Probability & Statistics Circle Graphs (Pie Charts)

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.

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.

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.

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)

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.

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

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:

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.

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

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.

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.

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!

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.

Circle Graphs T. Serino Using a Protractor

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

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.

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◦.

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.

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

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.

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.

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.

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

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.

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

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

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

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.

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.

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.

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.

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.

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

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.

athematical M D ecision aking