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.