The standard error of the numerator, s, and that of the denominator, Sy, may be calculated using formulas described earlier. In formula (10), r represents the coefficient of correlation between the numerator and the denominator of the estimate.

For one type of ratio, the denominator is a count of families or households and the numerator is a count of persons in those families or households with a certain characteristic. If there is at least one person with the characteristic in every family or household, use 0.7 as an estimate of r. An example of this type is the mean number of children per family with children.

For all other types of ratios, r is assumed to be zero. If r is actually positive (negative), then this procedure will provide an overestimate (underestimate) of the standard error of the ratio. Examples of this type are the mean number of children per family and the poverty rate.

NOTE: For estimates expressed as the ratio of x per 100 y or x per 1,000 y, multiply formula (10) by 100 or 1,000, respectively, to obtain the standard error.

The 90-percent confidence interval for the estimated ratio is calculated as 9.94 ±1.645x0.13.

Standard Errors of Estimated Medians. The sampling variability of an estimated median depends upon the form of the distribution and the size of its base. One can approximate the reliability of an estimated median by determining a confidence interval about it. (See the section "Standard Errors and Their Use" for a general discussion of confidence intervals.)

Estimate the 68-percent confidence limits of a median based on sample data using the following procedure. 1. Determine, using formula (4), the standard error of the estimate of 50 percent from the distribution.

2. Add to and subtract from 50 percent the standard error determined in step 1.

3. Using the distribution of the characteristic, determine upper and lower limits of the 68-percent confidence interval by calculating values corresponding to the two points established in step 2.

Use Pareto interpolation for any point in an income interval greater than $2,500 in width, and linear interpolation otherwise. The formulas for interpolation are:

A2, respectively.

exp is the exponential function.

Ln is the natural logarithm function.

A mathematically equivalent result is obtained by using common logarithms (base 10) and antilogarithms.

4. Divide the difference between the two points determined in step 3 by two to obtain the standard error of the median.

The new, more detailed income intervals used in this report have $2,500 increments up to $40,000 for households and families and up to $20,000 for persons, and Pareto interpolation is needed only when a median income falls in an interval of width larger than $2,500 (beginning with March 1980 CPS). Therefore, this type of interpolation will seldom be needed (i.e., only in cases where the estimated median income exceeds $40,000 for households and families and $20,000 for persons). For this reason, illustration of the use of Pareto interpolation in computing a confidence interval for a median has been omitted. An illustration of this procedure can be found in the source and reliability section of Current Population Reports, Series P-60, No. 123.

Use of the above procedure could result in standard errors which differ from those given in the detailed tables. The reasons for this discrepancy are the use of a more detailed distribution than that given in the tables in determining the published standard errors, and the rounding of numbers to thousands in the published tables. Linear interpolation was almost always used to compute the published medians and standard errors. Occasionally, a median may lie in an open-ended interval. To calculate its standard error the user must call Housing and Household Economic Statistics Division of the Census Bureau to obtain the methodology.