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Solution. We need to choose a picture, say a small house, to represent a certain number of house sales. One house picture could represent 10 sales or perhaps 5 sales,
332 PIE GRAPH
depending on how much space we wish to use for the graph. Suppose we use one house for 10 sales. We divide by 10 the number of houses sold by each person to obtain the number of pictures for each salesperson. Tom has 3 house pictures, Pat has 5.5, David has 4, and Joanne has 3.8 (see figure). A house picture can be cut in half to represent 0.5 for Pat, but it is difficult to draw 0.8 of a house picture for Joanne, and this is one of the drawbacks of this type of graph. The graph must have a title and a key.
Annual House Sales for “We Sell”
□ □ n □ □ n □ □ n Key:
□ □ n □ □ n □ □ n □ □ □□ ID JL JL Ü
= 10 house sales
„ □□ □□ □□ □□
David _Q_ JL JL JL
The pictogram has good visual impact, and at a glance it is possible to compare the size of one item of data with another, but it is not always clear what the actual size of each item of data is. The key is helpful for this.
References: Bar Graph, Discrete Data, Statistics.
A pie graph, or pie chart, is one of the statistical graphs used for displaying discrete data. A pie graph does not have axes like a bar graph. It is a circular diagram, and the circle is divided up into sectors. Each item of data is represented by a sector of the circle, whereas in the bar graph a column represents each item of data. The frequency of an item of data is proportional to the angle in the sector that represents it. The frequency is also proportional to the area of the sector. In the bar graph the height of the column is proportional to the frequency. When constructing a pie graph we make use of the fact that in a full turn there are 360°.
Example 1. Helen earns $600 per week and the table shows her weekly budget. Draw a pie graph of her weekly budget.
PIE GRAPH 333
Solution. There are 360° in a full circle, so we divide 360° by the total expenses of $600:
This tells us that in the pie graph each dollar is represented by an angle of 0.6°. We now add three extra columns to the table to find the total angle for each item of expenditure and to find the % each item is of the whole budget. For example, food is
x 100 = 33% of the weekly budget to the nearest whole number
Food $200 x 0.6° = 120° 33%
Phone $30 x 0.6° = 18° 5%
Rent $120 x 0.6° = 72° 20%
Clothes $80 x 0.6° = 48° 13%
Utilities $120 x 0.6° = 72° 20%
Other $50 x 0.6° = 30° 8%
Total $600 x 0.6° = 360° 99%
The total in the % column should be 100%, but there is a slight discrepancy due to rounding to the nearest whole number. The next stage is to draw a circle. It should be large enough to contain all the information and small enough to easily fit on the page. The angles representing the expenses are measured around the circle with a protractor, starting from a vertical radius at the top of the circle (see figure a). Each sector is labeled with the appropriate expense, or may be color-coded with a key at the side. It is often a good idea to include the percentage for each item of expenses. The pie graph needs a title, like all statistical graphs.
Pie Graph of Helen’s Weekly Budget
Example 2. The pie graph in figure b shows how William spends his day (HW= homework). Answer the following questions.
(a) How many hours did William spend at school?
(b) What percentage of his day did he spend on school activities?
Solution. There are 12 equally spaced marks around the circle. Each mark must represent 2 hours, since there are 24 hours in a day.
(a) William spent 3 markings at school, which is 6 hours. William spent 6 hours at school.
(b) In addition to 6 hours at school he spent 1 marking, or 2 hours, on homework (HW), which is a total of 8 hours on school activities. The fraction of his day spent on school activities is 8/24. To change a fraction into a % we multiply the fraction by 100:
£ x 100 = 33 to the nearest whole number
William spent 33% of his day on school activities.
A pie graph is mainly used for comparing data and at a glance it is possible to compare the size of one item of data with the others. The drawback is that we do not know the actual size of each item of data as we do in the bar graph. If there are too many categories, the pie graph loses its visual impact, is difficult to label, and may appear quite crowded.
References: Bar Graph, Discrete Data, Frequency, Percentage, Protractor, Rounding, Sector of a Circle, Statistics.
Reference: Imperial System of Units.
A placeholder is a zero that is inserted in a number to maintain the value of the number when we are rounding.
Example. The number of spectators at the annual soccer match between Rovers and Wanderers was 54,687. Round this off to three significant figures.