Statistical treatment of football numbers - Lord - 1935 - Article

Professor X sold 'football numbers'. The audience had to have a way of telling which football player was which, so each player had to wear a number on his football uniform. It didn't matter which number, as long as it wasn't more than a two-digit number.

Professor X loved numbers, when tests were made he couldn't wait to put the scores in his back pocket and hurry back to his office where he would lock the door, add the scores up, and then calculate the means and standard divisions for hours on end. Test scores are ordinal numbers, but ordinal numbers cannot be added. So, the professor came to the conclusion that it was wrong to compute means and standard deviations of test scores. This eventually lead to a nervous breakdown and Professor X retired. As an appreciation of his work, the school gave the Professor a 'football numbers' concession.

The Professor made a list of all the numbers given to him, and he found out he had 100,000,000,000,000,000 two-digit numbers to start with. The numbers were ordinal numbers, and the professor was tempted to add them up, square them and to compute means and standard deviations. But these numbers were only 'football numbers', such as letters of the alphabet. The teams brought there numbers to the professor, first the sophomore team, a week later the freshman team, but by the end of the week there was trouble. Information secretly reached the professor that the numbers in the machine had been tampered with. The freshman team appeared in person to complain. They said they had bought 1,600 numbers from the machine and complained that the numbers were too low and that they were laughed at because of the low numbers. 

The professor persuaded the freshman team to wait while he consulted the statistician who lived across the street. Maybe the freshman team got low numbers by chance. The statistician took the list of the professor, added them all together and divided them. 'The population mean', he said 'is 54,3'. But the professor expostulated 'You can't add them!'. 'Oh, I can't..? I surely just did it' said the statistician. 'But these are ordinal numbers, you can't add and divide them!'. 'The numbers don't know that' said the statistician. 'Since the numbers don't remember where they came from, they always behave just the same way, regardless'. And if you doubt my conclusions, I suggest you try and see how often you can get a sample of 1,600 numbers from your machine with a mean below 50,3 or above 58,3'. 

To date, the professor has drawn over 1,000,000,000 samples of 1,600 from his machine and only two samples were below 50,3 and above 58,3. He is happy because he is adding and dividing the football numbers that were given to him.