# Getting a percentile from a histogram

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Gurpreet Kaur on 9 Feb 2023
Commented: Jeff Miller on 10 Feb 2023
Let's say I have a large dataset which I have plotted on to a histogram with some given BinWidth. How would one let's say... get the 95th percentile from the data provided only by that histogram, and NOT the large dataset?
The reason I ask only from the data provided provided from the histogram itself is because I wish to test how changing the BinWidth can also change the value of the percentile.
Any help is appreciated!

Jeff Miller on 9 Feb 2023
Usually this is done by linear interpolation within the relevant bin. To stick with your 95th percentile example, suppose you have a bin of scores from 20-30 and you know from the other bins that 90% of scores are less than 20. If there are 8% of scores in the 20-30 bin, then 30 is at the 98th %ile. So, the value at the 95th %ile is estimated to be x95 = 20 + (30-20)*(95-90)/(98-90).
Gurpreet Kaur on 9 Feb 2023
Hmmmm is it possible you can provide some sort of example code so I can understand a bit better? The "large set of data" can just be generated randomly.
Jeff Miller on 10 Feb 2023
samplesize = 1000;
targetpctile = 65;
lsd = randn(samplesize,1); % large set of normal(0,1) data
binedges = -10:0.01:10; % make sure this covers the whole data range
bincounts = histcounts(lsd,binedges);
bincumpcts = 100*cumsum(bincounts)/samplesize - 0.5/samplesize;
relevantbin = find(bincumpcts>=targetpctile,1);
% Note that the relevant bin in binedges goes from binedges(relevantbin) to binedges(relevantbin+1)
startxat = binedges(relevantbin);
binsizex = binedges(relevantbin+1) - startxat;
startpat = bincumpcts(relevantbin-1);
binsizep = bincumpcts(relevantbin) - startpat;
pctileest = startxat + binsizex * (targetpctile - startpat) / binsizep;

Image Analyst on 10 Feb 2023
Try this
histObj = histogram(data)
Now look at all the properties of the histObject. Also use this function to get the CDF: cumsum
Jason on 10 Feb 2023
Hello Professor, I find that you have a deep understanding of MATLAB image processing, and could you please help look at this problem？I'd appreciate it a lot!

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