Median Question

Question

Suppose that the median age of 45 directors is 41, the median age of 85 art directors is 65, and the median age of 325 school teachers is 40. Could you obtain the overall median age for all of them? Calculate it or explain why not?

Answer 1

You would need more information for this to be solved.

For instance the median age for ARL is 51 you had 50 ppl which means person 25 + person 26 equals 102/2=51....What this hides is that the other 48 people could also be 51 years old as well. The same arguments can be made for public library directors and librarians.

Answer 2

HINT: Consider the following example.

The median of the $3$ numbers $4,5$, and $6$ is $5$, and the median of the $4$ numbers $7,8,8$, and $9$ is $8$. The median of all $7$ numbers is $7$.

The median of the $3$ numbers $1,5$, and $6$ is again $5$, and the median of the $4$ numbers $2,8,8$, and $9$ is again $8$, but the median of the $7$ numbers $1,2,5,6,8,8$, and $9$ is $6$.

And $6\ne 7$.

Answer 3

It's impossible to find out the overall mediaan. To illustrate this, imagine two extreme situations:

1)

All ARL library directors are 51

All Public library directors are 62

All School librarians are 44

This situation has the required medians and the overall median would still be 44 due to how many more school librarians there are when compared to the other categories.

2)

All ARL library directors are 51

All Public library directors are 62

The first 217 school librarians are 1, the 218th school librarian is 44, and the remaining school librarians are 152.

This set-up also has the same medians as you described, but now all the ARL library directors and public library directors slot above the median of the school librarians, forcing the median above 44, which is the age of only one librarian.

So these two situations have the same medians for each group but a different overall median, meaning that the medians of the individual groups is not enough to know the median of the overall group.