I've been told that the above summation is wrong because the part to the right of the summation has to be some function of K.
The expression I want to show is if n is 100 (people) add together z (their age) and divide by q. If I can't use z is there a way to say "I want to use K to get z"?
Or if I have got this completely wrong what other expression can I use?
If the age of the $k$th person is $z_k$ (for example, you might have $z_1=27, z_2=35, z_3=5, \ldots, z_{100}=65$), then adding the ages of all and dividing by $q$ can be written as $$ \frac{\sum_{k=1}^nz_k}{q}\qquad =\qquad \sum_{k=1}^n\frac{z_k}{q}\qquad=\qquad \frac1q\sum_{k=1}^nz_k.$$
You could write $$ \sum_{k=1}^n \frac{z_k}{q}. $$ This is the same as $$ \frac{z_1+z_2+z_3+\cdots+z_n}{q}. $$ This allows the $n$ ages to be different from each other.
One could also write $$ \sum_z \frac z q, $$ and then the different values of $z$ are different, just as the different values of $k$ are different in the sums above. This form does not explicitly say how many terms are added.
In mathematical notation, you shouldn't treat the lower-case $k$ and the capital $K$ as the same thing.
