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									    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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