Let's try to keep this simple. Let's say you have the following five age groups that you want to know listening habits for. Each group represents 20% of the audience. Ideally, you get 20 people to represent each age group. No those are not the actual numbers. Hopefully it might be 200 people for each age group. 20 samples is just to make it easy to understand:
12-24 20
25-34 20
35-44 20
45-54 20
55-64 20
100 = 100% of the audience
You send out a bunch of diaries knowing that not all of them will be returned, or that the members of households you send books to may have several age groups represented. The number of books returned from your sample audience look like this:
12-24 15
25-34 17
35-44 18
45-54 22
55-64 28
100 = 100% of the audience
As you can see, some of the age groups are under-represented. Some of the age groups are over-represented. So you take the actual number of books returned and weight them numerically to reach the target percentage. In other words:
For 12-24, 15 books need to represent 20% of the audience.
For 25-34, 16 books need to represent 20% of the audience.
For 35-44, 18 books need to represent 20% of the audience.
For 45-54, 22 books need to represent 20% of the audience.
For 55-64, 28 books need to represent 20% of the audience.
More older people returned books, skewing the ratings for all of the stations. When you weight the actual number of books returned for each audience group to achieve the correct percentage you get a more accurate representation of actual listening. That's why the raw numbers look different. The 12+ numbers are weighted to correct for differences between the number of diaries returned in an age group and the percentage of people they represent.