 For the 23 infants who survived SIRDS, the ordered birth weights are given in Table 9. The first quartile is

qL = x (¼(23+1)) = x (6) = 1.720kg.

The third quartile is

qU = x
Author(s): The Open University

During the above discussion of suitable numerical summaries for a typical value (measures of location), you may have noticed that it was not possible to make any kind of decision about the relative merits of the sample mean and median without introducing the notion of the extent of variation of the data. In practice, this means that the amount of information contained in these measures, when taken in isolation, is not sufficient to describe the appearance of the data. A more informative numer
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Getting Started: 04 Adding text and images
Personalize a website with custom text and images. Add assets using multiple workflows. Integrate Word, Excel, and Dreamweaver.
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The second measure of location defined in this course for a collection of data is the mean. Again, to be precise, we are discussing the sample mean, as opposed to the population mean. This is what most individuals would understand by the word ‘average’. All the items in the data set are added together, giving the sample total. This total is divided by the number of items (the sample size).

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Histograms provide a quick way of looking at data sets, but they lose sight of individual observations and they tend to play down ‘intuitive feel’ for the magnitude of the numbers themselves. We may often want to summarize the data in numerical terms; for example, we could use a number to summarize the general level (or location) of the values and, perhaps, another number to indicate how spread out or dispersed they are. In this section you will learn about some numerical summaries
Author(s): The Open University

Two common graphical displays, most frequently used for continuous data (arising from measurements), have been introduced in this section. A histogram is in a sense a development of the idea of a bar chart. A set of continuous data is divided up into groups, the frequencies in the groups are found, and a histogram is produced by drawing vertical bars, without gaps between them, whose heights are proportional to the frequencies in the groups. You have seen that the shape of a histogram drawn f
Author(s): The Open University

In our discussion of the data on body weights and brain weights for animals in section 1.7, we conjectured a strong relationship between these weights on the grounds that a large body might well need a large brain to run it properly. At that stage a ‘difficulty’ with the data was also suggested, but we did not say exactly what it was. It would, you might reasonably have thought, be useful to look at a scatterplot, but you will see the difficulty if you actually try to produce one. Did you
Author(s): The Open University

In this section, two more kinds of graphical display are introduced – histograms in section 3.2 and scatterplots in section 3.3. Both are most commonly used with data that do not relate to separate categories, unlike pie charts and bar charts. However, as you will see, histograms do have something in common with bar charts. Scatterplots are a very common way of picturing the way in which two different quantities are related to each other.

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Two common display methods for data relating to a set of categories have been introduced in this section. In a pie chart, the number in each category is proportional to the angle subtended at the centre of the circular chart by the corresponding ‘slice’. In a bar chart, the number in each category is proportional to the length of the corresponding bar. The bars may be arranged vertically or horizontally, though it is conventional to draw them vertically where the labelling of the chart ma
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Figure 8 shows a pie chart of the data on nuclear power stations from Table
Author(s): The Open University

The danger of using three-dimensional effects is really brought home when two data sets are displayed on the same bar chart. Table 2 may be thought of as consisting of two data sets, one for male workers and one for female workers. On its own, each of these data sets could be portray
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In this subsection we consider, briefly, some problems that can arise with certain ways of drawing bar charts and pie charts.

Figure 5 shows what is essentially the same bar chart as Author(s): The Open University

Figure 4 shows a bar chart for the data in Table 7 on the effectiveness
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A better way of displaying the data on nuclear power stations is by constructing a rectangular bar for each country, the length of which is proportional to the count. Bars are drawn separated from each other. In this context, the order of the categories (countries) in the original data table does not matter, so the bars in Author(s): The Open University

Figure 2 shows a pie chart of the number of nuclear power stations in countries where nuclear power is used, based on the data from Author(s): The Open University

Suppose we count the numbers of large, medium and small tattoos from the data in Table 7: there were 30 large tattoos, 16 of medium size and 9 small tattoos. These data are represented in Author(s): The Open University

The data set in Table 7 (section 1.8) comprised non-numerical or categorical data. Such data often appear in newspaper reports and are usually represented as one or other of two types of graphical display, one type is called a pie chart and the other a bar chart; these are arguably the graphical displays most familiar to the general public, and are certainly ones that you will have seen before. Pie charts are discussed in section 2.2 and bar charts in section 2.4. Some problems
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In this section you have met some real data sets and briefly considered some of the questions you might ask of them. They will be referred to and investigated in the remaining sections of this course. Some general principles that govern the efficacy and quality of data summaries and displays will be formulated. As you will discover, the main requirements of any good statistical summary/display are that it is informative, easy to construct, visually appealing and readily assimilated by a non-e
Author(s): The Open University

The final data set in this section is different from the others in that the data are not numerical. So far you have only seen numerical data in the form of measurements or counts. However, there is no reason why data should not be verbal or textual. Table 7 contains clinical data fro
Author(s): The Open University

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.