Question

conception clear up about sample variance

1. I heard that when the n is getting bigger, then the sample variance will be zero. I don't understand here,variance means the distance between the mean and the data value , in here does the mean is sample mean or population mean???

2. if the sample variance is 0, then all the data value will be same as the mean???

I am so confused, because how could that be possible, if we have large sample size n then, variance will be zero and all the data value will be same as the true mean?

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Answer 1

The mean used is sample mean while calculating the variance.

when the n is getting bigger, then the sample variance will be zero this hold for very large n that is some Millions of sample.

So, the assumption about the sample is that most of the sample values are close to each other where as teh population values are very far.

So, when sample values are closer the numerator is small and with large value of n ( in Millions ) then denominator is very large hence the value of variance is almost zero It is never exact zero it is approaching to 0 ( iit might be 0.0000001 ) but not exactly zero.