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Unformatted text preview: Dr. V.R. Bencivenga
Economics 329 Economic Statistics FREQUENCY DISTRIBUTIONS—INDEX CARD Q1 & Q2
INDEX CARD QUESTION 1
The table below gives relative frequency distributions of educational attainment in the US at
decade intervals from 1940 to 1990. These are computed from the Public Use Microdata
Samples provided by the Census Bureau, which are random samples of approximately one out
of every one hundred US residents. (Source: “A LaborIncomeBased Measure of the Value of
Human Capital: An Application to the States of the United States” by Casey B. Mulligan and
Xavier SalaIMartin, NBER No. 5018, Feb. 1995.)
How much did median educational attainment change from 1940 to 1990? Over what decade
was the largest gain made in median educational attainment? Compute median educational
attainment for each decade observation in order to answer this question.
Note: Each class interval extends up to the beginning of the one above it. In other words, use
0 to < 5 years, 5 to < 8 years, 8 to < 9 years, 9 to < 12, etc. The schooling categories “57 years”
and “8 years” were merged in the 1990 census. 2 1940 1950 1960 1970 1980 1990 No school .028 .016 .008 .006 .004 .007 0  4 years (0 to < 5) .095 .073 .038 .023 .012 .007 5  7 years (5 to < 8) .177 .150 .096 .070 .036 .034 8 years (8 to < 9) .270 .196 .163 .099 .044 13 years HS (9 to < 12) .160 .186 .207 .201 .131 .109 4 years HS (12 to < 13) .148 .219 .275 .346 .377 .300 13 years college (13 to <
16) .060 .080 .104 .116 .184 .289 4+ years college (16+) .062 .080 .108 .138 .212 .254 Schooling Note: These are relative frequency distributions with relative frequencies stated as proportions.
Each column sums to 1 (except for rounding error). 3 INDEX CARD QUESTION 2
Below are two relative frequency distributions of per capita income in 1993. The first is
unweighted (each of the 127 countries with available data counts as an observation). The
second is weighted by population (each person in a country counts as an observation, so each
country is weighted in proportion to its population). These data are from the 1995 World
Development Report.
a. In what percentage of countries in the sample was per capita income less than $200? Less
than $600? $10,000 or more? b. What percentage of the population in the sample lived in countries where per capita
income was less than $200? Less than $600? $10,000 or more? 4 Per capita income
0 to < 200 Relative
frequency
(unweighted)
6.3 Relative
frequency
(weighted)
4.2 200 to < 400 15.0 24.2 400 to < 600 7.9 26.5 600 to < 1000 12.6 8.1 1000 to < 1500 11.0 3.3 1500 to < 2000 4.7 1.2 2000 to < 2500 4.7 5.9 2500 to < 5000 14.2 8.7 5000 to < 10,000 4.7 2.0 10,000 to < 15,000 3.1 1.0 15,000 to < 20,000 6.3 3.5 20,000 to < 25,000 6.3 8.6 25,000 to < 40,000 3.1 2.8 Note: These are relative frequency distributions with relative frequencies stated as
percentages. Each column sums to 100 (except for rounding error). ...
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 Spring '12
 BENCIVENGA
 Economics

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