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Statistical
Terms of the Trade
Median
This is the
mid-point in a sample — the point at which half the values are less and
half the values are more. In our sample of 21 people's wages, the median
is what Jim Hightower earns, because ten people earn less and ten earn
more than him. Jim's wage, $12.61 an hour, also happens to be the actual
median wage for Ohio workers in the year 2000.
Average
An average
is calculated by adding together all the values in a sample, then dividing
by the number of members in the sample. In our sample, the average
wage ($18.77) is much higher than the median wage ($12.61). This
is because the two top earners made wages considerably higher than the
rest of the sample. In this case, you see that the average is a less accurate
measure of how the typical worker is doing, because sixteen members of
the 21-person sample actually earn less than the average wage. This breakdown
is typical of the way wage distributions work, and a good example of why
medians are a more useful statistic than averages for some variables.
Mean
The mean is
the same as the average.
Percentile
There are
a hundred percentiles in a sample. The tenth percentile is the value that
ten percent of the sample lies below. The 95th percentile is the value
that 95 percent of the sample lies below. The tenth percentile wage in
our sample is $6.44, which was the actual tenth percentile wage in Ohio
in 2000. This sample's twentieth percentile wage is $7.94, the actual twentieth
percentile wage in Ohio in 2000. Note that the fiftieth percentile is the
same as the median.
Decile
There are
ten deciles in a sample. The first decile is the tenth percentile, the
second decile is the twentieth percentile and so on. The fifth decile,
incidentally, is the fiftieth percentile, which is also the median. The
wage deciles in this sample correspond to the wage deciles in the actual
Current Population Survey of the US Census for the state of Ohio in 2000.
Quintile
There are
five quintiles in a sample. The first quintile is the twentieth percentile,
the second quintile is the fortieth percentile. Note that you could divide
samples other ways, though we typically don't -- quartiles would divide
a sample into four equal parts, making the bottom quartile the same as
the twenty-fifth percentile.
Mode
This is the
number that appears most often in a sample - it doesn't have much meaning
in the context of wage samples.
Why
it seems
like the
same statistics are often used used to draw opposite conclusions:
Without knowledge
of the circumstances and terms surrounding specific statistics, it's easy
to misunderstand the full story.
To critically
assess any statistic, look carefully at the terms being used (and use them
carefully yourself). See if the terms and definitions being used make sense
in the particular situation. See if similar things are being compared.
For example, it would not make sense to compare one person's wages with
another's income. Wages differ from income -- the first is hourly, the
second annual. Income may or may not include non-wage income, from things
like benefits or stocks, so the comparison would not mean anything.
When someone
gripes that "millions of dollars" are spent on something, you need to know
the context -- how many people are served, at what level of government,
how does it compare to another item in the budget? Without context, statistics
can be manipulated to prove almost anything.
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A Sample of
21 Real People's Imaginary Wages* |
| Ken
Lay $6.15 |
Average
wage $18.47 |
| Dennis Kucinich
$6.15 |
Median
wage $12.61 |
| Barbara Ehrenreich
$6.44 |
Mode
$6.15 |
| Bob Taft $7.00 |
10th
percentile $6.44 |
| Cornel West
$7.94 |
20th percentile
$7.94 |
| C.J. Prentiss
$8.15 |
30th percentile
$9.32 |
| Staughton
Lynd $9.32 |
40th percentile
$10.88 |
| Dan Savage
$10.00 |
Median wage
$12.61 |
| Paul Wellstone
$10.88 |
60th percentile
$14.58 |
| Cherrie Moraga
$11.50 |
70th percentile
$17.18 |
| Jim Hightower
$12.61 |
80th percentile
$20.19 |
| Vandana Shiva
$13.05 |
90th percentile
$25.21 |
| Irene Natividad
$14.58 |
95th percentile
$45.00 |
| Jesse Jackson,
Jr. $15.50 |
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| Ani Difranco
$17.18 |
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| Barbara Byrd-Bennett
$18.55 |
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| John Sweeney
$20.19 |
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| Ellen Malcolm
$22.40 |
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| Huey Freeman
$25.21 |
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Dolores Huerta $45.00 |
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| Sonia Sanchez
$100.00 |
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* Who's
Who in our sample?
A free unpaid
internship to anyone who can identify all names.
Answers are
below.
Economic
Terms of the Trade
Externality
A cost or
a benefit that comes with production of something but that is not measured
in the product's price. Using pesticides on a lawn pollutes groundwater,
but the cost of pollution is not borne by the person applying (or selling)
pesticides, which makes this pollution a “negative externality.” Fixing
up an abandoned house makes a neighborhood safer and increases the
value of nearby properties: the actual renovator doesn't directly get all
the benefits from the renovation, making this a "positive externality".
A totally unregulated market will produce too many negative externalities
and too few positive externalities.
One way to
reduce the number of negative externalities is to require a user to pay
the costs associated with an activity. For example, a gasoline tax could
be imposed that captures the economic costs of air pollution. We can also
reward people who try to reduce negative externalities, like creating tax
incentives for renovating in ways that increase energy efficiency.
Public Good
A good
that benefits everyone in society, that no one can be excluded from and
that does not lose part of its benefit when a new person uses it. The classic
example of a "perfect public good" is a lighthouse -- it protects all the
ships in a harbor, no ship can be stopped from seeing it, and one ship's
use does not reduce the benefit to other ships. A totally unregulated market
will not produce enough public goods, because the producer gets only some
of the benefits, and other members of society are tempted to be "free riders"
who use the benefit without paying for it.
An "imperfect
public good" is similar to a "perfect public good" in that everyone can
benefit, but it may be possible to exclude some users, and it may diminish
somewhat with additional users. Roads are a good example -- with too many
users they can get congested. Public education or police protection are
additional examples -- they require additional resources for each additional
user. But all share the feature that in an unregulated market, these goods
will not be as available as they should be, and that all of society benefits
when they are widely available (and justly provided).
Free Rider
A free rider
uses public goods or positive externalities without contributing to their
costs. "The free rider problem" occurs because people are unwilling
to help pay for something if they think that someone else will bear the cost instead.
Collective
Action Problem
Similar to
the free rider problem, this occurs when it would benefit any one individual
to act in a certain way, but if everyone acts that way, everyone suffers.
If there's a fire in a theater, any one individual could get out most quickly
by running toward the exit, but if everyone did that, people will get trampled
and trapped. Similarly, it may be to one person's advantage to cut
to the front of a line, but if everyone tries to do that the line disintegrates
and the whole process falls apart. SUVs have created a collective action
problem -- as more people drive them, smaller, more fuel-efficient, safer
cars become harder to use because small car drivers can't see around SUVs
and are more vulnerable in a collision with an SUV. Roads would be safer,
less congested and less polluted if we all avoided SUVs, but many individuals
now feel it is rational to choose one for themselves.
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