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October 17, 2011 (Regular Meeting) <br />Mean I Mode <br />Median <br />Median <br />E r."M <br />Medians <br />Skewness is a term for the degree of distortion from symmetry exhibited by a <br />frequency distribution. What this means is that if you were to graph the <br />sales ratios you would expect that all errors should be random and hence <br />symmetrical and not biased either low or high for certain properties. This <br />can be checked by using the common measures of degree of skewness. <br />SK1 = 3 (MEAN -MODE) <br />STANDARD DEVIATION <br />Note: (Pearson's Coefficient of Skewness) <br />and <br />SK = (Q3 - MEDIAN) - (MEDIAN - Q1) <br />(Q3 - Ql) <br />The second measure uses a "QUARTILE" which is something like the median (in <br />fact, the median is the Q2 or second quartile or quarter, EG 50% of the way <br />through the list, item) but is the item 250 (Q1) down the list and the 750 <br />(Q3) item down the list of ordered observations and may be determined much as <br />is the median. <br />NON PARAMETRIC STATISTICS <br />This class of statistics is useful in that unlike many statistical tools, <br />they do not depend on having normally distributed values to be meaningful. <br />The most usable is the chi - squared statistic. It is simple and is very <br />useful in testing a number of common questions or hypotheses which you pose <br />formally or informally in appraising. <br />Suppose, for instance, you have collected a set of observations of the sale <br />parcels in an area and you wish to compare the distribution of these sales <br />with the distribution of all parcels for the area to see if the distributions <br />match up and will give you some assurance that the sales are comparable to <br />the universe of all parcels. To do this let us assume you use a single <br />method of classification, age, and restrict the discussion to only a single <br />exterior wall type (a good discriminator). <br />How do you proceed? First classify the sale parcels into groups of 5 years <br />although the greater of lesser intervals could have been selected depending <br />on our data. For example: <br />TABLE OF ACTUAL FREQUENCIES <br />FOR SALE PARCELS <br />AGE (in years) <br />FREQUENCY <br />PERCENT OF <br />INTERVAL <br />IN NUMBER <br />TOTAL <br />1 - 5 <br />10 <br />13.2 <br />6 -10 <br />22 <br />28.8 <br />11 -15 <br />17 <br />22.4 <br />16 -20 <br />10 <br />13.2 <br />21 -25 <br />7 <br />9.2 <br />26 -30 <br />10 <br />13.2 <br />Page 767 <br />Made I Meant <br />