eli5: what does ‘positive skew’ and ‘negative skew’ mean in a case such as test scores

Question

i understand that it means the mean was either higher/lower than the average. i think. but what does that MEAN like why does it matter??? help

In: Mathematics

Answer 1

Any group with a distribution of values (such as test scores) can be described by a thing called ‘moment analysis’. basically:

Average value of x is the mean

Average value of x^2 is the variance*

Average value of x^3 is the skew*

Average value of x^4 is the kurtosis*

and after that we stop naming them

A lot of our statistical techniques start by assuming that mean and variance are the only two non-zero moments. A group of test scores having significant skew means that we can’t really use those statistical techniques

*The actual formulas are a bit more complicated than that, but it’s close enough for ELI5