closely to a given size, as there are regulations governing the sales of biscuit
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4.3.1 Pie charts

A pie chart is a diagram in the form of a circle, with proportions of the circle clearly marked. A pie chart is a good method of representation if we wish to compare a part of a group with the whole group. It gives an immediate idea of the relative sizes of the shares. So, for example, it can be used to consider advertising income. It can also be used to look at, say, shares of market for different brands, or different types of sandwiches sold by a store.

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1.4 Conclusion

The aim of this course has been to try to draw together work on numbers and text, and to try to be helpful to those who, like me, find numbers and statistics rather unapproachable. Evidence is used in social science to convince us of the value of a claim, and is a crucial element in our evaluation of theoretical perspectives.

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