Estimating time cost for sorting algorithm given the average time for sorting of 1000 elements
It is in general impossible to interpolate the running time of algorithms even if you know their asymptotic running time. There are many reasons for this – here are two:


The running time of an algorithm is usually composed of many different terms. For example, it could be of the form $An\log n + Bn$. This running time doesn't scale like $n\log n$, since for small $n$ the $Bn$ term might be important, whereas for large $n$ it might be negligible.
Resource access times do not scale in $n$, but rather jump. When $n$ is small, everything fits into the smallest cache, so data access is very quick. When $n$ gets larger, you need to use a larger cache, so all at once data access becomes slower. When $n$ gets even larger, you need to use main memory (or even beyond), and data access becomes even slower.


In some cases these reasons do not apply. For example, you might be interested in values of $n$ for which one part of the algorithm clearly takes almost all the time, and you can easily estimate how it scales in $n$; and furthermore, memory consumption is minimal so increasing $n$ doesn't result in reduced data access behavior. In such cases it is possible to extrapolate the running time.

An extreme example is when you are estimating some quantity empirically, and $n$ is the number of samples. The running time of such a program scales linearly with $n$.