High school Math: Finding the Median

Question

I have a problem trying to understand the following two questions:

In question 1, the median is found at the 50% of the total group. However, this strategy doesn't work for question 2. Why?

Answer 1

1) Order the percentages from Group 2 in ascending order.

3%, 4%, 5%, 6%, 10%, 11%, 21%

2) As there are 7 terms, The median will be the 4th term (6%)

3) 6% of 400 people in group 2 = 24 people

Answer 2

In question 1, median is found at the 50% of the total group. However, this strategy doesn't work for question 2. Why?

They're totally different questions. Question 1 asks for the "median area" (i.e., the median of the original variable), whereas Question 2 asks for "the medians of the numbers of people in group 2". I might opine that Question 1 has real-world application, while Question 2 is made-up busywork, and it's not even phrased correctly.

For Question 1, all of the 8000 apartments have a quantitative value for area, and if they were listed in order, the median would be at or close to the 4000th entry in the list; that is, after counting 50% of the list. Since the classes in the table are numerically increasing, we can use this to effectively count off the first 50% of the data and see which class it must fall in (namely after accounting for 5% + 18% + 23% + 4%, which puts us in the 4th class as indicated). This is something that can be practically useful; deducing the median of a data set when not all of the data is on display.

But in Question 2, the variable for the people in the study is a qualitative ailment, "Asthma, Hay Fever", etc. No median exists for such a data set, and also the classes are not in increasing value order (as they are non-numerical), so it doesn't even vaguely resemble Question 1. Instead, the questioner is simply drawing attention to the table of percentages for Group 2 and asking for the median of those numbers in the table, assuming they were converted from percents to raw counts -- not the median of the original variable (which doesn't exist). I can't think of how this would be useful statistically; it's just a made-up exercise with some found numbers. So in this case the question requires that you convert the listed percents to counts ($21\% \times 400 = 84$, etc.), sort those numbers, and take the middle value in accordance with the definition of the mean.