discrete signals - How to determine, calculate and plot a probability distribution for a given set of numbers?

A device is rotating with a particular wind speed and producing such pulse frequencies in a minute:

24.988 25.224 25.212 25.066 25.310 24.963 24.826 24.944 25.490 25.176 24.740 24.988   
24.994 24.722 24.510 24.863 25.249 24.931 25.218 24.907 25.459 25.292 25.163 25.447 
25.072 25.360 24.976 25.103 25.237 24.845 25.237 25.206 25.109 24.969 24.976 25.194 
25.218 24.975 24.777 24.832 24.564 24.637 24.919 24.931 24.944 24.994 25.378 25.042
25.182 25.151 25.097 25.103 25.030 25.018 24.783 24.722 24.667 24.963    

Is it possible to understand what type of distribution is this and plot it? Each number is the average of frequency for a second.

Each number is the mean pulse frequency for 1 second in Hz. So I want to see how are these frequencies distributed.

Answer

In Matlab that would look like the code below

Since your data set is very small, it'll be difficult to get an accurate estimation of the PDF. The more data you have, the better your estimate can get and the smaller you can make the intervals. To get the actual PDF you'd have to normalize to the interval width.

%% data
x = [24.988 25.224 25.212 25.066 25.310 24.963 24.826 24.944 25.490 25.176 24.740 24.988   ...
24.994 24.722 24.510 24.863 25.249 24.931 25.218 24.907 25.459 25.292 25.163 25.447 ...
25.072 25.360 24.976 25.103 25.237 24.845 25.237 25.206 25.109 24.969 24.976 25.194 ...
25.218 24.975 24.777 24.832 24.564 24.637 24.919 24.931 24.944 24.994 25.378 25.042...
25.182 25.151 25.097 25.103 25.030 25.018 24.783 24.722 24.667 24.963    ];


% create sum suitable bins
bins = 24.5:.1:25.4;
[count, intervals ] = hist(x,10); % 10 intervals;
clf;
bar(intervals, count);
grid('on');