Can anyone explain what standard deviation and skewness are?

Question

I'm a social sciences master's student on an introductory course to statistics - if you can give me the name of a really good site that deals with statistics in plain English for dummies, you'll make me one happy person!

Answer 1

To put it simply, the standard deviation is a way to show how spread out the numbers are from the mean. If most of the data is close to the mean, the standard deviation will be much smaller than if the data is spread out over a larger range. Wikipedia gives a decent explanation in fairly easy terms.

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


Skewed results are results that cluster to one side or the other of the results. For example, if you give a test and all the grades are 50's, the results are skewed to the low score side. If you give a survey rating a movie, and almost all the results are "1" worst movie ever, the frequency graph, or data will be skewed that way. But, if most of the results fall in the middle, it would not be called skewed, to be skewed it has to fall towards one of the ends or sides. Or in other words, the data will lean towards one side or the other.

http://davidmlane.com/hyperstat/A11284.html

Answer 2

I'll answer what standard deviation and skewness are, and you'll probably get other answers with web sites:

standard deviation: a measure of the variability of the data, expressed as the average sum of the squares of the distance of each point in the dataset from its mean.

simple example: three numbers 2, 3, 4. mean= (2+3+4)/3 = 3
std = (2-3)^2 + (3-3)^2 + (4-3)^2 divided by three = 2/3.

Note this answer would be larger if numbers were further away from the mean of 3.

The reason they are each squared is because the non-squared version would always sum to zero, so the squares are used and the larger the standard deviation,the larger the variability of the data.

skewness is a term describing the non-symmetry of a bell shaped distribution. skewed right is when too much data is on the left side of the curve, skewed left is when too much data is on the right side of the curve. Skewness is important to know because it can create some inaccurate estimates of means and standard deviations of data expected to be symmetric - like a normal distribution. Best explained using some visual graphs though.

Takes awhile to explain all this but I hope the example helps.

Answer 3

the standard deviation just gives you a measure of how spread out your data is. for example: the mean of 21,22,and 23 is 22. those numbers are very close together and therefore would have a low standard deviation. the mean of 1,22 and 43 is also 22. because these numbers are much more spread out, the standard deviation would be much higher. the actual number given for standard deviation is the average distance of your data from the mean. also, just as additional information, on a standard normal curve (the z-curve) the standard deviation is used to calculate z-scores and determine percentiles among other things. hope this helps