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 three-dimensional 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