My Math Forum Sample Variance

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 February 16th, 2018, 10:58 AM #1 Newbie   Joined: Feb 2018 From: UK Posts: 4 Thanks: 0 Sample Variance Just realised that I have posted a question in the wrong place, so here goes again with a 2nd post which hopefully now is in the right area. 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!) Thanks JJ
 February 16th, 2018, 01:05 PM #2 Global Moderator   Joined: May 2007 Posts: 6,527 Thanks: 588 It would be helpful if you would write the formulas you are using.
 February 17th, 2018, 03:40 AM #3 Newbie   Joined: Feb 2018 From: UK Posts: 4 Thanks: 0 Sorry This is what I used mean=sigma x / n var = sigma x^2/n - mean^2 but I also did them using the stdeva( ) function in Excel
 February 17th, 2018, 04:54 PM #4 Global Moderator   Joined: May 2007 Posts: 6,527 Thanks: 588 The formulas you are using give you estimates of the mean and variance of the underlying distribution. For large n these will converge to true mean and variance. I am not familiar with what Excel is doing. However if the variance gets smaller, I presume it is calculating the variance of the sample mean. This is the variance you have divided by n.
 February 18th, 2018, 09:52 AM #5 Newbie   Joined: Feb 2018 From: UK Posts: 4 Thanks: 0 Thanks for the explanation

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