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CABARRUS COUNTY 2012 APPRAISAL MANUAL <br />or in the previous example: <br />TOTAL ASSESSED VALUE /TOTAL SALES PRICE = weighted mean <br />This measure is affected by large values which have a proportionately greater impact on the ratio than smaller values. As a <br />general rule, this measure is, therefore, somewhat less useful for sales ratio work than the un- weighted mean. <br />A highly useful statistic is the MEDIAN. It is a measure which is least influenced by extreme values as it is based upon <br />position rather than on level. That is, it is the value half -way from either end of a list of values when the list is arrayed in <br />ascending (or descending) order. If the list contains an odd number of sales then the median is the middle value in the list. <br />However, if there is an even number of sales in the list then it is the average of the two values on either side of the theoretical <br />mid point in the list. Using our example it is: <br />MEDIAN = (TOTAL NUMBER OF SALES + 1) / 2 + (10 + 1) / 2 + 5.5th item in the list <br />That is in our list: Sales <br />Sales Ratio <br />1 <br />95% <br />2 <br />92 <br />3 <br />90 <br />4 <br />86 <br />5 <br />86 <br />Median 5.5 Sales ---------- > <br />6 <br />80 <br />7 <br />75 <br />8 <br />72 <br />9 <br />64 <br />10 <br />60 <br />The median is, therefore, halfway between the ratio 86 and 80 or: <br />MEDIAN = (86 + 80) / 2 = 166 / 2 = 83% <br />This statistic is generally is the one normally used in judging uniformity and level of assessment. (Note: you may also <br />calculate a median sales value as well as a median appraised value.) <br />MODE <br />The mode is a measure of central tendency that is easy to understand. It is the value in the set of observations which occurs <br />most frequently. In our example, the mode of sales ratios would be 86% (occurs 2 times). <br />MEASURES OF VARIABILITY <br />A classic example of reliance on the use of the mean only as a method of description may be rather graphically illustrated by <br />the following: <br />If you were fired upon one time and were missed by 100 yards and were fired upon a second time and were hit, you could <br />conclude that you were missed by an average of 50 yards. The point is the mean does not tell the whole story about the data. <br />Other tools are needed to better describe the data. These tools are measures of how much you miss the mean (in general) or in <br />more technical terms, measures of dispersion. <br />Cabarrus County — 2012 Revaluation STATISTICS & THE 10-4 <br />APPRAISAL PROCESS 8/9/11 <br />Attachment number 11 <br />G -6 Page 299 <br />