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

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Author(s): The Open University

This free course provided an introduction to studying Mathematics and Statistics. It took you through a series of exercises designed to develop your approach to study and learning at a distance, and helped to improve your confidence as an independent learner.

Author(s): The Open University

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
Author(s): The Open University

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 â€˜averageâ€™. If you have already studied Worki
Author(s): The Open University

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 â€˜word categoriesâ€™. 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 â€˜discrete variablesâ€™.

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
Author(s): The Open University

5.1.4 How do I draw a bar chart?

First, you need to decide what it is you want your chart to illustrate. This may be governed by the data you have access to or you might need to collect the data yourself. Then the process is as below.

1. Decide on a clear title.

The title should be a brief description of the data that you want to show.

2. Identify how many bars are needed.

The bars correspond to the number of categories you have. For instance, if you are look
Author(s): The Open University

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.

Author(s): The Open University

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
Author(s): The Open University

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 4â€“6.

Author(s): The Open University

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
Author(s): The Open University

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
Author(s): The Open University

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.

Author(s): The Open University

Conclusion

We have now looked at a number of different graphs and charts, all of which were potentially misleading. We hope that from now on if you have to work with a graph or a chart, you will always consider the following points:

• look carefully at any horizontal or vertical scale that is given;

• consider each graph or chart separately, don't compare them unless you are sure that they have the same scales;

• if it is not easy to
Author(s): The Open University

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
Author(s): The Open University

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,Â 1,Â 2,Â 5,Â 8,Â 10,Â 12,Â 15,Â 24This set of nine values is arranged in ascending order and the median is 8.
32,Â 25
Author(s): The Open University

We can use a number of different ways to indicate change â€“ 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
Author(s): The Open University

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
Author(s): The Open University

Histograms are a special form of bar chart in which the bars usually touch each other because histograms always show data collected into â€˜groupsâ€™ 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
Author(s): The Open University

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.

Author(s): The Open University

Some of the sentences we have looked at are harder to understand than they might be because they are not very well punctuated. Punctuation marks are the â€˜stopsâ€™ in a sentence that divide it up into parts. They make it easier to follow the meaning of the words. For instance, it is easier to read this sentence of Philip's if we put a comma after â€˜wealthyâ€™:

With society becoming more wealthy, it was possible for t
Author(s): The Open University