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A bar graph, or bar chart, is perhaps the most common data display used by the media. Like a pie chart, a bar graph breaks categorical data down by group, showing how many are in each group. A bar graph, however, represents those groups by using bars of different lengths, rather than as pie slices of varying sizes. And whereas a pie chart most often reports the amount in each group as percentages, a bar graph uses either the number of individuals in each group or the percentage of the total in each group. In a bar graph, the length of each bar indicates the number or percent in each group.
Tracking transportation expenses
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 1.
Figure 1: 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 to $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 1, make comparison between groups more difficult.
Highlighting mothers in the workforce
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 2, which asks the question, "Has the percentage of mothers in the workforce changed over time?" The answer is yes. Figure 2 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 2: Percentage of mothers in the workforce, by age of child (1975 and 1998).
Playing with the Ohio lottery
The Ohio lottery shows its sales and expenditures for 2002 using a bar graph (see Figure 3). 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 clearer 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. 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, you will find 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 3: Ohio lottery sales and expenditures for 2002.
Notice that throughout the Ohio lottery example, the units have been in terms of millions, so you see funny looking numbers like $1,983.1 million, which really should be written as $1.9831 billion. Why does the Ohio lottery use units in millions? Maybe to make it look like it isn't bringing in as much money as it really is. Don't think the lotteries fail to miss these subtleties: They are masters of subtlety. (Think about this: In order to figure out profits, you have to do the calculations yourself, and you need to go to two different places in order to get the numbers needed for those calculations. The lotteries don't make it easy!)
Don't assume that the information being presented in a data display represents everything you need to know; be prepared to dig deeper if you need to fill in any missing information (for which charts and graphs in the media are notorious!). It usually doesn't take too long to find what you're looking for (or to at least discount the information you're being presented, if what you find shows bias or inaccuracy).
Bar graphs allow a great deal of poetic license to whoever designs them. That's because the person designing the bar graph determines what scale he or she wants to use, and that means that the information can be presented in a misleading way. By using a smaller scale (for example, having each half inch of the height of a bar represent 10 units versus 50 units) you can stretch the truth, make differences look more dramatic, or exaggerate values. By using a larger scale (for example having each half inch of a bar represent 50 units versus 10 units) you can downplay differences, make results look less dramatic than they actually are, or even make small differences appear to be nonexistent.
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.
Evaluating a bar graph
To raise the statistical bar on bar graphs, check out these items:
- Bars that divide up values of a numerical variable (such as income) should be equal in width for fair comparison.
- Be aware of the scale of the bar graph (the units in which heights of the bars are represented) and determine whether it's an appropriate representation of the information.
- Don't assume the information being presented in the bar graph represents everything you need to know; be prepared to dig deeper if you need to.
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