It was this realization that led me to examine the distributions of available 

 samples of hominoid cranial capacities for symmetry or skewness (Tobias 

 1968b). 



Moderately asymmetrical or "skewed" distribution curves have been 

 defined by Simpson, Roe, and Lewontin as "those in which the highest 

 frequency is definitely not near the ends of the distribution." They con- 

 tinue: 



. . . skewed curves in which the right-hanil limb tapers off more gradually than 

 the left-hand limb, hence in which the class with highest frequency is below the 

 middle of the distribution, are said to be positively skewed, or skewed to the right. 

 Similarly, those with the left-hand limb longer and the class with highest fre- 

 quency above the middle are negatively skewed, or skewed to the left. [Simpson, 

 Roe, and Lewontin ig6o, pp. 54-55] 



Without access to most of the original data, it has not been possible 

 to determine the position of the class with highest frequency (mode) in 

 the gorilla and most other hominoid samples. Had the raw data been 

 available, it would have been possible to use the coefficient of skewness 

 based upon the standardized distance between the mean and mode (ibid., 

 p. 143). Since the mode is not known for most of these hominoid samples, 

 nor the median (from which the mode could be approximated by the for- 

 mula, mode = 3 median — 2 mean), it has not proved possible to assess the 

 coefficient of skewness in the present study. 



Resort has been had to an alternative method that, it is suggested, 

 yields an approximate answer to the question of how symmetrical or how 

 skewed the distribution is. The symmetry of the distribution curve has been 

 tested by comparing the highest with the lowest values in the sample. For 

 each sample, the extreme values have been expressed in terms of their devia- 

 tions from the mean, both in absolute units and in standardized units (devia- 

 tion divided by the estimated standard deviation of the sample mean). The 

 degree of symmetry or skewness has here been assessed by comparing the 

 absolute and standardized deviations of the highest value with those of the 

 lowest value and adding the algebraic sum of the two deviations (Table 12). 



The data recorded by Vallois (1954) for the gibbon showed so marked 

 a skewing as to suggest not a normal or Quetelet distribution but a T-shaped 

 distribution. Thus, Vallois's published mean of 89.3 c.c. is only 2.3 c.c. 

 greater than his stated minimum value of 87.0 c.c. for a sample of 86 crania, 

 while the higher values range right up to 40.7 c.c. greater than the mean. If 

 correct, these figures represent so extreme a departure from the patterns of 



& 50 



