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4.3 Decimals

A decimal number is a different way of representing numbers smaller than one. You put them after a full stop (the decimal point), for instance 0.5. The first digit after the decimal point represents tenths. If you sliced a cake into 10 slices, each slice would be a tenth of the cake. So 0.5 is the same as saying 5 tenths, and can be written Author(s): The Open University

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3 Division rules – order matters

An important thing to remember about division is that it has different rules from multiplication.

For example when you multiply two numbers together, it doesn’t matter what order you multiply them in. So 8 x 4 is exactly the same as 4 x 8. The result is 32 in both cases.

But in division, order matters. So 8 ÷ 4 is different from 4 ÷ 8.

The answer to the first is 2. If you multiply 4 by 2 you get 8.

But the answer to the second is 0.5 (a half). If you multiply 8 by
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3.6 Summary of Section 3

In this section, you have learned about appropriate ways of interpreting data in tables. By working through examples, you have seen how it can be useful to calculate appropriate proportions and ratios, and to present some of the data in graphical form. Guidelines for the choice of graphics have been given. When the data in a table are in the form of counts, you have seen that it can be useful to calculate the counts in a particular row or column as proportions (usually in the form of percenta
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3.2 Health care personnel in Thailand: activities

Activity 7 Health care personnel in Thailand: calculating percentages

Would it be helpful, in considering possible changes in the way health care personnel are divided into the five categories listed, to recalculate th
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3 Interpreting data in table

In Section 2, the main concern was with producing a table of data, for others to read, that communicates clearly the important patterns or messages in the data. In this section, the focus changes slightly. Your role will be that of the reader or user of the data in a table, and you will learn about approaches that make it easier for you to extract information from a table. However, manipulating tabular data into a form that makes it clearer to others will also, very often, make it clearer to
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2.5 Early retirement from the National Health Service

Example 2.2: Early retirement from the National Health Service

A study was carried out to investigate various aspects of early retirement from the British National Health Service (NHS). In 1998–99, 5469 NHS employees from England and Wales were granted early retirement because
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2.4 Including the results of useful calculation

Can Table 2.4 be simplified further by pooling more rows or columns? Perhaps it might be, but there may well be a risk of losing some important or relevant information. So, before considering any further simplification, we shall look at adding information to the table, in the form of the r
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2 Producing useful tables

In much of your statistical work, you will begin with data set, often presented in the form of a table, and use the information in the table to produce diagrams and/or summary statistics that help in the interpretation of the data set. However, in practice, much interpretation of data sets can be done directly from an appropriate table of data, or by re-presenting the data in a rather different tabular form. Dealing with data in tables is the subject of this section and the next. By the time
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1.6 Exercise

Activity 3 Exercise 1.1 Memory recall times

In a study of memory recall times, a series of stimulus words was shown to a subject on a computer screen. For each word, the subject was instructed to recall either a pleasa
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1.5 Summary

In this section you have been introduced to the boxplot. This is a graphic that represents the key features of a set of data. A typical boxplot is shown in Figure 1.8.

Figure 1.8Author(s): The Open University

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1.2 Boxplot activity

Activity 1 Drawing a boxplot: chondrite meteors

1 Boxplots

In this first section, you will learn how to construct a boxplot for a single set of data. The use of boxplots to compare two or more sets of data will then be discussed.


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Acknowledgements

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

Course image: Kjetil Korslien in Flickr made available under Creative Commons Attribution-NonCommercial 2.0 Licence.

Except for third party materials and otherwise
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5.11 Numerical summaries: summary

In this section, various ways of summarising certain aspects of a data set by a single number have been discussed. You have been introduced to two pairs of statistics for assessing location and dispersion. The median and interquartile range provide one pair of statistics, and the mean and standard deviation the other, each pair doing a similar job. As for the choice of which pair to use, there are pros and cons for either. You have seen that the median is a more resistant measure of location
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5.8 Sample variance

It is worth noting that a special term is reserved for the square of the sample standard deviation: it is known as the sample variance.

The sample variance

The sample variance of a data sample x 1, x 2, …, xn
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5.6.1 Quartiles for the SIRDS data

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
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5.5 Measures of dispersion

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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5.3 The mean

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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5 Numerical summaries

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
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