Proportional Pie Charts agricultural.pptx

Proportional pie chart

1. Proportional Pie Charts

2. Proportional or Comparative Pie Charts Pie charts are a good way of comparing data as it easy to see the proportions of the pie that each sector represents . In GCSE Statistics we will also look at comparative or proportional pie charts, where the area of the pie chart is proportional to the frequency.

3. Calculating angles To calculate the angles in a pie chart you use the formula: Example 1: The number of visitors to the following Northern Ireland Tourist attractions on a day in May 2018 is given in the table below: Calculate the angle for each attraction and complete the pie chart.   Attraction Titanic Belfast Ulster Museum W5 Belfast Zoo No. of visitors 2250 1350 850 550

4. Solution 1: First work out the total number of visitors: 2250 + 1350 + 850 + 550 = 5000 Using the formula: Titanic = Ulster Museum =   W5 = Belfast Zoo = = Always check that the total angles add up to 360 before you start to draw the pie chart.   Attraction Titanic Belfast Ulster Museum W5 Belfast Zoo Total No. of visitors 2250 1350 850 550 5000 Angle 162 97.2 61.2 39.6 360

5. Drawing the Pie Chart You may be asked to complete a pie chart on a given template once you have calculated the angles. Using a protractor measure each angle in a clockwise direction starting from the line given. Remember to label each sector of the pie chart with the correct label.

6. Comparative Pie Charts In a comparative pie chart the area is proportional to the number of people / frequency. The bigger the radius of the pie chart, the more people the pie chart will represent. This gives a good visual comparison of the two sets of data. Example 2 The pie chart representing the number of visitors in May at the NI tourist attractions has a radius of 2.5cm. On a day in July there are 7500 visitors in total at the attractions . What radius would the pie chart representing the visitors on the day in July have?

7. Solution 2 To work out the missing radius we set up an equation where we can divide the areas on one side and the frequencies on the other. The ration between the areas must be the same as the ratio between the frequencies. The information we have is: May: Radius = 2.5 Area = Frequency = 5000 July: Radius = r Area = Frequency = 7500 The equation is: We can then cancel out and rearrange to give: The radius for the July pie chart would be 3.1cm.  

8. Example 3 Two pie charts are drawn to represent the number adult and child tickets sold at NI tourist attractions on a day in 2018. The pie chart for adult tickets has a radius of 7cm and represents 4900 tickets. How many child tickets are represented by a pie chart with a radius of 4cm? Solution 3 The information we have is: Adults: Radius = 7cm Area = Frequency = 4900 Child: Radius = 4cm Area = Frequency = f The equation is: We can then cancel out and rearrange to give: = 1600  

9. Making Comparisons If you are asked to make comparisons for proportional pie charts make sure to talk about the proportion. For example you could make the mistake of saying that more people visited W5 in the day in May than in July as it is a bigger proportion of the pie chart. However as the July pie c hart represents more people this would not be correct. Some comparative statements you could make would be: A larger proportion of the visitors in May went to the Ulster Museum. A greater number of people visited the tourist attractions on the day in June.