1. Probability & Statistics Circle Graphs (Pie Charts)

2. Circle Graphs
T. Serino
Circle graphs are used to represent a “part” to “whole” relationship for categorical data.
The full circle represents the whole and each sector represents the part corresponding to the categorical data.

3. Constructing Circle Graphs
T. Serino
Constructing Circle Graphs
Steps:
Is the data suitable?
Determine if there is a “whole” for the data.
Determine what the different parts of the whole are.

4. Circle Graphs
T. Serino
Calculate the fractions, decimals, and/or percent for each category
Divide (part ÷ whole) to create a fraction.
(You can choose to work with the fraction, or you can divide to change the fraction to a decimal. Once you have a decimal, you can also divide by 100 to change to a percent.)
In general, it is easiest to use fractions if you do not have a calculator and decimals if you do have a calculator.

5. Circle Graphs
T. Serino
Convert each fraction, decimal, or percent to an angle of the circle.
Without a calculator, multiply the fraction by 360 to find the central angle.
With a calculator, multiply the decimal by 360 to find the central angle.
(there are 360° in a circle and we are trying to find the fraction of the circle that represents each category)
(if you are using percent, it is best to change to a decimal first and then multiply by 360)

6. Circle Graphs Use a protractor to measure the angle
T. Serino
Use a protractor to measure the angle
for each sector as accurately as possible.
Start with a radius drawn anywhere.
Measure the angle of the first sector starting at the radius drawn.
All subsequent sectors should be drawn adjacent to the previous sector drawn.
The last sector should be measured to check for accuracy.

7. Circle Graphs Necessary Skills
T. Serino
Necessary Skills
Change numbers to fractions, decimals, and percent
Find the angle of a sector of a circle
Use a protractor to draw angles

8. Circle Graphs Changing data to fractions, decimals, and percent
T. Serino
Changing data to fractions, decimals, and percent
Brand Name
Number Sold
Fraction
Reduced Fraction
Decimal
Percent
Adidas
150
Nike
192
Reebok 60
Asics
108
Other 90
Sneakers sold for November 1997 at The Shoe Source
To create a fraction remember
There were 600 pairs of sneakers sold, so for Adidas:

9. Circle Graphs Changing data to fractions, decimals, and percents.
T. Serino
Changing data to fractions, decimals, and percents.
Brand Name
Number Sold
Fraction
Reduced Fraction
Decimal
Percent
Adidas
150
Nike
192
Reebok 60
Asics
108
Other 90
Sneakers sold for November 1997 at The Shoe Source
To reduce the fraction, divide the numerator and denominator by the same number.

10. Circle Graphs Changing data to fractions, decimals, and percents. or
T. Serino
Changing data to fractions, decimals, and percents.
Brand Name
Number Sold
Fraction
Reduced Fraction
Decimal
Percent
Adidas
150
Nike
192
Reebok 60
Asics
108
Other 90
Sneakers sold for November 1997 at The Shoe Source
To change to a decimal, simply use a calculator to divide or

11. Circle Graphs Changing data to fractions, decimals, and percents.
T. Serino
Changing data to fractions, decimals, and percents.
Brand Name
Number Sold
Fraction
Reduced Fraction
Decimal
Percent
Adidas
150
Nike
192
Reebok 60
Asics
108
Other 90
Sneakers sold for November 1997 at The Shoe Source
To change the decimal to a percent, move the decimal two places to the right.
Complete the rest of the table on your own.

12. Circle Graphs Next we need to change each fraction, decimal or percent
T. Serino
Next we need to change each
fraction, decimal or percent
to an angle.
Recall that a circle contains 360◦.
Each sector of the circle will represent a fraction of the whole circle.

13. Circle Graphs Fraction x 360◦ Decimal x 360◦
T. Serino
To find the angle of the sector representing Adidas, recall the following information.
Brand Name
Number Sold
Fraction
Reduced Fraction
Decimal
Percent
Adidas
150
By hand:
With a calculator:
By hand, it is usually easiest to multiply the
Fraction x 360◦
With a calculator, it is easiest to multiply the
Decimal x 360◦
90◦ is ¼ of the whole circle!

14. Circle Graphs Use the table to find the angles for each category
T. Serino
Use the table to find the angles for each category
Complete the last three on your own.

15. Circle Graphs
T. Serino
Using a Protractor

16. Circle Graphs Measuring an angle Vertex
T. Serino
Measuring an angle
Be sure when measuring an angle, that the vertex on the protractor is lined up with the vertex on the angle you are measuring.
Vertex

17. Circle Graphs Measuring an angle
T. Serino
Measuring an angle
Also, be sure that the initial edge is lined up with the horizontal line on the base of the protractor.
The initial edge of the angle always represents zero. Be sure to use the correct scale on the protractor.
Initial Edge
When the initial edge of the angle lies on the right side of the protractor, you use the inner scale of the protractor.

18. Circle Graphs Measuring an angle
T. Serino
Measuring an angle
The measure of the angle is determined by the terminal edge
Terminal Edge
This angle measures approximately 46◦.

19. Circle Graphs Measuring an angle
T. Serino
Measuring an angle
When the initial edge of the angle lies on the left side of the protractor, you use the outer scale of the protractor.
Initial Edge
Sometimes, the terminal edge is too short to get an accurate measure. If this happens, simply use a straight edge to extend the line.

20. Circle Graphs Measuring an angle
T. Serino
Measuring an angle
This angle measures approximately 115◦.

21. Measuring an angle Greater than 180o
Circle Graphs
T. Serino
Measuring an angle Greater than 180o
A protractor can only measure an angle up to 180o.
To measure an angle greater than 180o, first remember that the whole circle is 360o.

22. Measuring an angle Greater than 180o
Circle Graphs
T. Serino
Measuring an angle Greater than 180o
If we measure the smaller angle, we can subtract that measure from 360o to calculate the measure of the larger angle.

23. Measuring an angle Greater than 180o
Circle Graphs
T. Serino
Measuring an angle Greater than 180o
The smaller angle is approximately 110o.
250o
110o
Therefore, the larger angle that we were trying to measure is approximately, 250o.

24. Circle Graphs Drawing an angle
T. Serino
Drawing an angle
Start by drawing an initial edge and determining which side will be the vertex.
Line the protractor up on the initial edge
Draw a dot at the measure of the angle where the terminal edge will be
Use the straight edge of the protractor to connect the vertex to the dot

25. Circle Graphs Drawing an angle To draw a 60 degree angle:
T. Serino
Drawing an angle
To draw a 60 degree angle:
Start by drawing an initial edge and determining which side will be the vertex.

26. Circle Graphs Drawing an angle To draw a 60 degree angle:
T. Serino
Drawing an angle
To draw a 60 degree angle:
Line the protractor up on the initial edge

27. Circle Graphs Drawing an angle To draw a 60 degree angle:
T. Serino
Drawing an angle
To draw a 60 degree angle:
Draw a dot at the measure of the angle where the terminal edge will be

28. Circle Graphs Drawing an angle To draw a 60 degree angle:
T. Serino
Drawing an angle
To draw a 60 degree angle:
Use the straight edge of the protractor to connect the vertex to the dot

29. Circle Graphs Drawing the circle graph.
T. Serino
Drawing the circle graph.
Brand Name
Number Sold
Angle
Adidas
150
90o
Nike
192
115o
Reebok 60
36o
Asics
108
65o
Other 90
54o
Start by drawing a circle with a radius.

30. Circle Graphs Drawing the circle graph. Measure each angle. Brand Name
T. Serino
Drawing the circle graph.
Brand Name
Number Sold
Angle
Adidas
150
90o
Nike
192
115o
Reebok 60
36o
Asics
108
65o
Other 90
54o
Measure each angle.

31. Circle Graphs Drawing the circle graph. Measure each angle. Brand Name
T. Serino
Drawing the circle graph.
Brand Name
Number Sold
Angle
Adidas
150
90o
Nike
192
115o
Reebok 60
36o
Asics
108
65o
Other 90
54o
Measure each angle.

32. Circle Graphs Drawing the circle graph. Measure each angle. Brand Name
T. Serino
Drawing the circle graph.
Brand Name
Number Sold
Angle
Adidas
150
90o
Nike
192
115o
Reebok 60
36o
Asics
108
65o
Other 90
54o
Measure each angle.

33. Circle Graphs Drawing the circle graph. Measure each angle. Brand Name
T. Serino
Drawing the circle graph.
Brand Name
Number Sold
Angle
Adidas
150
90o
Nike
192
115o
Reebok 60
36o
Asics
108
65o
Other 90
54o
Measure each angle.

34. Circle Graphs Drawing the circle graph.
T. Serino
Drawing the circle graph.
Brand Name
Number Sold
Angle
Adidas
150
90o
Nike
192
115o
Reebok 60
36o
Asics
108
65o
Other 90
54o
Be sure to measure the last angle, just to check for accuracy

35. Circle Graphs Drawing the circle graph. Label each category.
T. Serino
Sneakers sold for November 1997 at The Shoe Source
Drawing the circle graph.
Brand Name
Number Sold
Angle
Adidas
150
90o
Nike
192
115o
Reebok 60
36o
Asics
108
65o
Other 90
54o
Adidas
150
Nike
192
Other 90
Reebok 60
Asics
108
Label each category.
Be sure to include the graph title.

36. athematical M D
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