Why is the center of data important? I have recently begun learning statistics along with Python with the Anaconda IDE and started a Machine Learning course by Andrew Ng. I understand the mathematics behind what I am doing as the textbooks usually explain this part very well. However, whether it is the mean, median, mode, or any other technique used to find the center of data, I am wondering why we do this and what real-world results are after we apply it in a professional setting. Thank you.
 A: Actually it has nothing to do with being "in the center". In fact, those statistics can sometimes be far from what many people consider as "center", e.g. for skewed distribution. The point is rather that they provide a single-value summary of the distribution: mean is the value where probability mass concentrates, it is the outcome that we "expect on average", median is the value that divides your data in two halves (50% lies on the right of it, 50% lies on the left), while mode is the "most common" value. Each of those statistics gives you some simple summary of the data.
A: I think the question is too broad to be answered. But one example would be : assume $A$ is your data matrix, 

If you center columns (variables) of $\bf A$, then $\bf A'A$ is the scatter (or co-scatter, if to be rigorous) matrix and $\mathbf {A'A}/(n-1)$ is the covariance matrix.

Details can be found in 
Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
If no centering, such nice property will disappear. A related post here, explains why it matters in the application of PCA
How does centering make a difference in PCA (for SVD and eigen decomposition)?
