Chapter 5: Statistical Reasoning
Assignment #4: Unit 5D
Graphics in the Media
Pages 364-373
1. Briefly describe the construction and use of multiple bar graphs and stack
plots.
A multiple bar graph is a simple extension of a regular bar graph. It has 2
or more sets of bars that allow comparison between 2 or more data sets.
All the data sets must involve the same categories so that they can be
displayed on the same graph.
Another common type of graph, called a stack plot, shows different sets
in a vertical stack. The thickness of the wedge at a particular time tells
you its value at that time: When a wedge is thick it has a large value, and
when it is think it has a small value.
2. What are geographical data? Briefly describe at least two ways to
display geographical data. Be sure to explain the meaning of contours
on a contour map.
We are often interested in geographical patterns in data. Graphs are a
way of displaying geographical data. The legend explains that different
colors represent different income levels. Similar colors are used for similar
income levels. Thus, it is easy to see that income levels tend to be hihest in
the northeast and lowest in the south.
For data that vary continuously across geographical areas, contour map
is more convenient. Each of the contours connects locations with the
same temperature. Note that regions where contours are tightly spaced,
there are greater temperature changes. To make the graph easier to
read, the regions between adjacent contours are color-coded.
3. What are three-dimensional graphics? Explain the difference between
graphics that only appear three-dimensional and those that show truly
three-dimensional data.
Today, computer software makes it easy to give almost any graph a
three-dimensional appearance. It may look nice, but the threedimensional effects are purely cosmetic. They don’t provide any
information that wasn’t already in the two-dimensional graph.
In contrast, each of the three axes in Figure 5.20 carries distinct
information, making it a true three-dimensional graph.
All of the graphic types we have studied so far are common and fairly
easy to create. But the media today are often filled with many varities of
even more complex graphics.
4. Describe how perceptual distortions can arise in graphics and how they
can be misleading.
As we have seen, graphics can offer clear and meaningful summaries of
statistical data. However, even well-made graphics can be misleading if
we are not careful in interpreting them, and poorly made graphics are
almost always misleading. Moreover, some people use graphics in
deliberately misleading ways. Many graphics are drawn in a way that
distorts our perception of them.
5. How can graphics be misleading when the scales do not go all the way to
zero? Why are such graphics sometimes useful?
In graphs, when the vertical scale does not begin at zero and does not
end at 100%. The increase is still substantial but looks far less dramatic if
we redraw the graph with the vertical axis covering the full range of 0% to
100%. From a mathematical point of view, leaving out the zero point on a
scale is perfectly fine and can make it easier to see small-scale trends in
the data. Nevertheless, as the examples show, it can be visually
deceptive if you don’t study the scale carefully.
6. What is an exponential scale? When is an exponential scale useful?
Sometimes the scale may not be deceptive, but still required care to
avoid misinterpretation. Graphs that illustrate such a quick increase in
scale are called an exponential scale (or logarithmic scale) because
each unit corresponds to a power of 10. In general, exponential scales
are useful for displaying data that vary over a huge range of values.
Because the data in graphs grow so rapidly, the ordinary scale makes it
impossible to see any detail in the early years shown on the graph.
7. Explain how a graph that shows percentage change can show
descending bars (or a descending line) even when the variable of interest
is increasing.
If the vertical axis represents the percentage increase, a flat graph means
only that costs increased by the same percentage each year, not that
costs held steady.
8. What is a pictograph? How can a pictograph enhance a graph? How
can it make a graph misleading?
Pictographs are graphs embellished with additional artwork. The artwork
may make the graph more appealing, but it can also distract or mislead.
The artwork embellishments of this graph are deceptive in several ways.
Pictographs are very common, but you have to study the, carefully to
extract the essential information and not be distracted by the cosmetic
effects.
Exercises in your Textbook: Pages 374 – 378 Problems 19 - 48