2.3 cont. - Additional Graphs for Quantitative Data
A split stem-and-leaf plot is when we use two or more rows for each stem. This can be an
advantage if some stems have a big number of leaves.
ex.
When two data sets have values similar enough so that the same stems can be used, their shapes
can be compared with a back-to-back stem-and-leaf plot.
In a back-to-back stem-and-leaf plot, the stems go down the middle. The leaves for one of the
data sets go off to the right, and the leaves for the other go off to the left.
Consider the following course averages
from an English class and a History class.
The classes can be compared with a
back-to-back stem-and-leaf plot.
What can you conclude about the averages of
these two classes?
A time-series plot may be used when the data consist of values of a variable measured at
different points in time.
In a time-series plot, the horizontal axis represents time, and the vertical axis represents the value
of the variable we are measuring. The values of the variable are plotted at each of the times, then
the points are connected with straight lines.
2.4 - Graphs Can Be Misleading
Statistical graphs, when properly used, are powerful forms of communication. Unfortunately,
when graphs are improperly used, they can misrepresent the data, and lead people to draw
incorrect conclusions.
Below are two common forms of misrepresentation:
Incorrect position of the vertical scale
Incorrect sizing of graphical images
Incorrect Position of the Vertical Scale
With charts or plots that represent how much or how many of something, it may be misleading
if the baseline is not at zero.
The Area Principle
When amounts are compared by constructing an image for each amount, the areas of the images
must be proportional to the amounts. For example, if one amount is twice as much as another,
its image should have twice as much area as the other image. When the Area Principle is
violated, the images give a misleading impression of the data.
Which of the images below best represent the difference
of Jet Fuel cost?
Year
Cost of Jet Fuel per Gallon
2000
$0.90
2008
$3.16