Do you want to improve your ability to divide one number by another without having to rely on a calculator? This course will help you get to grips with division and give you some practice in dividing numbers.

You donâ€™t need to complete the whole course if only certain sections are relevant to you. I start with the basics, where youâ€™ll have the opportunity to get some practice in dividing small numbers in your head. Then I deal with dividing bigger numbers and decimals. If you are co
Author(s): The Open University

There are practically no new theories or new principles in this section. We shall work through some examples, and you will see how basic techniques and approaches that you have already learned can be combined to allow you to use tabular data efficiently.

## Example 3.1 Health personnel in Thailand

Author(s): The Open University

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.

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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, â€¦, xn
Author(s): The Open University

5.6 Quartiles and the interquartile range

The first alternative measure of dispersion we shall discuss is the interquartile range: this is the difference between summary measures known as the lower and upper quartiles. The quartiles are simple in concept: if the median is regarded as the middle data point, so that it splits the data in half, the quartiles similarly split the data into quarters. This is, of course, an over-simplification. With an even number of data points, the median is defined to be the average of the middle two: de
Author(s): The Open University

5.2.2 Birth weights of infants with SIRDS

The data in Table 3 are the birth weights (in kg) of 50 infants suffering from severe idiopathic respiratory distress syndrome. There are two groups of infants: those who survived the condition (there were 23 of these) and those who, unfortunately, did not. The data have not been sor
Author(s): The Open University

5.1 Measures of location

Everyone professes to understand what is meant by the term â€˜averageâ€™, in that it should be representative of a group of objects. The objects may well be numbers from, say, a batch or sample of measurements, in which case the average should be a number which in some way characterises the batch as a whole. For example, the statement â€˜a typical adult female in Britain is 160 cm tallâ€™ would be understood by most people who heard it. Obviously not all adult females in Britain are the same
Author(s): The Open University

2.3 Infants with SIRDS

The data in Table 3 are the recorded birth weights of 50 infants who displayed severe idiopathic respiratory distress syndrome (SIRDS). This is a serious condition which can result in death.

Learning outcomes

After studying this course, you should be able to:

• understand and use standard symbols and notation: for the pth value in a data set when the values are written in order, the sample lower and upper quartiles and the sample median, the sample mean and the standard deviation

• understand that data can have a pattern which may be represented graphically

• understand that the standard deviation and the interquartile range are measures of the dispersion in a
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3.2 Have I used the correct order for my calculation?

When calculating an answer it is important that you give careful consideration to the order of operations used in the calculation. If you are using a mixture of operations remember that certain operations take priority in a calculation. Consider the following, apparently, simple sum.

Â Â Â 1 + 2 Ã— 3 = ?

Did you give 7 as your response, or 9?

The correct answer is 7 but can you explain why?

If you have a calculator handy, check that it
Author(s): The Open University

2.1.1 Try some yourself

## Activity 14

Measurement of a ceiling gives a length of 6.28 m and a width of 3.91 m.

• (a) Make a rough estimate of the area of the ceiling (the length times the width).

Author(s): The Open University

2.1 Using estimations

Approximations are most useful when it comes to making rough estimates â€“
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1.5 Significant figures

Sometimes it doesnâ€™t make sense to round to a specific number of decimal places. If, say, you were calculating the cost of fencing at Â£10.65 per metre, for a garden boundary, the length of which had been given to you as 185 feet, then you would want to multiply 10.65 Ã— 185 Ã— 0.3048. (Conversion of feet to metres was given in Author(s): The Open University

Examples

• 1.Â Â  The condition â€˜is equal toâ€™ is a relation on any set of real numbers because, for any x, y in the set, the statement â€˜x is equal to yâ€™ is either definitely true or definitely false. This relation is usually denoted by the symbol =. For this relation, each real number in the set is related only to itself!

• 2.Â Â  The condition â€˜is less thanâ€™ is a relation on any set of real numbers, and we usually
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3.3 Operations in modular arithmetic

The Division Algorithm tells us that all the possible remainders on division by an integer n lie in the set

We denote this set by Author(s): The Open University

2.1 What is a complex number?

We will now discuss complex numbers and their properties. We will show how they can be represented as points in the plane and state the Fundamental Theorem of Algebra: that any polynomial equation with complex coefficients has a solution which is a complex number. We will also define the function exp of a complex variable.

Earlier we mentioned several sets of numbers, including Author(s): The Open University

Keep on learning

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## Study another free course

There are more thanÂ 800 coursesÂ on OpenLearnÂ for you to
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3.4 Cylinders and shapes with a uniform cross-section

An important idea when calculating volumes of simple shapes is that of a cross-section. In the case of the rectangular box considered above, it is possible to slice through the box horizontally so that the sliced area is exactly the same as the area of the base or top; in other words, the areas of the horizontal cross-sections are equal.

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