Sec. 6.2 DISTRIBUTION OF THE SAMPLE MEAN 155 



on a normal population with /a = 60 and a = 10, no one can say 

 what the arithmetic mean of the sample will be ; but a good estimate 

 can be made of its probable size because sample means from such a 

 population will have a frequency distribution over the long run of 

 experience. Therefore, it should be expected that probability state- 

 ments like those previously discussed herein can be made. 



The sample mean, to distinguish it from the unchanging population 

 mean, will be designated by X{, where the subscript refers to the ith. 

 sample. 



The frequency distribution of an approximately normal population 

 with n = 60 and a = 10 is presented in Table 6.21. Six hundred and 

 forty-eight random samples, each containing 10 measurements, were 

 drawn from that population. The arithmetic means of these samples 

 were then computed. The frequency distribution for the 648 sample 

 means also is given in Table 6.21, with the calculated mean (x) and 

 standard deviation (s/) of the X{ being given at the bottom of the 

 table. 



TABLE 6.21 



A Frequency Distribution Table for a Near-Normal Population op 

 Measurements X t , with fx = 60 and a = 10; and the Frequency Distri- 

 bution op 648 Sample Means, Xi, Taken from That Population with 10 

 Measurements per Sample 



Distribution of Population Distribution of Sample Means 



Class Interval / r.c.f. Class Interval / r.c.f. 



H = 60 a = 10 x = 59.98 8 S ' = 3.14 



* This interval was extended by 0.1 to include the remaining measurement 

 in the population. 



