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Part II: Number-Crunching Basics
In my opinion, this bar graph needs some additional info from behind the
scenes to make it more understandable. The bars in Figure 6-6 don’t repre-
sent similar types of entities. The first bar represents sales (a form of rev-
enue), and the other bars represent expenditures. The graph would be much
clearer if the first bar weren’t included; for example, the total sales could be
listed as a footnote.
Tipping the scales on a bar graph
Another way a graph can be misleading is through its choice of scale on the
frequency/relative frequency axis (that is, the axis where the amounts in each
group are reported), and/or its starting value.
By using a “stretched out” scale (for example, having each half inch of a bar
represent 10 units versus 50 units), you can stretch the truth, make differ-
ences look more dramatic, or exaggerate values. Truth-stretching can also
occur if the frequency axis starts out at a number that’s very close to where
the differences in the heights of the bars start; you are in essence chopping
off the bottom of the bars (the less exciting part) and just showing their tops;
emphasizing (in a misleading way) where the action is. Not every frequency
axis has to start at zero, but watch for situations that elevate the differences.
A good example of a graph with a stretched out scale is seen in Chapter 3,
regarding the results of numbers drawn in the “Pick 3” lottery. (You choose
three one-digit numbers and if they all match what’s drawn, you win.) In
Chapter 3, the percentage of times each number (from 0–9) was drawn is
shown in Table 3-2, and the results are displayed in a bar graph in Figure 3-1a.
The scale on the graph is stretched and starts at 465, making the differences
in the results look larger than they really are; for example, it looks like the
number 1 was drawn much less often, whereas the number 2 was drawn
much more often, when in reality there is no statistical difference between
the percentage of times each number was drawn. (I checked.)
Why was the graph in Figure 3-1a made this way? It might lead people to think
they’ve got an inside edge if they choose the number 2 because it’s “on a hot
streak”; or they might be led to choose the number 1 because it’s “due to come
up.” Both of these theories are wrong, by the way; because the numbers are
chosen at random, what happened in the past doesn’t matter. In Figure 3-1b
you see a graph that’s been made correctly. (For more examples of where
our intuition can go wrong with probability and what the scoop really is, see
another of my books, Probability For Dummies, also published by Wiley.)
Alternatively, by using a “squeezed down” scale (for example, having each
half inch of a bar represent 50 units versus 10 units), you can downplay dif-
ferences, making results look less dramatic than they actually are. For exam-
ple, maybe a politician doesn’t want to draw attention to a big increase in
crime from the beginning to the end of her term, so she may have the number

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