Statistics Section 10.1 Book Unit 6.1 Relative Frequency Graphs Essential Question : What is a relative frequency?
Relative Frequency graphs summarize data in categories, but instead of including the actual number for each category, they compare the number in that category to the total for all categories. Relative frequency graphs can be bar graphs or circle graphs, and they show fractions or percents, not values.
In this lesson you will see how to make relative frequency circle graphs and relative frequency bar graphs. Complete the investigation on page 550.
ContinentLand area (thousands of km 2 ) Australia7 Europe9 Antarctica14 South America18 North America24 Africa30 Asia45 Total147
Now, we will convert the data into a circle graph. We need to determine the angle measure for each section of the graph. To do this, use the fact that there are 360 degrees in a circle. For example, to find the number of degrees in the section representing Australia, solve this proportion:
Land area of Australia Angle measure for Australia section Total land area Total degrees in a circle 147x = 2520 x ≈ 17
ContinentAngle Measure Australia17º Europe 22º
ContinentAngle Measure Australia17º Europe22º Antarctica 34º
ContinentAngle Measure Australia17º Europe22º Antarctica34º South America 44º
ContinentAngle Measure Australia17º Europe22º Antarctica34º South America44º North America 59º
ContinentAngle Measure Australia17º Europe22º Antarctica34º South America44º North America59º Africa 74º
ContinentAngle Measure Australia17º Europe22º Antarctica34º South America44º North America59º Africa74º Asia 110º 360ºTotal
Label the circle graph on the bottom left of your notes handout with frequencies. You can find these counts in the first table you completed.
To find the percent of the total area Australia contains, solve the proportion: 147p = 700 p ≈ 5 Set up a proportion and solve to find the percentages for each continent. (Be sure all percentages add to 100%.)
Europe:Antarctica:
South America:North America:
Africa:Asia:
Label the relative frequency circle graph on the bottom right of your notes handout with the values you just found.
5% 6% 10% 12% 16% 20% 31%
In both circle graphs the relative size of each section indicates the portion of the total area that the continent contains. A relative frequency bar graph for this data shows percents of the total land area rather than the land area itself.
Australia Europe Antarctica South America North America Africa Asia
Notice that like box plots, relative frequency plots do not show actual data values. For example, both of the relative frequency graphs show that Asia makes up 31% of the total land area of the continents, but neither graph indicates what the land area of Asia is.
Example A: The table shows the number of students enrolled in each grade at RHHS. 9 th grade 10 th grade 11 th grade 12 th grade Percentages Angle Measure a) How many students are enrolled in RHHS? 1430 students
b) Set up a proportion to find what percent of the school is represented in each grade. Ninth GradeTenth Grade
b) Set up a proportion to find what percent of the school is represented in each grade. Eleventh Grade Twelfth Grade
9 th grade 10 th grade 11 th grade 12 th grade Percentages28% 23%21% Angle Measure
c) Now, create a frequency circle graph. First, compute the angle measure for each section of the graph. Set up a proportion to find these values. Ninth Grade Tenth Grade
c) Now, create a frequency circle graph. First, compute the angle measure for each section of the graph. Set up a proportion to find these values. Eleventh Grade Twelfth Grade
9 th grade 10 th grade 11 th grade 12 th grade Percentages28% 23%21% Angle Measure102º100º83º75º
Create the circle graph of RHHS enrollment using a protractor and the angle measures just computed. Label each sector and include the percentage for the sector.
RHHS Enrollment th grade 10 th grade 12 th grade 28% 21% 11 th grade 23%
RHHS Enrollment GRADELEVELSGRADELEVELS 9 th Grade 10 th Grade 11 th Grade 12 th Grade Create a relative frequency bar graph of enrollment at RHHS.