3.6.1 Try some yourself 1 The population of a village is 5481. Round this: (a) to the nearest thousand people; (b) to the nearest hundred people. 3.4.1 Try some yourself 1 For each of the following calculations make suitable rough estimates before doing the calculation on your calculator and check the result. (a) 22.12 ÷ 4.12 (b) 0.897 × 3.4 Did I make a rough estimate to act as a check? When using a calculator many people have ‘blind faith’ in its capacity to provide the correct result. Calculators invariably provide the co 1.6 Significant figures for numbers less than one You can use the same procedure for numbers less than one. In scientific work people deal with very small units of measurement. Suppose you read that the spacing between adjacent atoms in a solid was 0.000 002 456 84 metres. You could make the number more memorable by using two sign 1.5.1 Try some yourself 1 Round 2098 765 (a) to 1 s.f. (b) to 2 s.f. (c) to 3 s.f. (d) to 4 s.f. 1.4.1 Try some yourself 1 Round a measurement of 1.059 metres: (a) to the nearest whole number of metres; (b) to two decimal places; 1.4 Rounding decimals Using a calculator often gives a long string of digits. For example, 1 ÷ 3 might give .333333333. But very often, for practical purposes, this level o 1.3 Rounding in general Numbers are often approximated to make them easier to handle, but sometimes it doesn’t help very much to round to the nearest 10 or the nearest 100 if the number is very large. For example, suppose the monthly balance of payments deficit was actually £24 695 481. Rounded to the nearest 10, it's £24 695 480; and to the nearest 100, it's £24 695 500. But £24 695 500 is still a complicated number to deal with in your head. That's why it was rounded to £25 000 000 in the newspaper 5.1: What are the CPI and RPI? The Consumer Prices Index (CPI) and the Retail Prices Index (RPI) are published each month by the UK Office for National Statistics. These are the main measures used in the UK to record changes in the level of the prices most people pay for the goods and services they buy. The RPI is intended to reflect the average spending pattern of the great majority of private households. Only two classes of private households are excluded, on the grounds that their spending patterns differ greatly from t 1.4.2: Price indices Cast your mind back to why proportions and percentages were introduced in Section 2. It was because using actual price changes is unsatisfactory in comparing how the prices of different items have altered over time when their basic prices are very different. For example, if the price of a new motor car has gone up by £100 and the price of a new bicycle has gone 1.3.5 Generalising the formula for the mean household size This method of calculating the mean may be summarised as follows. The frequency of a household size is the number of responses corresponding to that size. The sum of the frequencies is the total number of households. One use of symbols in mathematics is in provi 1.3.2 The mean The mean, or the arithmetic mean as it is sometimes called, is found by adding together all the numbers in the batch and then dividing by the batch size. Thus, for the batch of heights, 1.3.1: The mean and the median This subsection looks at two ways of finding an ‘average’. The first produces the mean, which is what was originally meant by ‘average’, and what most people think of when they talk about an average. The second gives the median, which might more accurately be described as a ‘typical’ or middle value. They will be illustrated using the following batch of heights. The heights in metres (measured to the nearest centimetre) of a group of seven people are as follows 1.3: A statistical interlude—averages
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The main aim of this section is to discuss several ways of finding averages and to introduce you to the statistical facilities of your calculator. A single number which is typical or representative of a collection (or batch - statistical term for a set of collected data.) of numbers is commonly referred to as an average. There are several different ways of defining such a number. Two are discussed briefly in Author(s): Learning outcomes After studying this Unit you should be able to: calculate the mean, weighted mean and the median of a batch of numbers; calculate a percentage and a percentage price increase; use a weighted mean to find an average percentage price increase (given the weights); use the statistical facilities of your calculator to find the mean, the median and (given the weights) the weighted mean of a batch of numbers; calculate a perce 6.5.1 Another ‘making a lawn’ solution Suppose you have some friends who are planning to put a new lawn in their garden. The lawn is to be 12 m by 14 m and they have a choice of either laying turf or sowing grass seed. You have been asked to help them decide between the two. 3.2 Using formulas Formulas are important because they describe general relationships, rather than specific numerical ones. For example, the tins of paint formula applies to every wall. To use such a formula you need to substitute specific values for the general terms, as the following examples show. 2.5.1 Try some yourself 1 How would you add the following words to the list:  decimal, fraction, positive, negative. For each one, give the mathematical meaning and an example of its use. 2.3 Link words A lot of people use the equals sign wrongly in places where another word or phrase might actually make the meaning clearer. Sometimes a link word or phrase is useful at the beginning of a mathematical sentence: examples include ‘So’, ‘This implies’ or ‘It follows that’ or ‘Hence’. Learning outcomes By the end of this unit you should be able to: lay out and, where appropriate, label simple mathematical arguments; understand the precise mathematical meaning of certain common English words; understand and use common mathematical symbols; write clear, unambiguous mathematical solutions using appropriate notation; identify and modify some sources of ambiguity or inappropriate use of notation in a mathematical solution;
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