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# How to get the number of target audience?

Mon 12 Nov, 2018 09:45 am
I am currently working on a project, a sample start-up. Suppose I have these data:

N = total population.

n1 = number of mall shoppers.

n2 = number of people aged from 18-65.

n3 = number of people with smartphones.

The question is how do I get the number of mall shoppers who are aged 18-65 and also have smartphones from the total population of the country? This number would then result to the approximate target audience for my start-up project but I don't know how to get it.
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engineer

2
Mon 12 Nov, 2018 10:11 am
@dwanevalle,
You can't get there from here. If you know that the three populations are independent then you could get a pretty good guess using

n1 * n2 * n3 / N^2

Unfortunately, there is almost certainly an interaction between your numbers. For example, most people between 18 and 65 likely have cell phones.
dwanevalle

1
Mon 12 Nov, 2018 10:14 am
@engineer,
what do you call that formula?
and why is that N is raised to 2?
Thank you btw.
engineer

2
Mon 12 Nov, 2018 03:17 pm
@dwanevalle,
That formula doesn't have a name since I made it up from the data you provided, but here is the derivation. Call it the A2K formula if you must.

The fraction of mall goers in the total population is n1/N.
The fraction of 18-65 year olds in the total population is n2/N
The fraction of cell phone users is n3/N.
The fraction of all three is the product of those three numbers so n1*n2*n3/N^3 assuming they are independent.
The number of people total is that fraction times the total population or n1*n2*n3/N^2
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