Is the absolute value of $x$ a sufficient statistic to the continuous distribution which is symmetric about $y$ axis

Question

Does the absolute value of $x$ is sufficient statistic to the continuous distribution which is symmetric about $y$ axis? e.g. the standard normal.

Answer 1

The question makes no sense in its present form, since a single distribution, e.g. the standard normal, has no free parameters, and the concept of a sufficient statistic refers to families of distributions with free parameters.

The absolute value $|x|$ is a sufficient statistic for a single sample $x$ from a family of distributions parametrized by $\theta$ if $f_\theta(-x)=f_\theta(x)$ for all $\theta$.