Galton does give one example where he can ranks the abilities of mathematics students as represented by their scores on the Cambridge tripod examinations. He provides data for the top 100 scores in two years of the tripod. We will analyze this data as say a person has score 1 if raw score is in the range 500-1000, score 2 if it is between 1000-1500, etc with the highest score 15 being a score between 7500-8000. Then from his data we have:

Scores |
Number with given score |
Probability
(percent) |

1 |
74 |
42.1 |

2 |
38 |
21.6 |

3 |
21 |
11.9 |

4 |
11 |
6.3 |

5 |
8 |
4.6 |

6 |
11 |
6.3 |

7 |
5 |
2.8 |

8 |
2 |
1.1 |

9 |
1 |
0.6 |

10 |
3 |
1.7 |

11 |
1 |
.05 |

12 |
0 |
0 |

13 |
0 |
0 |

14 |
0 |
0 |

15 |
1 |
.5 |

total |
176 |
100 |

From the table we can see that the distribution of the scores is highly skewed. The mean score is 2.72 so there are only 2 scores less than the mean and 11 greater than the mean. Here is a bar chart of this frequencies of the scores:

and a scatterplot of the log of scores and the log of the frequency of those scores.

This suggests that the distribution of the number of students with a particular score can be described by a Lotka distribution with a = 1.77.