1. Graphing - Dr. Castro's Science Website

Name _______________________________________________________

Date _______________________

Class ________________________

TEACHING RESOURCES

BASIC SKILLS

1. Graphing

Graphs are used to show numerical information in a useful format. Graphs help

us understand and interpret data. They can be powerful tools for examining

cycles and trends. The three main types of graphs are circle graphs, line graphs,

and bar graphs.

Circle Graphs

A circle graph, sometimes called a pie chart, shows different parts of the data in

relation to all of the data. Each part of the circle represents a different part of the

data. The entire circle represents all of the data. For example, a biologist studying

a plot of land in a hardwood forest in Wisconsin found that there were five different types of trees in the plot. The data table below summarizes the biologist¡¯s

findings.

Wisconsin Hardwood Trees

Type of tree

Number found

Percentage of total

(rounded to nearest whole-number percent)

Oak

Maple

Beech

Birch

Hickory

539

758

319

1,327

222

17

24

10

42

7

Total

3,165

100

In order to understand the data, the biologist reorganized the chart to show the

number of trees in descending order.

Wisconsin Hardwood Trees

? by Holt, Rinehart and Winston, Inc.

Type of tree

Number found

Percentage of total

(rounded to nearest whole-number percent)

Birch

Maple

Oak

Beech

Hickory

1,327

758

539

319

222

42

24

17

10

7

Total

3,165

100

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Graphing

To aid in the interpretation of the data and to compare it with other sets of data,

the biologist constructed a circle graph of the data.

Figure 1

Percentage of

Wisconsin

Hardwood Trees

A Community of Wisconsin Hardwood Trees

Beech

319

Oak 539

Birch 42%

Hickory

222

Maple 24%

Oak 17%

Maple 758

Birch 1,327

Beech 10%

Hickory 7%

The following are important characteristics of a circle graph:

1. The pie sections are accurately calculated and drawn.

2. The sections are clearly labeled.

3. Labels, colors, or shading are used to represent each section of the circle.

4. The graph is easy to understand and interpret.

Practice Exercise 1

? by Holt, Rinehart and Winston, Inc.

1. For what kind of data is a circle graph more appropriate than a bar graph?

2

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Name ___________________________________________

Graphing

Date ________________ Class ____________________

2. The population of 100 large African animals in a zoo are listed in the chart

below. Construct a circle graph that indicates the percentage each animal is of

the total population.

Number of Animals

Animal

Baboon

25

African elephant

35

Leopard

12

Tiger

16

Giraffe

12

Line Graphs

While circle graphs are useful for depicting percentages, line graphs are most

often used to demonstrate continuous change. Examine the following data.

Population of the United States 1880¨C1990

Year

Population

Year

? by Holt, Rinehart and Winston, Inc.

(in millions)

Population

(in millions)

1881

50.2

1940

131.7

1890

62.9

1950

151.3

1900

76

1960

179.2

1910

92

1970

203.2

1920

105.7

1980

226.5

1930

122.8

1990

251.4

In the example given above, both the year and the population are variables. The

variable to which values are assigned, in this case the year, is called the independent variable. The population is determined by the year. The population is called

the dependent variable. Each set of values, the independent and dependent variables, is called a data pair.

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Graphing

Another way to think about independent and dependent variables is to think

about the amount of sleep that you get. You know that how alert or tired you

feel often depends on the number of hours of sleep that you had the night

before. The amount of sleep is the independent variable; your alertness is the

dependent variable. Throughout your year of studying biology you will see

many examples of dependent and independent variables.

Population of the United States, 1880 ¨C1990

Figure 2

Population (in millions)

300

250

200

150

100

50

0

1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020

To prepare a line graph, data pairs must first be organized in a chart. The following are important characteristics of a line graph.

1. The independent variable is put on the horizontal (x) axis.

2. The dependent variable is put on the vertical (y) axis.

3. The axes are labeled.

4. An appropriate scale and interval are used on each axis. The same scale and

interval must be used for the total length of the axis. If, for example, 1 cm

represents an interval of 10 years, 30 years must be represented by 3 cm.

5. Reasonable starting points are used for each axis. Examine the population

graph. The horizontal (x) axis goes from 1880 to 2020 and the vertical (y)

axis goes from 0 to 300 million.

6. The data pairs are plotted as accurately as possible.

7. The title of the graph accurately reflects the data presented.

8. If more than one set of data is presented on a graph, a key must accompany

the graph. For example, if the populations of Canada, Mexico, and the United

States from 1880 to 1990 were presented on the same graph, it would be

important to use a different color or type of line (solid, dotted, dashes, etc.)

for each country. The key indicates what each color or type of line represents.

9. The graph is easy to understand and interpret.

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Year

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Graphing

continued

Name ___________________________________________

Date ________________ Class ____________________

Using Graphs to Make Predictions

Graphs show trends in data that may not be obvious from a chart of numbers.

Examine the graph of the population of the United States from 1880 to 1990.

Do you notice any trends? Do you think you can predict the population of the

United States in the year 2000? The process of going beyond the data points in a

graph is called extrapolation. The further we extrapolate, the less certain we can

be of our predictions.

We can also use graphs to find data points between two sets of plotted data

pairs. For example, we can read the graph to determine that the population of

the United States in 1905 was approximately 84 million people. Determining

data points between two sets of data pairs is called interpolating.

Practice Exercise 2

1. Predict what the population of the United States will be in the year 2010.

2. Can you be as certain for this prediction as you were for your prediction of

the population in the year 2000?

? by Holt, Rinehart and Winston, Inc.

3. Use the graph to determine the approximate population of the United States

in 1935, 1945, and 1985.

4. What was the approximate population of the United States in 1870?

5. What will be the approximate population of the United States in 2020?

6. How certain are you of your answer? Why?

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