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I created a $k$-means with 3 clusters. Some of the variables had a big scale, so I used a $z$-score to standardize them. The others (mostly dummies), I left as is.

Now, when I create the table of all variable centers for each cluster, obviously the ones I standardized are still expressed in the $z$-score format. The others are in their non-standardized state.

So, how do I interpret the $z$-scored centers into a practical meaning (lets say I had normalized income, and its standardized center was -1.2). Do I convert that -1.2 back into something? Is it directly interpretable?

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If all you are doing is describing the clusters, then I see no reason you can't simply undo the z-score transformation. E.g. -1.2 would convert to 1.2 standard deviations below the mean. Recognize, though, that your clusters would have been different had you not standardized and make that clear in the write up.

You might even give both the standardized and unstandardized values, for clarity on this point.

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  • $\begingroup$ yes, that is essentially what I want to do is to "describe" the cluster to some marketing folks. Well, I can't tell them that people in Cluster One have a average income of -1.2 on a z-scale. So how "inaccurate" would I be to convert that -1.2 back into -1.2sd of the mean, and say this cluster has an average income (of say) $42,000? Am I making too much of a leap with this? $\endgroup$
    – mylesg
    Feb 1, 2014 at 21:37
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    $\begingroup$ It's not inaccurate at all. $\endgroup$
    – Peter Flom
    Feb 1, 2014 at 21:48

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