Show average value for time period

[CognosUser111]

Dear Cognos Community,

I want to model the following in Cognos Framework Manager:
I have a table which looks (simplified) like this:

PERSON_ID     MONTH      AGE
1                      1              19
1                      2              19
1                      3              20
1                      4              20
1                      5              20
1                      6              20
1                      7              20
1                      8              20
1                      9              20
(and no more entries for person '1').

So each row represents a person and a month and in this month, the person has an age. The age changes over time (as here).
Now, the user wants a report which answers the following question:
"Given a time period (a year, month or quarter), how many persons have which age?" For a quarter or year, the age of a person is defined as the average age within this period(rounded).
So person 1 is 19 in months 1,2 and afterwards 20. Person 1 is 19 in Quarter 1 and afterwards 20 and is 20 in the whole year.

So the user could want to create a report on a year basis. Then the expected result for our small table should be:

NUMBER OF PEOPLE      2020
age 19                              0
age 20                              1

Or on quarter basis:
NUMBER OF PEOPLE    Q1  Q2 Q3 Q4
age 19                         1    0   0   0
age 20                         0    1   1  0

Or monthly:
NUMBER OF PEOPLE    J  F M A M J J A S O N D
age 19                        1 1 0 0 0 0 0 0 0 0 0 0
age 20                        0 0 1 1 1 1 1 1 1 0 0 0

The time dimension and the age dimension is already modelled. Also the number 'NUMBER OF PEOPLE' (which counts distinct PERSON_IDs). But I don't know how to model the thing with the average age. I cannot simply take the average age per person, because then I would disregard the entries where Person 1 is 19 in Q1 (as in total, the average age is 20).
I am pretty sure I cannot model this in the database  (as the desired result depends on which time period the user wants to see in their report).
I would like to model this in Framework Manager -- write a filter like AGE = _round(average[Age] for [PERSON_ID], [TIME_DIMENSION]). But I don't know how to do this as this time_dimension is dynamically.

Note that "NUMBER OF PEOPLE' is used in our model in many other situations which do not involve the age. So, I would rather like to change something in the defintions of the dimensions, not in the definition of "NUMBER OF PEOPLE'.

Thanks in advance!