statistics section 10.1 book unit 6.1 relative frequency graphs essential question : what is a...
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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 relativefrequency bar graphs.
Complete the investigation on page 550.
Continent Land area
(thousands of km2)
Australia 7
Europe 9
Antarctica 14
South America 18
North America 24
Africa 30
Asia 45
Total 147
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 thesection representing Australia, solve this proportion:
360147
7 x
360147
7 x
Land area of AustraliaAngle measure for Australia section
Total land area Total degrees in a circle
147x = 2520 x ≈ 17
Continent Angle Measure
Australia 17º
Europe
04.22
3240147360147
9
x
x
x
22º
Continent Angle Measure
Australia 17º
Europe 22º
Antarctica
29.34
5040147360147
14
x
x
x
34º
Continent Angle Measure
Australia 17º
Europe 22º
Antarctica 34º
South America
08.44
6480147360147
18
x
x
x
44º
Continent Angle Measure
Australia 17º
Europe 22º
Antarctica 34º
South America 44º
North America
77.58
8640147360147
24
x
x
x
59º
Continent Angle Measure
Australia 17º
Europe 22º
Antarctica 34º
South America 44º
North America 59º
Africa
47.73
10800147360147
30
x
x
x
74º
Continent Angle Measure
Australia 17º
Europe 22º
Antarctica 34º
South America 44º
North America 59º
Africa 74º
Asia
21.110
16200147360147
45
x
x
x
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.
79
141824
3045
To find the percent of the total area Australia contains, solve the proportion:
100147
7 p
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:
12.6
900147100147
7
p
p
p
52.9
1400147100147
14
p
p
p
South America: North America:
24.12
1800147100147
18
p
p
p
33.16
2400147100147
24
p
p
p
Africa: Asia:
41.20
3000147100147
30
p
p
p
61.30
4500147100147
45
p
p
p
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 areathat the continent contains.
A relative frequency bar graph for this data showspercents 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 plotsdo 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.
9th grade
10th grade
11th grade
12th grade
407 396 328 299
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 Grade Tenth Grade
46.28
4070014301001430
407
x
x
x
69.27
3960014301001430
396
x
x
x
b) Set up a proportion to find what percent of the school is represented in each grade.
Eleventh Grade Twelfth Grade
94.22
3280014301001430
328
x
x
x
91.20
2990014301001430
299
x
x
x
9th grade
10th grade
11th grade
12th grade
407 396 328 299
Percentages 28% 28% 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
102
14652014303601430
407
x
x
x
69.99
14256014303601430
396
x
x
x
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
57.82
11808014303601430
328
x
x
x
27.75
10764014303601430
299
x
x
x
9th grade
10th grade
11th grade
12th grade
407 396 328 299
Percentages 28% 28% 23% 21%
Angle Measure 102º 100º 83º 75º
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 2008-2009
9th grade10th grade
12th grade
28%28%
21%
11th grade
23%
RHHS Enrollment 2008-2009
GRADE
LEVELS
9th Grade
10th Grade
11th Grade
12th Grade
Create a relative frequency bar graph of enrollment at RHHS.