HANDY HINTS Serving up a Good Pie
When presenting a pie chart, be sure to define what the whole is. In statistics, be very clear whether the whole is the population or the sample. If presenting multiple pie charts, be sure to define what the whole is, and what the group of divisions are, for each chart.
Compare and Contrast: The Bar Chart
One of the most common types of chart is the bar chart. In a basic bar chart, there is one bar for each value of the variable being illustrated. The length (or height) of the bar indicates the count, called thefrequencyof each value of the variable. The bar chart allows us to look at the sample distribution of a single variable, but it also has other uses. There are many variations on the bar chart. Some have their own special names, others do not. Those that have been named may have more than one name, each derived from different fields. The bar chart can also be combined with other types of charts. In this section, we will take a look at some of the more common and more useful types of bar charts, and try to keep track of their names.
proportions of the total, we are showing the counts in relation to one another, but not in relation to an image of the total. When displaying the same data in two or more different figures, it is useful to keep the color or shading consistent from one to the next, as we have done here.
Horizontal bar charts
When the length of the bar indicates something other than count or quantity, a horizontal bar chart should be considered. Time, for example, is best understood when laid out on a horizontal axis, often called a timeline. For example, the field of project management uses a variety of specialized horizontal bar charts, including the Gantt chart, to lay out project schedules over time.
Another important use of the horizontal bar chart is in the side-by-side Bar Chart. In the side-by-side chart, also called the mirrored chart, two distributions are compared by placing two bar charts, reflected back-to-back.
If we use a vertical bar chart, then one of the two distributions points upward and the other points downward. This gives a strong impression that the first distribution is a measure of something positive or ‘‘good’’ and the second is a measure of something negative or ‘‘bad.’’ Unless this is what we want to communicate, we should place the two distributions side-by-side with horizontal bars. Figure 7-3 uses a horizontal bar chart to show the percentage distribution of stocks in a personal portfolio compared to the distributions in the S&P 500. In general, people make this comparison to improve their investment strategy. Variance of one’s personal portfolio from the S&P 500 might be a matter of investment history or personal preference.
It could also be an indicator of conservatism (more manufacturing and retail), or a less risk-averse approach (more technology stocks). If you find that your portfolio has had significantly better—or worse—performance than the S&P 500 during the prior year, a table like this could help you
Fig. 7-2. Vertical bar chart: breeds of sheep in our flock.
identify reasons for the success—or issues—of your strategy. Just glancing at the chart, we can see that this portfolio has significantly less investment in pharmaceuticals, and somewhat less in manufacturing, than the S&P 500, while holding more in retail and financial, and matching the S&P 500 in technology stocks. (Note: the figures for the S&P 500 are illustrative, and do not actually represent that index.) On the graphical side, it would be better if the items lined up exactly with one another. Unfortunately, Microsoft ExcelÕ does not offer a side-by-side bar chart option, and we dummied this up using a grouped horizontal bar chart with negative numbers.
Figure 7-4 illustrates why we do not generally use vertical mirrored bar charts. Here, we see a diagram showing the difference of ethnic diversity and opportunity between the free peoples of Middle-Earth and the dominion of the Dark Lord, Sauron, in J. R. R. Tolkien’sThe Lord of the Rings.In each society, those who achieve the highest honor are members of ‘‘the nine.’’ For the good peoples, this is the nine walkers; for the evil Land of Mordor, this is the nine riders. If we note that there is, in fact, a diverse population of goblins
Fig. 7-3. Side-by-side bar chart: comparative portfolio weights.
Fig. 7-4. Vertical side-by-side (not recommended): Good versus evil.
(or, to use the more proper term, orcs), trolls, evil men, evil wizards, spiders, and others who all support the Dark Lord, we realize that this is a society with a glass ceiling. Sauron will allow only undead to rise to the highest positions of power, leadership, and recognition, becoming members of the nine riders. While statistics cannot establish causality, it may be the case that this inequality of opportunity is one of the aspects of Sauron’s realm which causes it legitimately to be considered evil.