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How can I estimate the average for each one of the intervals in an x axis?

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I need a method to split my x axis into intervals and estimate the average for each one of the intervals. The plots are polynomial curves, if that helps.
Any suggestion?
Thank you


Jan on 17 May 2019
The question is not clear yet: It does not make sense to "split the x axis". But if you have two vectors, one containing the x and the other the y values of a curve, you can calculate a blockwise average. So please post, what your inputs are.
Stelios Fanourakis
Stelios Fanourakis on 19 May 2019
Exactly as you stated. Two vectors of X,Y in a 2d plot. I want to define intervals for the X values and average each interval and all together.

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Accepted Answer

Adam Danz
Adam Danz on 19 May 2019
Edited: Adam Danz on 20 May 2019
This is relatively straight forward with histcounts() and splitapply().
% Create fake data
x = randi(1000,1,1000); %doesn't have to be sorted
y = rand(size(x));
% Define the edges of your x data
% There's lots of ways to do this - this is just 1 example.
binWidth = 100; %how wide is each bin?
edges = min(x) : binWidth : max(x);
% determine which bin each x element is in
[~, ~, hbin] = histcounts(x,[edges,inf]);
% Get mean of y within each bin
% Here I ignore NaN values, too.
binMean = splitapply(@(x)mean(x,'omitna'),y,hbin);
To interpret the results, binMean(n) is the mean for all y values where x is greater or equal to edges(n) and less than edges(n+1).
To plot the data, the bins, and display the average values per bin above the axis:
hold on
text(edges+binWidth/2, ones(size(edges)), strsplit(num2str(binMean,.1)), ...
'VerticalAlignment', 'Bottom', 'HorizontalAlignment', 'Center')
% * binMean must be a row vector


Stelios Fanourakis
Stelios Fanourakis on 20 May 2019
Yes indeed. You are magnificent Adam. Very good precision resolving the issue. Well done and thank you very much.
Although the plot comes a bit awkward. How should I margin it to appear properly?
Maybe I should play with axis margins, so I can make it look more like yours
Thanks once again
Adam Danz
Adam Danz on 20 May 2019
Glad I could help.
The 2nd input to text() indicates where along the y axis your labels should go. In my example I simply used y=1 for all labels because my data didn't span beyond 1. You could just do this
ylim([-0.5, 2])
text(edges+binWidth/2, ones(size(edges))*max(ylim()), ......
also, see the "rotation" text property. It might look better to rotate the labels by 90 deg.
Also, to draw the lines across your entire axis,
plot([edges;edges],[min(ylim()), max(ylim())],'k')
Stelios Fanourakis
Stelios Fanourakis on 20 May 2019
Thanks once again for your additional help. Althought, I might keep labels horizontally as they appear 'cause it looks better to me, than rotating them 90 degrees and have a vertical appearance.

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