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

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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

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

It is a way of describing the distribution of scores. A positive skew means the people scoring below the mean score tend to be close to the mean while some people had scores far higher than the mean. A negative skew means the opposite.

If there is a positive skew, adjusting the “passing” grade down a “little bit” from the mean allows a lot more students to pass. This also tends to happen if a test had, say 7 questions – 3 fairly easy, 2 average and 2 very difficult. Most students at least get the 3 easy ones correct but only a few students get all of them right.

It is useful to design tests this way because, it gives the “average” students a fair chance of passing while allowing the assessor to determine who are really the top/best students.