32 SUMMARIZATION OF DATA Ch. 2 



quencies, and hence to make the computations somewhat easier. Fol- 

 lowing are the required calculations based on Table 2.42; it is assumed 

 that the scores are necessarily integers. 



z f d f-d f-d* 



92 



2(/) = 1290 2(/-d) = +308 4160 = 2(/-d 2 ) 



By the formulas previously used, 

 ix = 92 4- (308/1290) (15) = 95.6 compared to the true mean of 95.7. 



4160 - (308) 2 /1290 



a = (15) A / = 26.7 compared to the true value of 



\ 1290 261 



In view of the fact that the scores were integers, these approxima- 

 tions certainly would be considered satisfactory, and the time and 

 labor saved by these methods are considerable. 



The distribution of the population of ACE scores is rather sym- 

 metrical, that is, there is a region of high frequency about halfway 

 between the extremes, and the frequency of occurrence of scores away 

 from this region diminishes at about the same rate as scores are 

 considered equally far above and below the region of highest fre- 

 quency. This distribution is shown in Figure 2.41. With this type 

 of distribution the arithmetic mean is an excellent average to use as 

 a part of the description of the population. 



Other distributions may be non-symmetrical, or skewed. For such 

 populations the median often serves as the more descriptive average. 

 As a matter of fact, the difference between the sizes of the arithmetic 

 mean and the median is an indication of the degree of skewness or 

 lack of symmetry, in the frequency distribution. If the distribution 



