
Comparing Graphs 

Unit 11 > Lesson 7 of 10 
In this unit, we learned about line, bar and circle graphs. We learned how to
read and interpret information from each type of graph, and how to construct
these graphs. If you were asked to create a graph from a given set of data, how
would you know which type of graph to use? Which graph we choose depends on the
type of data given and what we are asked to convey to the reader. The
information below will help you determine which type of graph to use.

Tables are used to organize exact amounts of data and to display
numerical information. Tables do not show visual comparisons. As a result,
tables take longer to read and understand. It is more difficult
to examine overall trends and make comparisons with tables, than it is with graphs. 

Line graphs are used to display data or information that changes
continuously over time. Line graphs allow us to see overall trends such as
an increase or decrease in data over time. 

Bar graphs are used to compare facts. The bars
provide a visual display for comparing quantities in different categories
or groups.
Bar graphs help us to see relationships quickly. However, bar graphs can be
difficult to read accurately. A change in the scale in a bar graph may alter one's visual
perception of the data. 

Circle Graphs are used to compare the parts of a whole. Circle
graphs represent data visually in the same proportion as the numerical
data in a table: The area of each sector in a circle graph is in the same
proportion to the whole circle as each item is to the total value in the
table. Constructing an accurate circle graph is difficult to do without a
computer. This is because you must first find each part of the whole
through several elaborate calculations and then use a protractor to draw
each angle. This leaves a lot of room for human error. Circle graphs are
best used for displaying data when there are no more than five or six sectors,
and when the values of each sector are different. Otherwise they can be
difficult to read and understand. 
Problem 1:

The table below shows the number of sneakers sold by brand for this
month. Construct a graph which best demonstrates the sales of each
brand.



Sneakers Sold This Month 
Brand 
Number Sold 
Adidas 
25 
New Balance 
18 
Nike 
32 
Reebok 
15 
Other 
10 


Analysis:

The numerical data in this table is not changing over time. So a line
graph would not be appropriate for summarizing the given data. Let's draw
a circle graph and a bar graph, and then compare them to see which one makes sense for this data.
Before we can draw a circle graph, we need to do some calculations. We must also
order the data from greatest to least so that the
sectors of the circle graph are drawn from largest to smallest, in a clockwise direction.



Sneakers Sold This Month 
Brand 
Number Sold 
Percent 
Decimal 
Angle Measure 
Nike 
32 
32 
0.32 
0.32 x 360° = 115.2° 
Adidas 
25 
25 
0.25 
0.25 x 360° = 90° 
New Balance 
18 
18 
0.18 
0.18 x 360° = 64.8° 
Reebok 
15 
15 
0.15 
0.15 x 360° = 54° 
Other 
10 
10 
0.10 
0.10 x 360° = 36° 
Total 
100 
100% 
1.00 = 1 
360° 











Circle graphs are best used to compare the parts of a whole. 



Bar graphs are used to compare facts. 
The circle graph above shows the entire amount sold. It also
shows each brand's sales as part of that whole. 



The bar graph stresses the individual sales of each brand
as compared to the others. 
The circle graph uses the total of all items in the table. 



The bar graph does not use the total of all items in the
table. 
Each sector of the circle graph is in the same
proportion to the whole circle as the number of sales for that industry is to
the entire amount of sales from the table. 



The bar graph simply gives a visual listing of the information in the
table. 
To construct an accurate circle graph, you must first order the data in the table from greatest to least. You also need to find each part of the whole
through several elaborate calculations and then use a protractor to draw
each angle. 



The number of sneakers sold for each item in the table matches
the value of each bar in the bar graph. This makes the bar graph a more direct
and accurate way of representing the data in the table. 
If we were asked to show that the Nike brand dominates the sneaker
industry, then the circle graph would be a better choice for summarizing this data. 



We were asked to construct a graph which best demonstrates the sales of each
brand. 
Solution: 
Each graph above
has its own strengths and limitations. However, the bar graph is the best choice for
summarizing this data based on what we were asked to convey to the reader. 
Problem 2:

The table below shows the humidity level, recorded in Small Town, NY for
seven days. Construct a graph which best demonstrates the humidity level for each
day.



Humidity Levels in Small Town,
NY 
Day 
Humidity Level (%) 
1 
51 
2 
59 
3 
65 
4 
68 
5 
70 
6 
67 
7 
72 


Analysis:

The humidity level is given as a percent. At first glance, this might lead one to think
that a circle graph should be used to summarize this data. However, the data in the table does not indicate any parts in
relation to a whole. Thus, a circle graph is not the right choice. The data in this table is changing
over time. So a line
graph would be the appropriate choice for summarizing the given data.


Solution:


Problem 3:

The table below shows the composition of Earth's atmosphere. Construct a graph which best
represents the composition of the Earth's Atmosphere.



Composition of Earth's Atmosphere 
Gas 
Percent 
Nitrogen 
77 
Oxygen 
21 
Other 
2 


Analysis:

The word composition indicates that we are looking at the parts of a
whole. The Earth's Atmosphere is the whole (100%) and each gas is a part
of that whole. Accordingly, a circle graph is the best choice for
summarizing this data.


Solution:


Problem 4:

The table below shows the surface area of each continent in square
kilometers. Construct a graph which best
represents this data.



Surface Area of Continents 
Continent 
Surface Area (km^{2}) 
Africa 
15,000,000 
Antarctica 
14,200,000 
Asia 
44,936,000 
Australia 
7,614,500 
Europe 
10,525,000 
North America 
23,500,000 
South America 
17,819,100 


Analysis:

The numerical data in this table is not changing over time. So a line
graph would not be appropriate choice for summarizing the given data. Let's draw
a circle graph and a bar graph and compare them to see which one makes sense for this data.
Before we can draw a circle graph, we need to do some calculations. We must also
order the data from greatest to least so that the
sectors of the circle graph are drawn from largest to smallest in a clockwise direction.



Surface Area of Continents 
Continent 
Surface Area (km^{2}) 
Percent 
Decimal 
Angle Measure 
Asia 
44,936,000 
33.64 
.3364 
.3364 x 360° = 121.104° 
North America 
23,500,000 
17.59 
.1759 
.1759 x 360° = 63.324° 
South America 
17,819,100 
13.33 
.1333 
.1333 x 360° = 47.988° 
Africa 
15,000,000 
11.23 
.1133 
.1133 x 360° = 40.788° 
Antarctica 
14,200,000 
10.63 
.1063 
.1063 x 360° = 38.268° 
Europe 
10,525,000 
7.88 
.0788 
.0788 x 360° = 28.358° 
Australia 
7,614,500 
5.70 
.0570 
.0570 x 360° = 20.52° 
Total 
133,594,600 
100.00 
1.00 = 1 
360° 











Do Africa and Antarctica really have the same surface area?
The tool we used to create this circle graph rounded each value to
the nearest whole percent. As a result, the circle graph shows that Africa and Antarctica
both have a surface area of 11%; whereas the table shows numbers for these
continents that are similar, but not the same. 



The bar graph shows the surface area in millions of square
kilometers. This was necessary in order to create a bar graph that is not
confusing because of too many gridlines. The bar graph shows a surface area of
15.00 million sq. km for Africa and
a surface area of 14.20 million sq km. for Antarctica. 
Circle graphs are used to compare the parts of a whole.
However, they are best used when there are no more
than five or six sectors and when the values of each section are different. 



Bar graphs are used to compare facts. The bar graph stresses the individual
items listed in the table as compared to the others. The bar graph does not
show the total of all items in the
table. 
The circle graph above has several sectors with similar sizes. It
also has seven sectors. This makes it a bit difficult to compare the
parts and to read the graph. However, the world has seven continents, so it
does make sense to use a circle graph to compare the parts
(continents) with the whole (world). 



The bar graph above allows us to compare the surface area
of each continent. However, it does not allow us to compare the parts to the whole. So
we cannot see the relationship between the surface area of each continent
and the surface area of all seven continents. 
Solution: 
It is difficult to determine
which type of graph is appropriate for the given data in this
problem. Each graph above
has its own strengths and limitations. You must choose one of these
solutions based on your own judgment. 
Summary:

Graphs help us examine trends and make comparisons by visually displaying data.
Before we can graph a given set of data from a table, we must first determine
which type of graph is appropriate for summarizing that data. There are
several types of graphs, each with its own purpose, and its own
strengths and limitations. Which one we choose depends on the type of data
given, and what we are asked to convey to the reader.

Exercises
Directions: Enter one of the following answers for each exercise below:
line, bar or circle. For each exercise below, click once in the ANSWER BOX,
type in your answer and then click ENTER. Your answer should
be given as a word or as a whole number. After you click ENTER, a message will
appear in the RESULTS BOX to indicate whether your answer is correct or
incorrect. To start over, click CLEAR.

1.

The ages of 7 trumpet players in a band are 13, 12, 11, 12, 11,
10 and 12. What type of graph would be appropriate for comparing the
ages of these trumpet players?

2.

The federal hourly minimum wage was recorded each year from 1990
to 2007. What type of graph would best show the changes in minimum wage
during this time period?

3.

When asked if "antidisestablishmentarianism" has 28
letters, 50 people said yes, 35 people said no and 15
people said I don't know. What type of graph would best compare
these responses to each other and with the total?

4.

The growth of 7 different plants was recorded in centimeters. What type of graph would
be best for comparing the growth of each plant?

5.

In a city, the rainfall was recorded in inches each month for 12
months. What type of graph would best display the change in rainfall?

This lesson is by Gisele Glosser. You can find me on Google.
