1.4 Boxplot activity 2 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 educatio 5.6.1 Quartiles for the SIRDS data For the 23 infants who survived SIRDS, the ordered birth weights are given in Table 9. The first quartile is qL = x (¼(23+1)) = x (6) = 1.720kg. The third quartile is qU = x (¾ 5.6 Quartiles and the interquartile range The first alternative measure of dispersion we shall discuss is the interquartile range: this is the difference between summary measures known as the lower and upper quartiles. The quartiles are simple in concept: if the median is regarded as the middle data point, so that it splits the data in half, the quartiles similarly split the data into quarters. This is, of course, an over-simplification. With an even number of data points, the median is defined to be the average of the middle two: de 5.3 The mean The second measure of location defined in this course for a collection of data is the mean. Again, to be precise, we are discussing the sample mean, as opposed to the population mean. This is what most individuals would understand by the word ‘average’. All the items in the data set are added together, giving the sample total. This total is divided by the number of items (the sample size). 5.2.2 Birth weights of infants with SIRDS The data in Table 3 are the birth weights (in kg) of 50 infants suffering from severe idiopathic respiratory distress syndrome. There are two groups of infants: those who survived the condition (there were 23 of these) and those who, unfortunately, did not. The data have not been sor 3.4 Did I make a rough estimate to act as a check? When using a calculator many people have ‘blind Try some yourself Without using your calculator solve the following calculations. (a) 3 + 5 × 2 = ? (b) 12 − 6 + 6 = ? (c) 6 + (5 + 3.2 Have I used the correct order for my calculation? When calculating an answer it is important that you give careful consideration to the order of operations used in the calculation. If you are using a mixture of operations remember that certain operations take priority in a calculation. Consider the following, apparently, simple sum.    1 + 2 × 3 = ? What answer would you give? Did you give 7 as your response, or 9? The correct answer is 7 but can you explain why? If you have a calculator handy, check that it Learning outcomes After studying this course, 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 +, −, × and ÷, giving the answer to a specified accuracy (e.g. decimal places or significant figures) and checking the ans Acknowledgements The content acknowledged below is Proprietary (see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence Course image: Bill Bu 3.4 Modular multiplication In the last subsection we stated that, for any integer n ≥ 2, the set 3.3 Operations in modular arithmetic The Division Algorithm tells us that all the possible remainders on division by an integer n lie in the set We denote this set by 3.5 Scaling areas and volumes In OpenLearn course Diagrams, graphs and charts you saw how a scale is used on plans of houses and other structures. The scale makes it possible to take a length on the plan and calculate the correspond Try some yourself Which of these triangles are similar? 2.7 Rotational symmetry There is another kind of symmetry which is often used in designs. It can be seen, for instance, in a car wheel trim. Look at the trim on the left. It does not have line symmetry but 1.4 Parallel lines Two straight lines that do not intersect, no matter how far they are extended, are said to be parallel. Arrows are used to indicate parallel lines. Try some yourself Calculate all the angles at the centres of these objects. 4.2 A better solution Here is an improved solution which shows working. Suppose you plan to redecorate your bathroom. The end wall has the following shape, with dimensions as shown on the diagram. The quality of the plasterwork is not good and you are considering tiling the wall. 4.3 ‘Find’ questions Suppose you have decided to tile the wall using square tiles of side 10 cm. You are proposing to use the tiles across the full 5 metre width of the wall up to a height of 1.8 m. Find the number of boxes of tiles that you will require to cover the wall if the tiles a 4.3 Section summary The modulus function provides us with a measure of distance that turns the set of complex numbers into a metric space in much the same way as does the modulus function defined on R. From the point of view of analysis the importance of this is that we can talk of the closeness of two complex numbers. We can then define the limit of a sequence of complex numbers in a way which is almost identical to the definition of the limit of a real sequence. Another analogue of real analysis arises
Activity 2 Boxplots of family sizes
Activity 21
n satisfies the same rules for addition modulo n as the real numbers satisfy for ordinary addition. When it comes to multiplicat
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