I have this exercise:
The attached table indicates the result of a survey that was carried out to 2000 people, about whe will be the champion of the 2014 world cup. $$ \begin{array}{|l|c|} \hline \text{Country} & f \\ \hline \text{Brasil} & 545 \\ \hline \text{Alemania} & 500 \\ \hline \text{Holand} & 150 \\ \hline \text{Argentina} & 225 \\ \hline \text{Espana} & 320 \\ \hline \text{Chile} & 260 \\ \hline \end{array} $$ Then, the measures that can be obtained from said table are:
- Only mode.
- Only the median.
- Mode and the median.
- The arithmetic average, mode and median.
- None of the measures mentioned.
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Well, surely I can get the mode that is Brasil.
The average I can not get it, because the data are qualitative variables.
However, my problem is that I do not know if I can calculate or not the median.
I think so, regardless of whether it is qualitative or quantitative variable.
For example,
pink, pink, pink, blue, blue, blue, green
Here there are 7 data, and the data that is in the middle is the first “blue”.
However, the correct answer is “1. Only mode”.
So, why can not I calculate the median?
The question I have for you is, how do you order the different countries in order to compute the median? Alphabetically? What is your rationale for doing that? You could just as easily order them by decreasing or increasing frequency, or by population. The same question applies to your example using colors--why are the data ordered in the way that you have stated?
This is why the median cannot be calculated. The frequency of responses for each category does not tell you anything about how those categories should be ordered.