```Date: Wed, 1 Jul 1998 17:57:10 -0400 Reply-To: "Powhatan J. Wooldridge, Ph.D." Sender: "SPSSX(r) Discussion" From: "Powhatan J. Wooldridge, Ph.D." Subject: Re: Is it possible to develop an average using categories??? Comments: To: Mark In-Reply-To: <199807012054.PAA08194@ns1.dialnet.net> Content-Type: TEXT/PLAIN; charset=US-ASCII The basket categories ("under 15k" and "75k+") make it difficult to calculate mean income accurately. For this reason median income would indeed be the most appropriate average to report. (I am assuming that you didn't set up intervals so poorly that a majority of your sample falls into one of the basket categories.) First locate the income category within which the midpoint occurs. Subtract the cumulative frequency for the next lower category from the midpoint frequency, and divide the result by the frequency for the midpoint category. Multiply the resulting fraction times the income interval for the midpoint category (probably \$10,000), and add the result to the lower category limit. You should subtract \$50 from the lower number and add \$50 to the higher number, in order to calculate the "true" category limits. (For example, you should use \$24,950 rather than 25,000 as the "true" lower limit of your \$25k - \$34.9k category.) The result will be a reasonably accurate and unbiased estimate of the median income of your sample. (There may be some slight tendency to overestimate the median, due to skewing within the midpoint category; but that isn't likely to amount to much.) Formulas for this computation can be found in most introductory statistics texts, but it is somewhat uncommon for anyone but a statistician to remember them. You could also validly report the modal income, of course; but that is so much a function of your choice of intervals in setting up the categories that it is not nearly as useful an "average" as the median is. *************************************************************************** Powhatan J. Wooldridge, Assoc. Professor, Nursing, State Univ. NY at Buffalo On Wed, 1 Jul 1998, Mark wrote: > I have been working with the following categories for income: > > Under \$15k > \$15k - 24.9k > \$25k - 34.9k > \$35k - 44.9k > \$45k - 74.9k > \$75k + > > Is it possible to develop an average, or median for income? Thank you in > advance for any help. > > Mark > ```

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