is there any concept in statistic that make a variable unit free? I am very amatory in statistic . my question is that is there any concept in statistic that remove unit of a variable? For example suppose I have age and wight, finding the mean of theses two is meaningless for me because they have different units. How I can make them unit free?

One way you can consider is standardizing the random variable.

$$Z =\frac{X-\mu}{\sigma}$$

where $\mu$ is the mean of the random variable $X$ and $\sigma$ is the standard deviation of $X$.