I'm investigating survey data where participants are asked to answer based on a scale of 1 to 10
typically, the average is around 8.5 with most responses between 7-10, with a lower numbers like 3 scattered around
what is the best way to describe the distribution since it's skewed? I would stay away from using standard deviation since it's clearly not normal, but obviously some are distributed differently than others and I would like to quantitatively capture that
You're looking at a multinomial distribution I think. Since you can look at each number 1-10 as a different category, and each category $p_k, k=1,...,10$ gets a particular probability, it definitely sounds a if we are dealing with the multinomial distribution.
We know it is not normal since it is a discrete distribution. But multinomial discrete has the multivariable normal as its counterpart in the continuous case.
http://en.m.wikipedia.org/wiki/Multinomial_distribution