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Good day,

I'm currently trying to figure out if it's possible to calculate the number of people in a certain group, using other known values. Specifically in my case:

If the total population of a state, as well as the number of males, Hispanics and young (18 - 24 years old) are known, is it possible to find the number of people who are all of the three categories (young, Hispanic and male) combined?

My thought process:

My math says yes, but I'm not convinced by it! Let the variables be:

  • $T \equiv$ Total population
  • $N_M, P_M \equiv$ Number, percentage of males
  • $N_F \equiv$ Number of females
  • $N_H, P_H \equiv$ Number, percentage of hispanics
  • $N_Y, P_Y \equiv$ Number, percentage of young people

Is it possible to assume that $P_H = \frac{N_H}{T} = \frac{N_H}{N_M + N_F} \longrightarrow N_H = P_HN_M + P_HN_F$ ??

(If, say, the percentage of hispanics was 30%, can't 20% of them be female and the other 10% be male?)

Continuing assuming the previous stands, then the number of hispanic males $N_{HM}$ is found, $N_{HM} = P_HN_M$

Which means I could find the number of young hispanic males, $N_{YHM} = P_Y N_{HM} = P_Y P_H N_M$

I greatly appreciate your help on the matter!

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If your math checks out (and it seems that it does) it means that you are correct if your assumptions are correct. You are right to not be convinced by math alone, you must also convince yourself that your assumptions are true.

For example, you say that $N_{HM}=P_H *N_M$, but that is only true if being Hispanic and being male are two independent events. If being male means you are more likely to be Hispanic (or vice versa) then your assumptions are false and therefore your answer could be as well (though I think most people would agree that these two events are independent of each other). In this case you would need to use conditional probability in order to calculate the number of Hispanic males.

For your problem I think it is reasonable to assume that your assumptions are correct, but often times in the real world making similar assumptions about independent events in populations can lead to many statistical errors. When designing an experiment or conducting analysis, you should be able to justify your assumptions or at the very least acknowledge the assumptions you are making so that if the results don't align with your expectations/calculations then you can go back and reevaluate your assumptions.

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