STANDARD DEVIATION (STD) Standard deviation is one of the best and the most useful measures of the spread of valuation data. It measures the distance of data from the mean and can be calculated as follows: CALCULATING STANDARD DEVIATION FOR THE SUMMERTON SALES 1. Determine the MEAN = 598.4 2. For each value determine the deviation from the MEAN: SCORE MEAN SCORE - MEAN (SCORE-MEAN)2 250 589.4 -339.4 115192 300 589.4 -289.4 83752 350 589.4 -239.4 57312 350 589.4 -239.4 57312 400 589.4 -189.4 35872 400 589.4 -189.4 35872 400 589.4 -189.4 35872 450 589.4 -139.4 19432 450 589.4 -139.4 19432 450 589.4 -139.4 19432 500 589.4 -89.4 7992 500 589.4 -89.4 7992 600 589.4 10.6 112 650 589.4 60.6 3672 700 589.4 110.6 12232 750 589.4 160.6 25792 1000 589.4 410.6 168592 1200 589.4 610.6 372832 1500 589.4 910.6 829192 NB: differences in calculation due to rounding. 3. The differences are squared to get rid of negative numbers 4. The sum of the differences is divided by n-1 to give the VARIANCE: VARIANCE = SUM DIFF/(n-1) = 1907894/18 = 105994 5. The standard deviation is found by the square root of the variance: STD = square root of variance = square root of 105994 = 325.5 DETERMINING STANDARD DEVIATION WITH SPREADSHEET COMMANDS In Excel the STD can be found for both the population and the sample: =STDEV() = 325.5 (sample) =STDEVP() = 316.9 (population) The standard deviation (population) for Williamville is 177.7. Therefore, since 177.7 is much smaller than the STD of 316.9 for Summerton, the Williamville data is much more concentrated around the mean or "less dispersed". Prima facie, we are more confident of the mean value presented by the Williamville data than that for Summerton because there is less variability in the sample.