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I have a set $A$ that consists of 5 million objects. Each object has a color, size and cost. I'd like to do a cluster analysis, e.g. K-means, on cost. However, it is computationally not feasible to use all 5 million objects to do the analysis.

I have 2 options:

Option 1: Someone else performed a stratified random sample of the set $A$ on color and size. I can take that sample and do my cluster analysis.

Option 2: Perform a simple random sample of size $k$ on the entire set $A$ and then do my cluster analysis on the simple random sample.

My question is from a statistical standpoint, i.e. bias, consistency, etc. is their a preference between options 1 and 2? In other words, is expected that I should get different results from the two options. If I cluster into 2 groups, perhaps with option 1 I'll get $10$ as the dividing point between the clusters and with option 2, I'll get $40$ as the dividing point.

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Stratified random sampling should give you better performance in accuracy. There is no way of knowing how much better without seeing your data. The following table, from Chapter 5, "Choosing The Type of Probability Sampling", is a good summary of comparing the two options (i.e. simple random sampling versus stratified sampling):

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