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I only have two variables and they are on the same scale. However, the variance corresponding to the first variable is approximately 0.609, whereas for the second variable is 0.154. So my question is should I standardize the observations (subtracting off the mean and dividing by the standard deviation) or leave it as is?

My professor said if the variables are on the same scale (i.e. measuring the same thing) standardization is not critical, and you could do it if you want to, but it will not have a big effect. However, I think it does have a somewhat significant impact if the variances differ significantly. Though I'm not sure if still is best to standardize or not. Would standardizing cause me somehow lose what the original data was trying to convey or is it the best course of action when applying K-means?

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    $\begingroup$ For what it's worth I ended up doing it both ways and in this particular, simple case the clusters ended up being the same regardless of if standardization was done or not. $\endgroup$
    – Grid
    Commented Mar 30, 2014 at 15:55

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