Which of the following sentences is mathematically correct:
- The harmonic mean of a set of numbers is directly proportional to the sum of numbers.
- The arithmetic mean of a set of numbers is directly proportional to the sum of the numbers.
In my opinion, the first sentence is incorrect because, for example, if the sum of the numbers increases twice the harmonic mean does not increase twice. Whereas the second sentence is true.
Am I right? Thanks in advance
A y B are directly proportional if A/B is some constant.
Since your hipothesis, the aritmetic mean $\frac{n_1+n_2+\cdots+n_k}{k}$ isdirectly proportional to $n_1+n_2+\cdots+n_k$, because cocient is constant ($1/k$).