Sampling frequency for any Continous Signal on a Time Interval

While learning about Sampling Frequency I came across two definition

First :

The sampling frequency in a given time interval represents the number of samples taken per unit of time during that interval.

Second :

It is Reciprocal of Sampling Period(1/ Sampling Period). Where Sampling Period is the time taken between two consecutive samples.

So for Instance we are having Samples at time t=[0, 25, 50, 75, 100] in the time interval 0 - 100

Going by the first definition :

Sampling Frequency = (No.of Samples)/ (Time Interval)
                   = 5/100
                   = 0.05 Hz

By Second definition :

Sampling Period = 25

Sampling Period = (1 / Sampling Period)
                = 1/25
                = 0.04 Hz

Now I am confused out of both, which one is correct? And what it actually is Sampling Frequency over a Time interval and how does it changes with it..?

Solution

The second one seems correct. You cannot include both the first and last samples to find the total interval. Choose either one and your calculation will be OK (4/100). To understand this another way, think of a data point being representative of an average time interval, eg what happens between t=12.5 and t=37.5 is encapsulated in the data point corresponding to t=25. Then it becomes clear that your data is basically giving you information from t=-12.5 to t=112.5, in which case you also get the correct answer (5/125)