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I know how to calculate percentage; but the reason I am posting this question is, I might have misunderstood the question itself.

We have the following question from research methodology:

In a survey of students involving the following variables: Student Name, Age, Gender, Height, Weight, Eye color, Hair color, and Marital status.

What percentage of the survey variable cannot be deduced by observation?

  1. $25\%$
  2. $\approx 30\%$
  3. $\approx 40\% $
  4. $50\% $
  5. $\approx 60\% $

It is clear that qualitative variables in the above set with the length of $5$ (say $L_1$) are:

Qualitative$=\{$Student name,Gender,Eye Color,Hair Color,Martial Status$\}$

While Quantitative$=\{$Age,Weight,Height$\} $ with the length of $3$ (say $L_2$). So total variables we have is $8$.

Now we can represent different percentages, for example:
$$\frac{L_1}{L_2}=\frac{3}{5}$$

which is actualy $60$% ,it means that number of quantative variables is $60$% of qualitative variables, also we can calculate $\frac{3}{8} \times 100=37.5\%$, or by taking two of quantitative variables and four qualitative it is $\frac{2}{4} \times 100=50\%$, or it can be $\frac{1}{4} \times 100=25\%$.

So I think $\approx 30\%$ is the correct answer. Or maybe I have not understood the question correctly?

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Can you edit your question such that it becomes readable? Maybe you are no native speaker, but you could at least do proper punctuation. –  Konstantin May 4 '12 at 13:36
    
thanks @ Konstantin for advice,i will try sure –  dato datuashvili May 4 '12 at 13:46
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1 Answer

up vote 3 down vote accepted

I don't think Qualitative/Quantitative has anything to do with it. The question is, what percentage cannot be deduced by observation? Can you deduce someone's height by observing the person? Sure. Can you deduce someone's name by observing the person? No, not in general. So, how many of the 8 can you not deduce by observing the person?

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so if it is a question,by observing person,i can't deduce martial status yes? –  dato datuashvili May 4 '12 at 13:40
    
now i think that 25% is correct answer –  dato datuashvili May 4 '12 at 13:44
    
am i right?after observing person,i may reduce hair color,eye color,age,weight,gender,only two name and martial status i can't reduce,so 25% is right yes? –  dato datuashvili May 4 '12 at 13:58
    
any idea about this? –  dato datuashvili May 4 '12 at 14:16
    
I think the question is ambiguous. Certainly you can't deduce name and marital status by observation. Can you deduce gender? I'd say that depends on what you are allowed to observe. Can you deduce age? Well, you can deduce something about age, but you probably can't tell a 24 year old from a 26 year old. Still, if I had to give an answer, I'd probably go along with your 25 percent. –  Gerry Myerson May 4 '12 at 23:05
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