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October 17, 2011 (Regular Meeting) Page 766 One of these properties is that one may determine what percent of the observations lie within; one, two, or three times the calculated standard deviation by using pre- computed tables. (In fact, any fractional part of the standard deviation may also be used.) The way it would likely be useful to you is in making a statement about the uniformity of your values which is in part what it measures. For instance, if you have a set of sales with a mean of 87% and a Standard Deviation of 100, you could conclude that 95.46% of all sales would fall between the limits of 75.46% and 115.46 %. Extrapolating that sales represent the rest of the parcels in your county (we leave the question of the validity of this assumption up to you), you could then have some mental picture of how your county roll values would distribute themselves in relation to the market values of the parcels. For all the statistically astute, we do include two things: (1) remember that the distribution must be normal or approximately so for this to be true and (2) if there is ever a source of disagreement, sales ratio studies are surely prime material. However, we will let the relative merits of the case go untouched in this text. One final word on the description of a distribution. When you first begin to work with these tools, please get a simple straight forward text such as one of the "cram course" texts on statistics available in any college bookstore with an appealing title such as STATISTICS MADE SIMPLE, etc. You will find it most useful in attacking problems. One we recommend is available from Barnes & Noble in their college outline series titled "STATISTICAL METHODS ". RELATIVE MEASURE OF VARIATION Handy statistical tools are the relative measures. They are ways of relating back to the mean or median in discussing the degree of variance in a set of observations. Three common ones are: AVERAGE DEVIATION ABOUT THE MEAN X 100 = Coefficient of dispersion of the average deviation MEAN STANDARD DEVIATION X 100 MEAN = Coefficient of dispersion of the standard deviation STANDARD DEVIATION ABOUT THE MEDIAN X 100 = Coefficient of dispersion of the median deviation The last two yield the most useful statistic in that the standard deviation is significant in appraising in relationship to the level as there are few who would want a ratio to go consistently over 100% (which is one use of the standard deviation) or whom would want a mean of 70% with a relative error of 35% on 68% of all parcels. SHAPE How do you describe the shape of a distribution? Well, we have used the mean, median, mode, average and standard deviation. We also would like to be able to tell the extent to which our values were consistently biased either high or low. The statistics measuring this are the coefficients of skewness. That is, a measure of the degree to which the distribution departs from the normal distribution. There are three, more or less, classic shapes a distribution, may take (although it may look like anything!) They are: SKEWED LEFT NORMAL SKEWED RIGHT