normal distribution
I have some data samples , used histfit in matlab and did some integrated tests in matlab to test if the data is normally distributed, but i`m not convinced.
I have around 200 values in my sample
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Some cautions:
Symmetry is essential for a normal distribution but an approximate bell shape is not enough to establish normality.
12 data values can sometimes rule out normality fairly convincingly; otherwise the unsurprising advice is that 12 values is a small sample to answer this question. Perhaps you have more data hidden from us.
The best plot to check is arguably not a histogram but a normal quantile-quantile plot, often known as a normal probability plot. Here points would fall on a straight line if a sample were exactly normal. In this case, an informal summary of the fit is "not too bad". A serious advantage of this plot is that no arbitrary decisions are needed on binning and you show all the detail too.
Small print: Common recommendations are
To have unambiguous bin boundaries (which bin would get 1250 if it were a value?)
Never be content with Excel's lousy default of bars that don't touch when your bins do.
What software you have to hand is not really material here as software-specific questions are off-topic any way. But many readers here would advise that you can download R for free, regardless of what your institution has made available to you.
Here is the full quote:
K-means, being an instance of the Gaussian Mixture Model (GMM), assumes Gaussian data distribution [20][26]. It then follows that nearly all inliers (precisely 99.73%) will have point- to-centroid distances within 3 standard deviations ($\sigma$) from the population mean.
It appears in section IV.A.
The application to the Iris dataset, which, as you note, is not normally, distributed, appears in section V ("Experiments").
I do not see a logical problem with first noting an algorithm's properties under certain assumptions, such as normality, and then testing it in cases where the assumption is not valid.
And of course, k-means can be applied to any dataset. Whether it yields useful results is a different matter.
Best Answer
Perfectly normally distributed data is in practice effectively non-existent. While one can manipulate bin widths to show many things or end up with misleading plots, your data does not look normal.
But why do you want to know? If you care about what analysis method to use, then firstly you should not care about the data (i.e. dependent and independent variables), but the regression residuals. Secondly, deviations don't necessarily invalidate a model with normally distributed error terms.