94 INHERITANCE IN ANIMALS 



dozen yards more or less ; the difference is too small to 

 matter for most purposes. But if I tell you that English- 

 men are 5 feet 7! inches high, you remember your father 

 who is five feet ten, and your cousin who is over six feet, 

 and you think I am talking nonsense. The discrepancies 

 between various observations of the height of English- 

 men are so great that we cannot replace them by a single 

 statement of this kind without immediate and palpable 

 absurdity. If we want to make a statement about the 

 stature of Englishmen, we must find a way of describing 

 our whole experience ; we must find some simple way of 

 describing our whole experience, so that we can easily 

 remember and explain to others how many men of any 

 given height we find among a thousand Englishmen. 

 We must give up the attempt to replace all our experi- 

 ences by a single average value, and try to describe the 

 whole series of results our observation has yielded. I 

 want to show you how this can be done, and in order to 

 show you, I will choose a kind of experience in which the 

 uncertainty affects not merely a part of the result of any 

 single observation, but the whole of it. 



Suppose I take twelve dice and toss them. I do not 

 know how many will show me more than three points in 

 any one trial ; none of them may show me more than 

 three points, or one, or two, or any number up to the 

 whole twelve may do so. If I make only a few tosses, I 

 can find no sort of regularity among the results ; but as 

 the number of trials increases, I find that the frequency 

 with which each of the thirteen possible results occurs 

 approaches a constant and predicable percentage of the 

 whole number. With my wife's help I have made three 

 independent series of such tosses, each series containing 

 2 12 = 4,096 trials, and here are the results: 



