7.1. Line Graphs http://www.ck12.org
for different elements, or members, of the population, whether it is the entire population or a sample. The value of
the variable is referred to as an observation, or a measurement. A collection of these observations of the variable is
adata set.
Variables can be quantitative or qualitative. Aquantitative variableis one that can be measured numerically. Some
examples of a quantitative variable are wages, prices, weights, numbers of vehicles, and numbers of goals. All of
these examples can be expressed numerically. A quantitative variable can be classified as discrete or continuous.
Adiscrete variableis one whose values are all countable and does not include any values between 2 consecutive
values of a data set. An example of a discrete variable is the number of goals scored by a team during a hockey game.
Acontinuous variableis one that can assume any countable value, as well as all the values between 2 consecutive
numbers of a data set. An example of a continuous variable is the number of gallons of gasoline used during a trip
to the beach.
Aqualitative variableis one that cannot be measured numerically but can be placed in a category. Some examples
of a qualitative variable are months of the year, hair color, color of cars, a person’s status, and favorite vacation spots.
The following flow chart should help you to better understand the above terms.
Variables can also be classified as dependent or independent. When there is a linear relationship between 2 variables,
the values of one variable depend upon the values of the other variable. In a linear relation, the values ofydepend
upon the values ofx. Therefore, thedependent variableis represented by the values that are plotted on they-axis,
and theindependent variableis represented by the values that are plotted on thex-axis.
Linear graphs are important in statistics when several data sets are used to represent information about a single topic.
An example would be data sets that represent different plans available for cell phone users. These data sets can be
plotted on the same grid. The resulting graph will show intersection points for the plans. These intersection points
indicate a coordinate where 2 plans are equal. An observer can easily interpret the graph to decide which plan is
best, and when. If the observer is trying to choose a plan to use, the choice can be made easier by seeing a graphical
representation of the data.
Example A
Select the best descriptions for the following variables and indicate your selections by marking an ’x’ in the appro-
priate boxes.