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Q:  

Why are there zero weights in the 1990 public use microdata file for the U.S. census?

A:  

The Census Bureau used integer values for weights to avoid complications in rounding for tabulated data. If the final weight of the persons in a particular group was .80, then 4/5 of them were randomly assigned to get a weight of 1 and 1/5 of them were randomly assigned to get a weight of 0. This logic applies to other weights. A weight of 5.5 for a group of persons means half of the persons in this group were randomly assigned a weight of 5 and half of the persons in this group were assigned a weight of 6.

For further discussion of this, see page 4-3 in the technical documentation to the 1990 PUMS.

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