GCSE Modular Mathematics Key Skills Application of Number GCSE Mathematics Statistics and Handling Data Unit 13 Pie Charts And Comparative Pie Charts Objectives On completion of this unit you should be able to: 1. Draw pie charts (revision) 2. Draw pie charts to compare different total components Statistics and Data Handling Unit 13 Pie Charts and Comparative Pie Charts Pie Charts A pie chart is a circular diagram that is divided into sectors (slices) whose angles (or areas) represent each part of the whole data. Advantages. When completed it is easy to compare the sizes of each part to each other and also each part in relation to the whole data. Disadvantages. Sometimes difficult calculations are required to find the angles. Care is needed when using a protractor to draw the angles. Always check that the calculated angles add up to 3600 before you begin to draw the pie chart. Calculating the angles Bill is a car salesman. He recorded the number of cars of each make that he sold in April. Make Frequency Ford 22 Skoda 3 Vauxhall 14 Rover 11 Mercedes 10 1. Find the total number of cars sold. Here the total is 60 cars. 2. Work out the angle that represents each make of car, eg Ford is 22 out of 60 Skoda is 3 out of 60 Vauxhall is 14 out of 60 22 0 3 0 14 x 360 = 840 60 x 360 = 132 60 x 360 = 18 60 Rover is 11 out of 60 Mercedes is 10 out of 60 11 10 x 360 = 660 x 360 = 600 60 60 Check 132 + 18 + 84 + 66 + 60 = 360. You can now draw these angles on your circle to represent the data. Remember to label each sector with the name it represents. Note: If your calculated angle is a decimal, for example 65.70, round it off to the nearest degree, 660 Statistics and Data Handling Unit 13 Pie Charts and Comparative Pie Charts Comparative Pie charts. To compare the different totals of two sets of data the areas of each circle must be proportional to the total it represents. If we let R and r be the radii of the two pie charts then area of larger circle = πR2 and for the smaller one area = πr2. Example 1 This table shows the number of students studying Science subjects Subject AS A2 Biology 28 50 Chemistry 16 37 Physics 20 34 Total 64 121 If r and R are the radii of AS and A2 we need this ratio: πr2 : πR2 = 64 : 121 so r2 : R2 = 64 : 121 and r : R = √64 : √121 so r = 8 and R = 11 If we decided to work in centimetres we would have two quite large circles. When using this method in Key Skills or GCSE coursework we need to be able to have some control over the size of our circles. Statistics and Data Handling Unit 13 Pie Charts and Comparative Pie Charts Example 2. Let us draw the circle for AS with a radius of 3 cm. How do we calculate the radius for A2? From example 1, r : R = √64 : √121, and we want r = 3 So 3 : R = √64 : √121 R = √121 3 √64 R = 3 √121 √64 so R = 3 x 11 = 33 8 8 = 4.125 cm (4.1 correct to 1 decimal place or to the nearest millimetre) Angles are calculated and drawn as normal.
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