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February 16th, 2018, 11:50 AM   #1
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variance of a sample

I know that to find the variance of a sample, we can use the formula sigma^2/n. I realise that this means that with big samples, the sample variance gets very small and with small samples, it is much closer to the population variance.
I thought I'd test this on random samples of discrete data.
When I picked a small sample (say n=10) I then worked out the mean and variance using the formulas.
I then picked a bigger sample, (say n=50) and expected the variance to be smaller. It wasn't and in fact it tends always to be bigger, allowing for the random nature of the samples. Even when say 10 samples of each are completed, the bigger sample is invariably the one with the bigger variance.
What is going on? Where is my misinterpretation of what is going on here (I'm clearly doing something wrong!)
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February 16th, 2018, 02:06 PM   #2
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