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
1.4.3 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; 1.9.2 Single-track minders You should read through this subsection, including the activities at the end, and then watch the video ‘Single-track minders’ in the parts indicated by the activities. The video lasts about 25 minutes. At certain points you will be asked to stop the video and complete an activity. In the 1960s, many of the UK’s passenger and freight railway services were closed down as part of an economic re-evaluation of the railway system. Some lines were dismantled and forgotten, but others att 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 7 Subtracting decimals by lining them up Subtracting whole numbers such as 52 from 375 is fairly straightforward. Subtracting decimal numbers such as 6.892 from 223.6 uses the same process but with one extra step – you have to line the decimal points up first. Rather than arranging your two numbers so that they line up on the right-hand side, you need to line up the decimal points, regardless of how many numbers there are after the decimal point. In the example below, the top number has one number after the decimal point. It 10 Dividing by big numbers – long division In the previous sections you saw how to divide a big number by a small number up to 10. Things get harder if you want to do a division where both the numbers are big. This kind of calculation is called long division, probably because you write the steps of the calculation out on paper in a long sequence. The principle of doing long division is the same as when you divide by a number up to 10. The only difference is that, because the numbers involved in long division are usually too big 6 Dividing on paper If the numbers you want to divide are too large for you to do the calculation in your head, you can use a calculator. Alternatively, you can do the calculation on paper. In the example below, click on each step in turn to see how to divide 126 by 6. 5: Summary In this unit, you have been introduced to a number of ways of representing data graphically and of summarizing data numerically. We began by looking at some data sets and considering informally the kinds of questions they might be used to answer. An important first stage in any assessment of a collection of data, preceding any numerical analysis, is to represent the data, if possible, in some informative diagrammatic way. Useful graphical representations that you have met in this unit i 4.3: The median The median describes the central value of a set of data. Here, to be precise, we are discussing the sample median, in contrast to the population median. The median of a sample of data with an odd number of data values is defined to be the middle value of t 1.2.8 Problems with graphics: nuclear power stations
Figure 8 shows a pie chart of the data on nuclear power stations from Table 1.2.6 Problems with graphics 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):
Example 18 Making a lawn
Example 8
The sample median
