A DFT doesn't have any external units inherently associated with it. There are N sampled points in a frame, and you get N output bins from taking the DFT. If the signal is real valued, the upper half of the DFT will be the conjugate mirror image of the lower half. The frequency of a bin is its bin index in units of cycles per frame.
The frequency of a bin in your application, in external units, depends on your sampling frequency, and is easiest understood by following the units in your calculation. The key elements are:
$ N $ the number of samples in your frame.
$ f_s $ in samples per unit time. The unit time is so often seconds that many people memorize these formulas in terms of Hz. This can be confusing because Hz can refer to either samples per second when talking about sampling rate, or cycles per second when talking about tones.
$ k $ the bin index which is cycles per frame.
So the frequency of a bin value is calculated like this:
$$ f_k = k \cdot \frac{f_s}{N} $$
Where the units are:
$$ \frac{cycles}{second} = \frac{cycles}{frame} \cdot \frac{\frac{samples}{second}}{\frac{samples}{frame}} $$
This answers your question, but there is a lot more to understand in order to get meaningful results from a DFT.
Hope this helps,
Ced
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Answers to the comment:
It's all in the units.
Your sampling frequency is
$$ 1 \frac{sample}{minute} \cdot \frac{ 1 minute}{60 seconds} = \frac{1}{60} \frac{samples}{second} $$
So, correct, $ f_s = \frac{1}{60} Hz $
No, your sampling frequency pertains to how often you are taking readings per unit of time, it has nothing to do with how many samples you take.
You can either choose to use minutes or seconds (or hours, days, etc.) for your time scale, and substitute it in the equation above. For instance, if you did your DFT on sixty samples. the most straightforward unit for your frequencies would be cycles per hour. The equation would be:
$$ f_k = k \cdot \frac{60}{60} = k $$
Where the units are:
$$ \frac{cycles}{hour} = \frac{cycles}{frame} \cdot \frac{\frac{samples}{hour}}{\frac{samples}{frame}} $$
So bin 1 would mean one cycle per hour, bin 2 means two cycles per hour, etc.
You are not required to use per seconds, aka Hz.