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Date: Mon, 17 Apr 2000 09:58:35 -0400
From: "Patrick L. Mason" <firstname.lastname@example.org>
When the revolution comes, you will not be the statistics czar!:)::) I
fervently hope you make saugage better than you make statistics. :):):)
Your exercise A don't provide much meaningful information. All you are
saying is 1) sort every family in the economy by its income, ranging from
lowest income to highest income, and 2) calculate the mean income for all
families with zero income up to that family that is just one family over
the median. In other words, calculate the mean for those families that are
below the median. Yes, this number will be lower than the median. But, you
cannot say this is the average for the majority of families. Why? Because
it is no more representative that taking the mean for the top 50% (+ 1) of
all families. The latter number would be higher than the median and it
would include more than half of all families.
The median, combined with information on the dispersion and mobility would
be much more useful and accurate.
Your exercise B merely discovers percentile rankings. By definition x
percentage of all families earn below the xth percentile, while (1 - x)
percentage earn above a given percentile. It may even be useful to
calculate average income for the bottom 90 percent versus the average
income for the top 10 percentage. But, neither is an average for the entire
Again, he median, combined with information on the dispersion and mobility
would be much more useful and accurate.
Your exercise C is considerably stronger point than A or B. The income
earned by undocumented families would certainly alter the figures for the
distribution of income if 1) undocumented workers are a substantial
fraction of the overall workforce, 2) undocumented workers have median
families earnings that are statistically significantly different from the
overall workforce, and 3) undocumented workers are substantially less
likely to have their family income counted than legal workers. There are
large numbers of undocumented workers in some states, but they do not
represent a substantial fraction of the national average. Undocumented
workers may have incomes at or above the national average for two reasons.
First, they tend to be concentrated in states with above average income
(California, New York, Washington, D.C., Boston) or states like Florida and
Texas (which are probably not very far behind the national average).
Second, there are many undocumented workers with nice business suites
roaming around the money centers of Boston and New York. Finally, it may be
the case that undocumented workers are less likely to be counted than legal
workers, or for that matter, it may be the case that low income workers in
general are less likely to be counted but I'd be stunned if this undercount
changed the median by very much. There are at 130 million workers in the US
labor market. The government tends to do a very good job of counting their
earnings - tax revenue depends on accurate information. Morever, although
well to do persons are more likely to be counted they are also more likely
to be less forthcoming on their true income. The latter would create a
downward bias in the median figure.
Finally, you are surely correct that there are massive inequalities in
capitalist economies; hence, there is no need at all to doctor the
statistics. Thoroughly documenting the current reality will strongly prove
peace, patrick l mason
>* Exercise A:
> Find the income for a mathematical majority of families (> 50%)
> *who earn income less than the remaining families*.
> Then calculate the average income for this group. Note how this group
> could indeed be accurately said to be the majority of families. Note
> also how because of variations in income distribution we would
> anticipate that this statistic will differ significantly from the
> figures on median family income.
>* Exercise B:
> Take the same data that Patrick used to say that the median income of
> African-American and Latino families was approximately $27,000.
> Subtract the data on the top 100f income earners in that group to
> fill-in the following statement: "Ninety percent of all
> African-American and Latino families earn an average income of
> I think that the result will be significantly different from the
> aggregate statistic.
>* Exercise C
> Assume that some (significant) percentage of families are composed of
> undocumented workers whose existence is not adequately measured by BLS
> statistics. Assume further that most of these families are part of
> the working poor.
> If we then had the data (which we don't) then we could deflate the
> result of Exercise A still further. E.g. if 30f families fit into
> this category, then it would mean that we would have to knock-off the
> top 30f income earners in the Exercise A sample to obtain a new
> figure for a simple majority of families.
>We live in a capitalist society: differences in income distribution tend to
>be very significant.
>In solidarity, Jerry
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