# How to test if a distribution is symmetric?

How to test if a distribution is symmetric??

Hi all:
To test if a distribution is symmetric or not, I knew we can use the
mean-median == 0
and
skewness == 0
I am wondering if there is any other methods of doing so? Also, which one of them are more sensitive to the data changes please? I mean if I slightly change some data in order to destroy the symmetric, which way is more sensitive to detect the changes please?
Thanks

JasonRox
Homework Helper
Gold Member
Hi all:
To test if a distribution is symmetric or not, I knew we can use the
mean-median == 0
and
skewness == 0
I am wondering if there is any other methods of doing so? Also, which one of them are more sensitive to the data changes please? I mean if I slightly change some data in order to destroy the symmetric, which way is more sensitive to detect the changes please?
Thanks

I would say if the Variance is low then small data change can through everything off. If the Variance is high, data change doesn't really do much since it's already all over the place.

Also, to check if it is symmetric, I would assume if f(x) is your distribution function then f(x)=f(-x) tells us it is symmetric.

D H
Staff Emeritus