How does the variance measure the information about the data? Variance measures the amount of information in the data set. How?
Mathematically, the variance is the measure of the variability in the data. So, how this can be explained as a measure of the amount of information in the data? Could you please explain this with a simple example?
I read the following post, here, which makes me confused about, how the variance measures the information about the data? I thought it is just a measure of how the point is far away from the mean.

Say you have a dataset about persons with two features: weight and number of eyes. Which of these two features do you think is more informative for describing persons, i.e. given a data point, which feature makes it easier for you to identify the person it represents?
Here, given enough data, weight will have a much greater variance than number of eyes, whose variance will be close to zero. Therefore, we can conclude that weight is more informative than number of eyes.
