SciForums.com > Science > Physics & Math > Standard Deviation PDA View Full Version : Standard Deviation Post ReplyCreate New Thread JOHN.B02-18-03, 02:50 PMWhat does standard deviation show... and how do you compare it together? What does a SD of 0.54 and an SD of 0.77 mean?? thanks john Crisp02-18-03, 02:59 PMHi John.b, To interpret the standard deviation, you can best look at its definition through the variance: Denoting the standard deviation by s and the average operation by E(-), we have that: Variance s2 = E[ (X - E(X) )2] In words: the variance is the average, squared deviation from the mean E(X). Taking the square root of this expression gives you the standard deviation: S.D. s = sqrt( E[ (X - E(X) )2] ) which you can interpret as the "average deviation from the mean". In words: the standard deviation tells you something about "how widely spread" a distribution is (if the standard deviation is large, then the distribution gives the most weight at points that are far away from the mean E(X) ). Bye! Crisp zanket02-18-03, 03:42 PMAn example of “how widely spread”: The standard deviation of the set {1, 2, 3, 4, 5} is 1.6, whereas the standard deviation of the set {2, 3, 3, 3, 4} is 0.7. The sets have the same mean (average), 3. Jim Osborn02-19-03, 10:16 AMHi John, If you have an experiment, as in a laboratory project, with several independent observations of the same phenomenon and each is characterized by its own experimental variance, then the "weighted mean" value is , statistically speaking, better than any other. I.e., the relative "weight" to be multiplied by each independent "mean" is its 1/sigma-squared. Cheers, Jim RDT202-19-03, 11:34 AMOriginally posted by JOHN.B What does standard deviation show... and how do you compare it together? What does a SD of 0.54 and an SD of 0.77 mean?? thanks john Usually applied to some quantity that follows a 'bell-curve' or 'normal distribution', eg the height of the adult male population, the standard deviation shows how sharp the bell-curve is. About 68 percent of such a population will lie within one S.S of the mean (above or below), 95 percent within 2 S.D, etc. It has many practical applications, e.g you might choose to design an aircraft seat to fit 2 S.D of the travelling public. Conversely, you might choose aircrew that lie within one S.D of the mean and so make their seats cheaper to produce. Cheers, Ron. Post ReplyCreate New Thread