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

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

• divide one number by another;

• divide using decimals;

Author(s): The Open University

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

You donâ€™t need to complete the whole unit 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 confid
Author(s): The Open University

In much of your statistical work, you will begin with data set, often presented in the form of a table, and use the information in the table to produce diagrams and/or summary statistics that help in the interpretation of the data set. However, in practice, much interpretation of data sets can be done directly from an appropriate table of data, or by re-presenting the data in a rather different tabular form. Dealing with data in tables is the subject of this section and the next. By the time
Author(s): The Open University

Boxplots of family sizes

The table below contains data on the sizes (numbers of children) of the completed families of two samples of mothers in Ontario. One sample of mothers had had fewer years of education than the other sample (si
Author(s): The Open University

Example 1.2 Infants with SIRDS: boxplots

Boxplots are particularly useful for making quick comparisons. The following example relates to birth weights of infants exhibiting severe idiopathic respiratory distress syndrome (SIRDS), and the question â€˜Is it possible to relate the chances of eventua
Author(s): The Open University

Histograms provide a quick way of looking at data sets, but they lose sight of individual observations and they tend to play down â€˜intuitive feelâ€™ for the magnitude of the numbers themselves. We may often want to summarize the data in numerical terms; for example, we could use a number to summarize the general level (or location) of the values and, perhaps, another number to indicate how spread out or dispersed they are. In this section you will learn about some numerical summaries
Author(s): The Open University

In this unit, you have looked at a variety of problems all of which involved using patterns or formulas and you have also extended some of your strategies for solving problems. One of the first steps in tackling any problem is to check that you understand both the problem and the information you have been given. This step can concentrate on what the question means. However, this can also involve looking up or checking on mathematical terms, notation or definitions as in Goldbach's conjecture.
Author(s): The Open University