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CABARRUS COUNTY 2012 APPRAISAL MANUAL <br />RANGE <br />The range is simply the lowest and highest value in your set of observations subtracted from one another; although it may be <br />reported as the minimum and maximum values themselves. In our example, you could say the range (for the sales ratios) is: <br />35% or from 60% to 95% <br />As a general statement it is not too useful in analysis due to its obvious dependence on extreme values. <br />MEAN DEVIATION & MEDIAN DEVIATION <br />This measure is the average of the difference between the mean (or median) and the individual observations. <br />MD= [d] /Nor[x] /N <br />That is, the mean or median deviation is the sum of the absolute value of the differences between the mean (or median) and <br />each observation divided by the number of observations. (Absolute value means the signs are ignored, that is assumed to be <br />positive, when accumulating [x] or [d].) <br />For our example: <br />SALES RATIO <br />- MEAN <br />= [x] ([d] is used for the median) <br />95 <br />- 80 <br />= 15 <br />92 <br />- 80 <br />= 12 <br />90 <br />- 80 <br />= 10 <br />86 <br />- 80 <br />= 6 <br />86 <br />- 80 <br />= 6 <br />80 <br />- 80 <br />= 0 <br />75 <br />- 80 <br />= 5 <br />72 <br />- 80 <br />= 8 <br />64 <br />- 80 <br />= 16 <br />60 <br />- 80 <br />= 20 <br />Hence: MD = 98 / 10 = 9.8% <br />This ratio expresses the average amount by which the data varies from the mean (or median) in a particular set of data. It is <br />influenced by extremes as is the mean and even when computed about the median, it is likewise influenced. It also is not <br />useful in making further statistical analysis of the data. <br />STANDARD DEVIATION <br />To overcome the handicaps of the mean deviation, the standard deviation is used. It is a numerical measure of the degree of <br />dispersion, variability, or non - homogeneity of the data to which it is applied. In calculation, it is similar to the average <br />deviation but differs in its method of averaging differences from the mean. It does this by squaring each difference and <br />eventually summing all squared differences averaging them and taking the square root thereof giving an "average deviation" <br />from the mean. <br />In practice it is quite easy to compute using a handy "working formula" to make the task easier. First the formal formula: <br />STANDARD DEVIATION = � U) 2 or Y x - Where u = "mu" <br />N N -1 (arithmetic mean) <br />Cabarrus County — 2012 Revaluation STATISTICS & THE 10-5 <br />APPRAISAL PROCESS 8/9/11 <br />Attachment number 11 <br />G -6 Page 300 <br />