Solution to question 3.5
If we first tabulate the number of partners each of the mean and women had we can then calculate the 'average' number of partners for men and women
| Men | Women | |
|---|---|---|
| 0 | 5 | |
| 1 | 3 | |
| 1 | 2 | |
| 3 | 1 | |
| 3 | 1 | |
| 3 | 1 | |
| 3 | 1 | |
| Mode | 3 | 1 |
| Median | 3 | 1 |
| Mean | 2 | 2 |
The problem here is what the survey's authors meant by 'average'. If they were referring to either the mode or the median then it was perfectly possible to have different values for the two groups. 'Average' used without any qualification, however, usually refers to the mean and it would not be possible for the two groups to have different values for the mean unless there was some lying going on or one of the simplifying assumptions we made was invalid.
The key lesson here is to avoid the use of the word 'average' as it is too imprecise. Always let your audience know which 'average' you are using.
