Unit 7 Averages and range Sampling 1 2 A printer produces books in batches of 1000. A sample from each batch is checked for quality. a Explain why sampling is used. b How many books should be included in the sample? 10 30 200 500 c If the books from the batch are in a line, what would be wrong with choosing all of the sample from one end? d Describe a better way to choose the sample. Jenny wants to find out how many people do their weekly shopping online. She asks people in her local town centre on a Saturday morning to complete her questionnaire. Explain why her results may be biased. Q1a hint Imagine testing all 1000 books every time a batch is produced. What can you say about the cost and the time it would take? Q1c hint Remember, you want to have a good chance of finding a fault wherever it occurs in the batch. Q2 hint Do you think that the people in a town centre on a Saturday morning include a fair proportion of people who do their weekly shopping online? 7 Extend 1 Find the mean of the first 5 square numbers. 2 Problem-solving The mean of the numbers shown on these cards is 6. 7 6 9 4 ? Work out the value on the fifth card. 3 Here are some fractions. __ 2 3 5 __ 12 _38 _56 _34 a Work out the mean. b Work out the range. 4 Exam-style question Julie is x years old. Kevin is x + 3 years old. Omar is 2x years old. Write an expression, in terms of x, for the mean of their ages. (2 marks) Nov 2011, Q3, 5MB1H/01 5 Exam hint Find the total by collecting like terms. Divide the total by the number of people. Which average should you use for each of these? Choose mean, median or mode. Explain your choices. a One value appears a lot more often than any other and it is not at one end of the data set. b There are no extreme values and every value should be taken into account. c The data is not numerical. d The data is fairly evenly spread but there is one extreme value. 203