202 



STATISTICAL TREATMENTS 



no question about the meaning, the simpler expression, w = S x/N, can 

 be used in place of the one above. 



m. = nrip 



Fig. 15-1. A pair of normal curves having the same mean (tn) but different 

 standard deviations (o). 



Another characteristic of the normal curve is an amount of variability. 

 Figure 15-1 illustrates two normal curves with the same mean but differ- 

 ent variability. The deviations from the mean are much greater and more 

 numerous in the lower curve. This relationship is made quantitative 

 by calculating the variance. Each variate differs from the mean by an 

 amount x — m, and those values lying below the mean are negative. 

 The negative signs are eliminated by squaring each deviation. The sum 

 of the squared deviations, divided by the number of such values, yields 

 the variance (cr-). 



o- ^ 



^{x — my 



N 



The square root of the variance is called the standard deviation cr. 



The mean and the variance provide enough information to determine 

 the shape of the normal curve. 



Parameters of samples 



Because the mean m and the variance cr" refer to the normal distribu- 

 tion of the population, they are rarely known precisely. They can be esti- 



