Author(s): The Open University

By the end of this unit you should be able to:

• round a given whole number to the nearest 10, 100, 1000 and so on;

• round a decimal number to a given number of decimal places or significant figures;

• use rounded numbers to find rough estimates for calculations;

• use a calculator for decimal calculations involving +, âˆ’, Ã— and Ã·, giving your answer to a specified accuracy (e.g. decimal places or significant figures) and checking your an
Author(s): The Open University

For many calculations you use a calculator. The main aim of this unit is to help you to do this in a sensible and fruitful way. Using a calculation to solve a problem involves four main stages:

• Stage 1: working out what calculation you want to do;

• Stage 2: working out roughly what size of answer to expect from your calculation;

• Stage 3: carrying out the calculation;

• Stage 4: interpreting the answer â€“ Doe
Author(s): The Open University

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:

Author(s): The Open University

This Unit has looked at a variety of ways of comparing prices, and the construction of a price index. Important statistical ideas that contributed to this included mean, weighted mean and median, as well as the general notion of an index.

You now know quite a lot about the CPI, the RPI, and price indices in general, and so you should be able to explain what politicians and journalists really mean when they make sweeping statements about inflation and the cost of living. In the course of
Author(s): The Open University

This final subsection is an overview of the various modes of mathematical communication used so far, like words, tables and graphs, and diagrams. You may have a preference for one over the others as a way of presenting ideas and of receiving information. However, they can all aid your understanding and communication of different mathematical ideas. So you need to develop your skills in using and interpreting all of them.

Look back at Author(s): The Open University

A common criticism of many children's and some adults' drawings is that certain parts are not â€˜in proportionâ€™. That means that they are either too big or too small in relation to the rest of the masterpiece. â€˜In proportionâ€™ means being in the same ratio. Imagine that you have drawn a picture of the front of your house, reducing it in scale to one twentieth of its size.

Author(s): The Open University

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?

Author(s): The Open University

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.

Author(s): The Open University

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 â€˜Using the price indicesâ€™.

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
Author(s): The Open University

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 â€˜infla
Author(s): The Open University

In the audio session, two methods of constructing a price index for bread were described. They were called the â€˜previous yearâ€™ method and the â€˜base yearâ€™ method. In both cases, the value of the index in the base year is 100. So, for the base year method,

For the prev
Author(s): The Open University

In Chapter 1, Section 1.4 of the Calculator Book, you saw that multiplying a price by, say, 1.30 is equivalent to increasing it by 30%. Similarly, multiplying a price by 0.94 is equivalent to decreasing it by 6%. The figures 1.30 and 0.94 are called price ratios. In Table 6, the price of a loaf of bread went up from 50p to 65p. The price
Author(s): The Open University

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.

Author(s): The Open University

The concise formula that you have just used is useful in itself for calculating a mean when you are given data in frequency form. But, even more useful, it can be extended, leading to the idea of a weighted mean, that has many applications, as you will see.

## Example 5: Assignment scores

Author(s): The Open University

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
Author(s): The Open University

The median is essentially the middle value of a batch when the values are placed in size order; it is found in the following way.

1. First, all the values in the batch are sorted into ascending order; that is, smallest first, then second smallest, and so on, ending with the largest.

2. Then, see if the batch size is odd or even. If there is an odd number of values in the batch, then the middle value in the list is the median. If there is an
Author(s): The Open University

1 Here is a poor example of mathematical writing, although the final answer is correct. Rewrite it, correcting the layout and the mathematical punctuation.

Author(s): The Open University

Now that youâ€™ve learned how to do subtraction on paper, you might want to practice your new skills.

To practice subtracting whole numbers, including borrowing where necessary, go to the Practice SubtractingÂ  section of the Numbers website and click on Get sum. Then follow the instructions.

To practise subtracting decimals, go to the
Author(s): The Open University