3.1 Have I done the right calculation? Once you have done a calculation, with or without the aid of a calculator, it is important that you pause for a moment to check your calculation. You need to ask yourself some questions. Have I done the right calculation in the right order? Have I given due consideration to units of measurement? Is my answer reasonable? Did I make a rough estimate to act as a check? Your calculation wil
Acknowledgements The content acknowledged below is Proprietary (see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence Grateful acknowledgement is made to the following sources for permission to reproduce material in this Unit: Ficure 2: Crown copyright
1.7.2: Ratio and proportion It is easy to distinguish children from adults. For one thing, children are usually much smaller. But how are we able to tell them apart from a drawing alone? Have a look at the two outline drawings. Which one do you think represents the child and which the adult? 7.1:Relative and absolute comparisons The distinction between relative and absolute comparisons is an important one that has run through this Unit. Here, its meaning and significance will be made more explicit. The subsection begins with examples which illustrate the difference between absolute and relative measures, and you will be asked to reflect on why calculating in relative terms is often a better way to make a fair comparison. Start with a simple example based on comparison of births between countries. In 2002, there 1.7: Some mathematical themes
Aims
The main aim of this section is to review some of the mathematical skills and ideas you have been using, and for you to reflect on some of their more general features and applications. 1.6: Using the price indices
Aims
In this section various uses of the RPI and CPI are discussed. The RPI and CPI are intended to help measure price changes. How they are used to do this is discussed in the audiotape band which follows.
Now listen to the audio clip below, called ‘Using the price indices’. 1.5.2: Calculating the price indices This subsection concentrates on how the RPI is calculated. Generally the CPI is calculated in a similar way, though some of the details differ. To measure price changes in general, it is sufficient to select a limited number of representative items to indicate the price movements of a broad range of similar items. For each section of the RPI, a number of representative items are selected for pricing. The selection is made in such a way that the price movements of the representative ite 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 1.5: The UK Government price indices
Aims
The main aim of this section is to discuss what the UK Government price indices (CPI & RPI) measure and how they are calculated. How often have you read statements like these in the newspapers or heard them on the radio? Have you ever wondered how ‘infla 1.4.3 A price index for the shopping basket In the audio session, two methods of constructing a price index for bread were described. They were called the ‘previous year’ method and the ‘base year’ method. In both cases, the value of the index in the base year is 100. So, for the base year method, For the prev 1.4: Price ratios and price indices
Aims
The main aim of this section is to look at some different ways of measuring price increases. In this section you will be looking at measuring price changes using price indices. In order to do this you will need to understand the concept of a price ratio. Price ratios are another way of looking at price increases or decreases, related to the proportional and percentage increases and decreases you have seen before. 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, 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. 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; 1.7 Every picture tells a story: summing up In summary, this section has looked at time-series graphs, conversion graphs and mathematical graphs. Like all representations, graphs draw from a range of common conventions and styles to convey meaning. From a mathematical point of view, graphs give a visual impression of the relationship between two (or sometimes more) variables; but bear in mind that this impression is largely under the control of whoever draws the graph. When you are drawing graphs for yourself or others, you need to cho 1.5.2 Mathematical graphs: How do you read them? The coordinates of a point are always given in the form (value along the x-axis, value along the y-axis). Two values separated by a comma and enclosed in round brackets form a coordinate pair.Author(s): 1.4.1 Introduction The term ‘conversion graph’ describes a graph used to convert a quantity measured in one system of units to the same quantity measured in another. For example, you can draw up a conversion graph to convert temperatures expressed in degrees Celsius to temperatures expressed in degrees Fahrenheit; to convert liquid volumes expressed in pints to the same volumes expressed in litres; to convert a sum of money expressed in one currency to the same amount expressed in a different currency. Acknowledgements Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit: The content is taken from an activity written by Marion Hall for students taking courses in Health and Social Care, in particular those studying K101 An Introduction to Health and Social Care. The original activity is one of a set of skills activities made available to all HSC students via the HSC Resource Bank. Except for third party materials and otherwise stated (see
Author(s):
Example 18 Making a lawn
Example 8
