The Caribbean islands have many different species of birds.
To determine
if there is a relationship between area and number of bird species, we can graph
the data points in a scatter
plot. In a scatter plot, two sets of data are plotted as ordered
pairs in the coordinate plane.
For example,
the point with the box around it is at (95, 236). The area is
the independent quantity, and the number of species is the dependent quantity.
You can use
the scatter plot to draw conclusions and make predictions about the data.
Often, when
data are displayed in a scatter plot, you can determine whether there is a
pattern, trend, or relationship between the variables.
·
Data
points that appear to go uphill show a relationship that is positive.
·
Data
points that appear to go downhill show a relationship that is
negative.
In the
opening application, suppose a line were drawn close to most of the data points.
The line would have a negative slope. That is, as the area increases, the number
of species decreases. Thus, area and number of species would have a negative relationship.
Example
School Link
1.
The
scatter plot at the right shows the word processing speeds of 12 students and
the number of weeks they have studied word processing. Determine whether the scatter
plot shows a positive relationship, negative relationship, or no
relationship. If there is a relationship, describe it.
Alternative Solutions:
The plot indicates that
as the number of weeks of experience increases, the word processing speed
increases. Thus, there is a positive relationship between experience and word
processing speed.
Example
School Link
2.
The
table shows the amount of time students in math class spent studying and the scores
they received on the test.
Alternative Solutions:
A.
Make a scatter plot of the data.
Let the horizontal axis represent
study time, and let the vertical axis represent test scores. Then plot the
data.
B.
Does the scatter plot show a relationship between study time and test
scores? Explain.
In general, the scatter
plot seems to show that a higher grade is directly related to the amount of time
spent studying. There is a positive relationship.
C.
Describe the independent and dependent variables. Then state the domain
and the range.
Because test scores
depend on the amount of study time, test scores is the dependent variable, and
study time is the independent variable. The domain is the set of all study
times and the range is the set of all test scores.
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