Can some one explain sample variance to me? in simple terms please?

Question

I'm currently taking ap statistics and I don't understand what my text book is saying about sample variance. I understand standard devation but I need to know how to do sample variance.

Answer 1

Sample variance is the SQUARE of standard deviation.

Suppose the expected value for data is 50. If the responses cluster between 45 and 55, the "sample variance" is SMALLER than if the data cluster between 35 and 65.

How far does the data in the sample populatio vary from the expected value = sample variance. the formula for this is:

If is the expected value (mean) of the random variable X,

then expected mean = u = E(X) for ariable X

and

then the variance is

E((X-u) squared))

See:

http://en.wikipedia.org/wiki/Variance

Standard deviation is, in a sense, handier, because the first deviation tells you that 68% of the data is between plus one and minus one deviation and the second deviation tell you that 95% of the data is between plus 2 and minus 2 standard deviations. How far those deviations are from the exected value is very useful information indeed.

Answer 2

For any given set (we are going to call it limitless factors) of data, there is an regularly occurring fee. it fairly is the "actually regularly occurring" of the set. in case you randomly take samples from "limitless factors" (say 2 or greater factors at a time, 20 cases each and every) and regularly occurring them, and chart them, the chart will contain a chain of 20 averages which would be someplace around the "actually regularly occurring". The greater factors interior the pattern (3, 4, 5 at a time, 20 cases each and every, and so on.) the greater you recommendations-set the "actually regularly occurring". In different words, the chart could have further and further numbers nearer and nearer to the "actually regularly occurring" as your pattern selection will improve. The critical minimize theorem means that simply by fact this (charted) "distribution" of numbers gets nearer and nearer to the "actually regularly occurring" simply by fact the style of things interior the pattern will improve, the chart of the averages of any set of samples will look statistically "typical", whether the full set (limitless factors) itself is random or chaotic. This "typical" representation is termed the traditional distribution and is graphically represented simply by fact the classic bell curve. finally in case you took a limiteless style of samples and averaged them you may have via defninition the "actually regularly occurring".

Answer 3

http://www.animatedsoftware.com/statglos/sgssquar.htm
http://www.mste.uiuc.edu/hill/dstat/variance.html
http://www.ds.unifi.it/VL/VL_EN/sample/sample4.html
http://mathcentral.uregina.ca/qq/database/QQ.09.99/freeman2.html