Statistics for Dummies (14 page)

The Internal Revenue Service (IRS) wants you to know where your tax money goes, and if you tell them how much money you paid in taxes last year, they will show you how your tax dollars were sliced up.
Figure 4-6
shows an example of the results that you get from the IRS if you tell them you paid $10,000 in taxes last year.

Figure 4-6:
How the tax dollar is sliced up (2002).

This data display is creative but a bit different (dare I say "odd", at the risk of being audited?). First, this chart appears to be more of a pizza chart than a pie chart. But you have to ask what the pizza is doing there, if it's not being sliced up to show you where your money is going. The percentages are in the table next to the pizza, so they're available. This chart would have more visual impact if the IRS had shown the actual "slices" of pizza that correspond to the percentages in the table. What's nice about this display, however, is that it shows the amount of money as well as the percentages that are spent in each area. (By the way, no matter what the total amount of tax dollars is, the percentages showing where the money is allocated don't change; only the dollar amounts do.)

Examining
Figure 4-6
, you can see that the biggest slice of your tax dollars go to Social Security (23%), and the second biggest slice goes to national defense (17%). It seems strange, though, that the IRS breaks down certain categories as low as single digits (for example 7% going to Medicaid), but the third highest slice of the pie (or in this case, pizza) actually shows up as "other expenses" (16%).

Perhaps you're wondering what those "other expenses" are in the IRS chart. If you probe further on the IRS Web site, the IRS tells you that "other expenses" means "federal employment retirement benefits, payments to farmers, and other activities." This doesn't provide a great deal of additional information, but maybe that's all you really want to know. In fairness to the IRS, I'm sure the details are all spelled out in some neatly filed government report.

The U.S. Census Bureau provides many data displays in its reports about the U.S. population.
Figure 4-7
shows two pie charts comparing the racial breakdown of the United States in 1995 (actual figures) with the projected racial breakdown in 2050, if current trends continue. You can see that in 1995, about 73.6% of the U.S. population was White, while Blacks made up the second highest group at 12.0%, closely followed by those of Hispanic origin, who comprised 10.2% of the population. (Note that although Hispanics are typically white or black, they are shown here as a separate category, independent of racial background.) The Census Bureau projects that Whites will be a declining share of the total U.S. population in the future, whereas the Hispanic share of the population will grow faster than that of non-Hispanic Blacks. This point is made well using the two pie charts, as opposed to tables simply showing the percentages.

Figure 4-7:
Ethnicity trends for the United States.

How much of their income do people spend on transportation? It depends on how much money they make. The Bureau of Transportation Statistics (did you know such a department existed?) conducted a study on transportation in the United States in 1994, and many of their findings are presented as bar graphs like the one shown in
Figure 4-8
.

Figure 4-8:
Transportation expenses by household income for 1994.

This particular bar graph shows how much money is spent on transportation for people in varying household-income groups. It appears that as household income increases, the total expenditures on transportation also increase. This probably makes sense, because the more money people have, the more they have available to spend. But would the bar graph change if you looked at transportation expenditures not in terms of total dollar amounts, but as the percentage of household income? The households in the first group make less than $5,000 a year and have to spend $2,500 on transportation per year. (Notice that the table reads "2.5", but because the units are in thousands of dollars, the 2.5 translates into $2,500.) This $2,500 represents 50% of the annual income of those who make $5,000 per year; it's an even higher percentage of the total income for those who make less than $5,000 per year. The households earning $30,000–$40,000 per year pay $6,000 per year on transportation, which is between 15% and 20% of their household income. So, although the people making more money spend more dollars on transportation, they don't spend more as a percentage of their total income. Depending on how you look at expenditures, the bar graph can tell two somewhat different stories.

This bar graph has another peculiarity. The categories for household income as shown aren't equivalent. For example, each of the first four bars represents household incomes in intervals of $5,000, but the next three groups increase by $10,000 each, and the last group contains every household making more than $50,000 per year, which is a large percentage of households, even in 1994. Bar graphs with different category ranges, such as the one shown in
Figure 4-8
, make comparison between groups more difficult.

Bar graphs are often used to compare two groups by breaking down the categories for each group and showing them as side-by-side bars. One example of this is shown in
Figure 4-9
, which asks the question, "Has the percentage of mothers in the workforce changed over time?" The answer is yes.
Figure 4-9
shows that the overall percentage of mothers in the workforce climbed from 47% to 72% between 1975 and 1998. Taking the age of the child into account, fewer mothers work while their children are younger and not in school yet, but the difference from 1975 to 1998 is still about 25% in each case, as shown by the side-by-side bars.

Figure 4-9:
Percentage of mothers in the workforce, by age of child (1975 and 1998).

The Ohio lottery shows its sales and expenditures for 2002 using a bar graph (see
Figure 4-10
). This bar graph takes some additional work behind the scenes to make it understandable. The first issue with this bar graph is that the bars don't represent similar types of entities. The first bar represents sales (a form of revenue), and the other bars represent expenditures. This bar graph could be made more clear if the first bar weren't included; for example, the total sales could be listed as a footnote. Also, the expenditures could be represented in a pie chart, as is done by some of the other state lotteries (refer to
Figures 4-3
and
4-4
). The next issue is that the sum of all of the expenditures ($2,013.2 million — in other words, $2.0132 billion) is greater than the sales ($1.9831 billion), so some additional revenue is not being shown in this bar graph (either that, or the Ohio lottery is about to go out of business!). Looking deeper into more of the information provided on the Ohio lottery Web site, I found out that besides sales, additional revenue was reported to be $124.1 million, earned through "interest and other revenues." That brings the total revenues to $1.9831 billion + $124.1 million = $2.1072 billion in 2002, leaving a profit of $2.1072 billion – $2.0132 billion = $.094 billion, or $94,000,000.

Figure 4-10:
Ohio lottery sales and expenditures for 2002.

Note that in a pie chart, however, the scale can't be changed to over-emphasize (or downplay) the results. No matter how you slice up a pie chart, you're always slicing up a circle, and the proportion of the total pie belonging to any given slice won't change, even if you make the pie bigger or smaller.