Calculating an unknown total with the percentages

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ichbi

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Hello, I'm working as a teacher on a secondary school. Unfortunately, I teach no math, so I need your help with this case:

One of my students did a survey for her research project about discrimination on the Dutch labor market. However, the results were wrong. Why is that? She told that 100 people responded on the survey. She asked them all about their gender. 61.3% are female and 38.7% are male. Since every person is 1%, it is not possible to get the numbers behind the dot. Skipping the question was no option, they really had to choose one answer.


In addition to the 61.3% and 38.7%:
She also asked: Where are you from?
29.0% said Netherlands
12.9% said Marocco
6.5% said Turkey
3.2% said Latin-America
6.5% said Germany
41.9% said somewhere else

Later on she asks:
Were you ever a victim of discrimination?
29.0% said yes
71.0% said no.

Idk if this information also helps to find the answer.

So my question is; is it possible to calculate the amount of total respondents? How do you do it? I like to know how many people responded to her survey. Thank you!

Note: I think the student is cheating.
 
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Let x be any positive number. If the student surveyed 100x people and 61.3x were female and 38.7 were male then the results would be that 61.3% of the people surveyed were females and 38.7% were males.

But you bring up a good point that x can't be 1 since that implies that exactly 100 people were surveyed and that is not possible.

What about x=10? Then there would have been 1000 people surveyed with 613 being females and 387 being males. You would be happy with that!

But the question is can there be other values for x?

I'll let you decide on that. Can x=200? How about x=50? Does the fact that the greatest common factor of 613 and 387 is 1 help you to find x values that will work?
 
I'm sorry, I still have no clue, I tried everything in my Excelsheet ):
 
It is not a simple thing. I ALWAYS ask for the sample size when anyone presents any such information. Reconstruction from multiple roundings is not an exact science. There are many solutions.

1) The fact that the results are reported to 3 decimal places suggests immediately that 1,000 is plausible. Too many? Unlikely?
2) There are 6 categories, so there must be at least 6 respondents.
3) To get a value so low as 3.2%, there must be in the neighborhood (rounding prevents precision) 1 / 0.032 = 31.25 respondents. News flash! 31 works - giving 9, 4, 2, 1, 2, 13 in the respective categories. This MUST mean that 62 will also work. So also, 93, 124, etc.
4) Somewhat oddly, 1,000 is NOT a multiple of 31. This is just a rounding problem.
5) Any solution noted here is pure luck.
6) Since Netherlands = 0.29 and Victim = 0.29, obviously 31 respondents will work for the victim question.
7) 31 respondents also works for the Male/Female question
8) Never let another student get away with failing to report the sample size.
9) Somewhat oddly, 0.387 Male = Netherlands + Germany + Latin America = Netherlands + Turkey + Latin America

31 seems plausible.
 
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