Learning to read complex math formulas

could anybody point me to a book or article where I could learn how to read formulas like this one:

I have no idea what that means.

The following points may be helpful:

1. $i$ is used to index the various numerical values $x_i$ you have. Usually, unless specified otherwise, it is understood that $i$ ranges from $1$ to some finite value $n$.

   Thus, in your example, you have $n$ observations each one of them is denoted by $x_i$.

2. $\bar{x}$ denotes the mean of the $n$ observations i.e.,

   $$\bar{x} = \frac{x_1+x_2+\ldots+x_n}{n}$$

   The same interpretation holds for $y_i$ and $\bar{y}$.

3. $\Sigma$ stands for sum and hence we could have re-written the mean as follows:

   $$\bar{x} = \frac{x_1+x_2+\ldots+x_n}{n}=\frac{\Sigma_i{x_i}}{n}$$

I hope that helps decipher what is going on in the equation.

For this particular formula, any introductory statistics book will be a good start. Conceivably you won't have the background for this book, and then you would need to backtrack.

In particular, for this question you could look up "sigma summation notation," as that is the only really strange symbol here. The other symbols, such as $\bar x $, would need to be defined. The formula you asked about happens to be the formula to calculate Pearson's correlation coefficient, measuring how much change in one variable corresponds to change in the other. In this case, the values come from data points on the plane, and having a bar means an average (so $\bar x$ means the average of all the $x$).

This comprehensive pdf could be useful: Handbook for Spoken Mathematics

It represents the mathematical symbols and explains how to read them.

for example:

https://ibb.co/cjturF

We are talking here about two points (data sets) $(x_1,\ldots, x_n)$, $\>(y_1,\ldots, y_n)$. Here the $x_i$ are to be interpreted as measurements of a quantity $x\in{\mathbb R}$, and similarly for the $y_i$. For some "unknown" reason a new origin $\bar x$ on the $x$-axis and a a new origin $\bar y$ on the $y$-axis is chosen, and you are actually interested in the quantities $$\xi_i:=x_i-\bar x,\quad \eta_i:=y_i-\bar y\qquad(1\leq i\leq n)\ .$$ In terms of the new coordinates $\xi_i$, $\>\eta_i$ your quantity $r$ appears as $$r={\sum\nolimits_i\xi_i\>\eta_i\over\sqrt{\sum\nolimits_i\xi_i^2}\sqrt{\sum\nolimits_i\eta_i^2}}={\xi\cdot\eta\over|\xi|\ |\eta|}=\cos\phi\ ,$$ where $\phi$ is the angle between the vectors $\xi$, $\>\eta\in{\mathbb R}^n$, measured in the $2$-dimensional plane spanned by $\xi$ and $\eta$.