Defining the 95% of data which are around the mean value

For a given set of data, how can I define which of those correspond to the 95% of the data which are around the mean value?

Answer 1

[Jan]

x = rand(1, 1000) - 0.5;
m = mean(x);
dist = abs(x - m);
[sortDist, sortIndex] = sort(dist);
index_95perc = sortIndex(1:floor(0.95 * numel(x)));
x_95percent = x(index_95perc);

[Giorgos Papakonstantinou]

Thank you Jan. It was easier than I expected. Before your answer I was doing the folllowing:

vals=abs(slope);

[CdfY,CdfX] = ecdf(vals,'Function','cdf');  % compute empirical function

cr=CdfY<0.95;

where vals is my dataset.

Answer 2

[Image Analyst]

I'd sort the data using sort(). Then use cumsum() to get the cdf. Normalize the CDF then go from the 2.5% element to the 97.5% element using find() to find the elements (values) where the data starts and stops. It's pretty easy, but let me know if you can't figure it out.

Answer 3

[Giorgos Papakonstantinou]

Thank you for your answer Image Analyst. The data contain also negative values. I am not sure but I think that poses a problem when I normalize the data after the cumsum.

[Tom Lane]

It sounds like Image Analyst is talking about the cumsum of a vector that assigns probability 1/N to each of N points. However, you could take the 0.025*N and 0.975*N values from the sorted vector directly, converting the index to an integer as you see fit.