Page 53 - Statistics for Dummies

Chapter 3: Taking Control: So Many Numbers, So Little Time
Before believing statistics indicating “the highest XXX” or “the lowest XXX,”

take a look at how the variable is measured to see whether it’s fair and whether
there are other statistics that should be examined too to get the whole picture.
Also make sure the units are appropriate for making fair comparisons.
Zeroing in on what the scale tells you
Charts and graphs are useful for making a quick and clear point about your
data. Unfortunately, many times the charts and graphs accompanying everyday
statistics aren’t done correctly and/or fairly. One of the most important ele-
ments to watch for is the way that the chart or graph is scaled. The scale of a
graph is the quantity used to represent each tick mark on the axis of the graph.
Do the tick marks increase by 1s, 10s, 20s, 100s, 1,000s, or what? The scale can
make a big difference in terms of the way the graph or chart looks.
For example, the Kansas Lottery routinely shows its recent results from the Pick
3 Lottery. One of the statistics reported is the number of times each number (0
through 9) is drawn among the three winning numbers. Table 3-2 shows a chart
of the number of times each number was drawn during 1,613 total Pick 3 games 37
(4,839 single numbers drawn). It also reports the percentage of times that each
number was drawn. Depending on how you choose to look at these results, you
can again make the statistics appear to tell very different stories.
Table 3-2 Numbers Drawn in the Pick 3 Lottery
Number No. of Times Drawn Percentage of Times Drawn
Drawn out of 4,839 (No. of Times Drawn ÷ 4,839)
0 485 10.0%
1 468 9.7%
2 513 10.6%
3 491 10.1%
4 484 10.0%
5 480 9.9%
6 487 10.1%
7 482 10.0%
8 475 9.8%
9 474 9.8%
The way lotteries typically display results like those in Table 3-2 is shown in
Figure 3-1a. Notice that in this chart, it seems that the number 1 doesn’t get
drawn nearly as often (only 468 times) as number 2 does (513 times). The
difference in the height of these two bars appears to be very large, exaggerating
the difference in the number of times these two numbers were drawn. However,

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