Standard Deviation and Variance Explained Statistics Class

Tutorial on calculating the standard deviation and variance for statistics class. The tutorial provides a step by step guide.

Category:

Education

Tags:

• standard deviation
• variance
• mean
• statistics
• sum of squares
• GCSE
• GRE

[Scotthawki]

but why is it n-1 to begin with? What's the relevance, or why do we subtract 1 from the sample size? rather than just dividing by n ?

[statisticsfun]

@Scotthawki wow, that is a great question without an easy answer. It has to do with a correction of sample that is potentially biased.

Another way to think about it is If we have a sample of just 1, with n-1 the standard deviation = undefined. Which makes sense, but if we don't subtract 1 then the standard deviation = mean which does not make sense.

This French guy thought this up and his name was Friedrich Bessel (may have been Daniel Bernoulli).

Make better sense now?

[statisticsfun]

@statisticsfun oops... not that it really matters but Bessel was a German mathematician not French.

[Scotthawki]

Why is the denominator n - 1? and not just n ?

[statisticsfun]

@Scotthawki n-1 is used for samples and n is population. Notice as n (sample) size gets large the n-1 does not make a lot of difference.

[pinksnowbeach]

Why does my textbook have the denominator as N and not N-1 in the Variance equation?



[statisticsfun]

@pinksnowbeach Great question, n is for a population and n-1 is for a sample, sooooo... you are more than likely looking at the equation for a population. Also, as the sample gets large the n-1 part becomes less important.

I probably should have been more clear in my explanation in the video and compared and contrasted t n and n-1 -- oh well something to add in another video.

[5COTTx]

when do we use variance in real life? how does a number squared help us? and not just use the standard deviation?

[04lewzale]

beast explantion

[pinksnowbeach]

@statisticsfun Thank you so much! Yeah, I am in statistics for social sciences, so that is why. Had I read the rest of the chapter I wouldn't have panicked. But, oh well, the explanation is much appreciated!!!