18 



Procedure: 



1. Find the n means of n distributions, X ^, X^, X^. 



2. Assume the mean of the population to equal the average of these means and compute 



= ^ X^+ X^i- X^ ^ci] 



n 



3. Assume that the standard deviation of the means of n yearly distributions is equal to 

 the standard deviation of the population of means of yearly distributions and compute 



-Vi^i 



[20] 



where d is the distance of the m.ean of the sample from the mean of the population. 



4. The mean of any one distribution of c yearly means may take on a range of values 



A' is the mean value of the population, 



a is the standard deviation of the population, 



- k a ~ 



- - A- is a sample of c means of the population, 



A- = A ± L21J ' 



\fc' k is taken from a student's "i!" table at probability level 



0.90 and (c - 1) degrees of freedom, and 



c is the number of distributions required; in other words 



the number of independent observations. 



5. From Equations [18] and [21] obtain 



k a 



^ 



< 0.05 lA. 



Thus, solving for ^Jc, gives 



^ -0.05 A, 



6. Values of c are assumed until Equation [22] is satisfied. 



Example: 



Assume each Weather Bureau yearly distribution to represent one sample. Then, from 



Figure 1 (with ti = 4) _ 



A^ = 7.36 (year 1949) 



A^ = 7.50 (year 1950) 



A^ = 7.40 (year 1952) 



