By Sophie Goldie
This fresh sequence has been written for the college of Cambridge overseas Examinations path for AS and a degree arithmetic (9709). This identify covers the necessities of S1 and S2. The authors are skilled examiners and academics who've written largely at this point, so have ensured all mathematical techniques are defined utilizing language and terminology that's applicable for college kids the world over. scholars are provded with transparent and designated labored examples and questions from Cambridge overseas previous papers, so that they find a way for many crucial examination perform. every one publication features a unfastened CD-ROM which beneficial properties the original 'Personal teach' and 'Test your self' electronic assets that may aid scholars revise and toughen ideas clear of the study room: - With own train each one pupil has entry to audio-visual, step by step aid via exam-style questions - The try out your self interactive a number of selection questions establish weaknesses and element scholars within the correct path
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Additional resources for Cambridge International AS and A Level Mathematics: Statistics
Number of students 110–119 1 120–129 3 130–139 10 140–149 28 150–159 65 160–169 98 170–179 55 180–189 15 Exercise 1D Height (cm) S1 1 Choose suitable mid-class values and calculate an estimate for the mean height. 2 A junior school teacher noted the time to the nearest minute a group of children spent reading during a particular day. The data are summarised as follows. Time (nearest minute) Number of children 20–29 12 30–39 21 40–49 36 50–59 24 60–69 12 70–89 9 90–119 2 Choose suitable mid-class values and calculate an estimate for the mean time spent reading by the pupils.
Ii) Using a suitable assumed mean, find the mean and standard deviation of Felicity’s data. For a set of ten data items, ∑(x – 20) = – 140 and ∑(x – 20)2 = 2050. Find their mean and standard deviation. (i) 7 8 9 10 11 For a set of 20 data items, ∑(x + 3) = 140 and mean and standard deviation. ∑(x + 3)2 = 1796. 4. Find the value of a and the standard deviation. ∑(x + a)2 = 1854. 9. Find the value of a and the standard deviation. ∑(x – a)2 = 75. The mean The length of time, t minutes, taken to do the crossword in a certain newspaper was observed on 12 occasions.
1 Simon was using an assumed mean to ease his arithmetic. Sometimes it is easier to work with an assumed mean in order to find the standard deviation. 9 Using an assumed mean of 7, find the true mean and the standard deviation of the data set 5, 7, 9, 4, 3, 8. SOLUTION It doesn’t matter if the assumed mean is not very close to the correct value for the mean but the closer it is, the simpler the working will be. Let d represent the variation from the mean. So d = x – 7. f. So the true mean is 7 – 1 = 6.