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October 17, 2011 (Regular Meeting) Page 762 <br />hypothesized relations between the phenomena, and to aid in making reliable <br />inferences from empirical observation." The preceding, from FOUNDATIONS OF <br />BEHAVIORAL RESEARCH by Fred N. Kerlinger, states very well what statistics <br />are, their usefulness, and implications for our work. His book is highly <br />recommended to all who wish to gain an understanding of many statistical <br />tools and the requisite knowledge of the "scientific method" of constructing <br />cases for analysis. A somewhat less advanced text for the beginner is AN <br />INTRODUCTION TO BUSINESS AND ECONOMIC STATISTICS by John R. Stockton. <br />It is not our intent to try and present a programmed text to teach statistics <br />but we will hopefully indicate which are useful where and what they tell the <br />property appraiser about his values. <br />STATISTICS AND THE APPRAISAL PROCESS <br />Sales offer the only real set of data which can be established as indicating <br />market value for properties. Appraisals which are done to supplement sales <br />as parcels to which one may relate for purposes of comparison are merely <br />attempts to predict what the sales price would be should that parcel actually <br />sell. It is our belief that surrogates for actual sales are needed only when <br />parcels (for a class) show a statistically insignificant number of sales. <br />Particularly for single family residential properties sales are usually <br />always available and are in most cases legitimate arm's length transactions. <br />The most frequently asked question is usually "Where am I in relation to <br />market ?" There are ways of describing this relationship; each of which will <br />help you understand "where" you are in relation to the market. <br />Level of assessment in relation to market is one part of the answer. It is <br />usually expressed as a ratio of appraised values to sale values. Common <br />measures of this ratio, overall, for a county are "MEAN ", MEDIAN, "MEASURES <br />OF CENTRAL TENDENCY ", and "PRICE RELATED DIFFERENTAL ". <br />SIMPLE OR UNWEIGHTED MEAN <br />This measure is found by dividing the sum of all individual sales by the <br />number of sales. That is, given the following hypothetical list of sales, <br />compute the means: <br />OBSERVATION NUMBER <br />SALE PRICE <br />APPRAISED VALUE <br />SALES RATIO <br />1 <br />$22,600. <br />$21,500. <br />95 % <br />2 <br />31,000. <br />28,600. <br />92 <br />3 <br />37,800. <br />34,000. <br />90 <br />4 <br />38,400. <br />33,000. <br />86 <br />5 <br />34,300. <br />29,500. <br />86 <br />6 <br />20,000. <br />16,000. <br />80 <br />7 <br />13,000. <br />9,800. <br />75 <br />8 <br />18,700. <br />13,500. <br />72 <br />9 <br />26,900. <br />17,200. <br />64 <br />10 <br />40,800. <br />24,500. <br />60 <br />$283,500. <br />$227,600. <br />800 % <br />Mean Sale Ratio = 800/10 = 80 %. <br />Mean Appraised Value = $227600/10 = $22,760. <br />Mean Sales Price = $283500/10 = $28,350. <br />As you can see, there are several "MEANS" which may be computed; each of <br />which is an expression of central tendency. <br />There is another type of mean called a WEIGHTED MEAN which reflects the <br />impact of the dollar magnitude of the values in the calculation of the mean. <br />It is obtained by dividing the total of all appraised (or assessed) values by <br />the total of all.sales prices. For example: <br />$227,600/$283,500 = 8.3% <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 <br />