calling the_g_man....

[hedya]

help needed from a fellow mathematician who has a much wider understanding of stats than myself: when calculating the std dev of a sample rather than the whole population, WHY on earth do I divide by n-1 rather than n? I know it's a newbie question, but I avoided stats like the plague all of my life, and now I'm forced to teach it... I'd like not

Comments

[the_g_man]

Okay, I'll see what I can do...

Intuitively, it is because the smaller the sample the less likely you are to see an extreme outlier. Therefore a smaller sample will tend to underestimate the mean distance from the mean for the whole population.

More technically, it is because the expected mean-difference-squared is a biased estimator for the variance.

If you want to do the working on this my hint is,

[ Xi - m(X) ] = Xi - (1/n)*(X1 + X2 + .... ) = (n-1/n)*Xi + (1/n)*X1 + ... (1/n)*X(i-1) + (1/n)*X(i+1) + ...

Hopefully, that's some help - although perhaps not a lot.

[the_g_man]

...although the +s should be -s in the last term. Doh!

[hedya]

thanks for this. I'm munching on it, and I think I'm beginning to see some light. Still can't see why it relates to degrees of freedom and why do we loose one with the sample but not the population..... Are you going to enlighten me further, Oh Master of Stats ? :P
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