# How do I find the most stable N consecutive numbers?

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Ali Almakhmari
on 17 Feb 2024

Commented: William Rose
on 17 Feb 2024

##### 0 Comments

### Accepted Answer

William Rose
on 17 Feb 2024

How about this:

x=rand(1,2500);

n=50;

stdx=zeros(1,length(x)-n+1); % allocate array for stdev(x(i:i+49))

for i=1:length(stdx)

stdx(i)=std(x(i:i+n-1));

end

[y,idx]=min(stdx);

fprintf('Minimum st.dev. segment with length %d starts at index %d, s.d.=%.3f.\n',...

n,idx,stdx(idx))

Good luck.

##### 2 Comments

William Rose
on 17 Feb 2024

The st.dev. for the the uniform distribution, with width 1, is 1/sqrt(12)=0.289. You can plot the st.dev. as a function of segment position within the vector:

x=rand(1,2500);

n=50;

stdx=zeros(1,length(x)-n+1); % allocate array for stdev(x(i:i+49))

for i=1:length(stdx)

stdx(i)=std(x(i:i+n-1));

end

[y,idx]=min(stdx);

fprintf('Minimum st.dev. segment with length %d starts at index %d, s.d.=%.3f.\n',...

n,idx,stdx(idx))

plot(1:length(stdx),stdx,'-b',idx,stdx(idx),'r*')

hold on; grid on;

yline(1/sqrt(12),'--g',Linewidth=2)

xlabel('Segment start position'); ylabel('St.Dev.')

title(['St.Dev.(segment with length ',num2str(n),')'])

legend('st.dev.','minimum','expected s.d.')

OK.

William Rose
on 17 Feb 2024

### More Answers (1)

John D'Errico
on 17 Feb 2024

The mean difference? What is that exactly? In terms of mathematics?

Are you looking for the 50 element consecutive subset with the smallest standard deviation? Or perhaps the smallest maximum absolute deviation from the local mean? I could argue for either of those definitions, based on your question. I'm sure you may be thinking of something completely different, as I always seem to get these things wrong.

The smallest standard deviation is trivial. Download my movingstd utility from the file exchange. It will compute a sliding window standard deviation. Take the smallest, and you are done.

In the second case, I would compute a local sliding mean for a window of width 50. This is most simply done using conv. Now find the element in each sliding window that is maximally different from that sliding mean. This will not be difficult to do.

But again, I can't even guess what your real intent is here. So, what do the words "mean difference" describe in your mind?

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