Teach GCSE Maths Discrete and Continuous Data

© Christine Crisp Discrete and Continuous Data "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

Suppose we have data giving the number of children in 10 families. Data sets with numbers between the lowest and highest that cannot occur are called discrete. The numbers can only be integers ( whole numbers ). Ans: A number such as 1·5 is not possible. e.g Tell your partner a number between 1 and 5 that could not occur in a data set giving the number of children in families. Quantitative data are given as numbers. There are 2 types.

Examples of discrete data sets are: Discrete data are usually, but not always, integers. e.g. A shop might stock shoes in British shoe sizes 3, 3 ½, 4, 4 ½, 5, 5 ½, 6, The number of books carried by each of 10 students. The attendance figures at 20 football matches. The number of light bulbs in the rooms of a house. There are values the shoe sizes cannot be, such as 5 ¼, so the data are discrete.

Now think of a ruler. It has no gaps, so the lengths it measures can be any number ( up to the length of the ruler ! ). Suppose we measure 4 pieces of wood to the nearest millimetre. A set of lengths could be given as 75, 84, 87 and 99 mm The piece measuring 75 mm could be any length between 74·5 and 75·49999….. We say that data giving lengths is continuous. There are no gaps in the lengths that are possible.

Ans: Numbers giving lengths, heights, distances, times, weights and temperatures are all continuous data. Can you and your partner think of other quantities that give continuous data ? The 1 st three of these are really all the same ( think about the units they are measured in ). Tip: When deciding whether data are discrete or continuous don’t think about how accurately the numbers can be measured. Think about whether there can be gaps in the quantity itself. For example, there is no gap in time from one second to another even though a digital watch may only show each second.

Decide with your partner which of the following are discrete and which are continuous: Discrete Marks in a test Times for components to fail. Number of goals in football matches. Maximum temperatures Ages of children Distance between towns British weekly earnings Discrete Continuous Discrete Answers Discrete The last one is tricky but there are gaps because, for example, £140·125 is not possible. Exercise