c is the number of groups; i indicates a specific group, thus taking on values 1 through c.

p, is the estimated proportion of households, families or persons whose values, for the characteristic (x-values) being considered, fall in group i.

is (Z.1+Z)/2 where Z., and Z, are the lower and upper interval boundaries, respectively, for group i. x, is assumed to be the most representative value for the characteristic for households, families, and unrelated individuals or persons in group i. Group c is open-ended, i.e., no upper interval boundary exists. For this group the approximate average value is

The standard error of the numerator, s, and that of the denominator, sy, may be calculated using formula (2). Alternatively, use formula (1) and tables C-1, C-2, and C-5. In formula (10), r represents the 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.

Standard error of a median. The sampling variability of an estimated median depends on the form of the distribution and the size of the base. One can approximate the reliability of an estimated median by determining a confidence interval about it. (See the section on sampling variability 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.

=

A1, A2 the lower and upper bounds, respectively, of the interval containing XpN

N1, N2 = for distribution of numbers: the estimated number of units (persons, households, etc.) with values of the characteristic greater than or equal to A, and A2, respectively.

= for distribution of percentages: the estimated percentage of units (persons, households, etc.) having values of the characteristic greater than or equal to A, and 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 the 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.

FACSIMILE I. FORM CPS-260 CONTROL CARD

At the time of the first CPS interview, the interviewer prepares a list of all persons who are staying in the selected sample unit. The roster is constructed using the field control card, form CPS-260. The roster and questions on the control card are used to identify the living space constituting the sample unit.

A control card is prepared for each housing unit. It provides for recording the personal characteristics of each person who is determined to be a member of a sample household, i.e., a person for whom the sample unit is the usual place of residence. This record of members, which is brought up to date at each subsequent interview to take account of new or departed

residents, changes in age, marital status, etc., constitutes the complete sample of persons from which subsamples, having specified characteristics, are selected for specific studies.

FACSIMILE II. ORIGIN OR DESCENT FLASHCARD

Hispanic persons were identified by a question that asked for self-identification of the person's origin or descent. Respondents were asked to select their origin (and the origin of other household members) from the flashcard. Hispanic persons were those who indicated that their origin was Mexican-American, Chicano, Mexican, Puerto Rican, Cuban, Central or South American (Spanish countries), or other Spanish origin.