Compare distributions of two ECDFs I am investigating the achieved mark in a math test in grade 8 in two different cities. The plot shows the two Empirical Cumulative Distribution Functions (ECDF).

How can I evaluate whether these two ECDFs follow the same distribution or not?
 A: You can never answer for absolute certainty whether they come from the same distribution or not; we are dealing with random numbers.
However, there is a class of statistical tests of the goodness of fit between two empirical distributions, testing if the hypothesis that they come from the same distribution can be rejected or not. Examples of these tests would include the two-sample versions of the Cramer-von Mises and Anderson-Darling tests. 
With just a few observations, as your graph implies, it isn't hard to run a two sample CvM test in a spreadsheet. For more data, or ease, there used to be a R package that did two-sample CvM testing. The paper is A C++ Program for the Cramer-von Mises Two-Sample Test (Xiao et al. 2006). Unfortunately, the package fell off CRAN as it didn't pass an update, Yakovlev's e-mail was dead, Gordon didn't write the program and sent me to Xiao, who said he would update the package back in April of 2014 and I haven't heard anything since.
The package itself is still in the CRAN archives if you want to install it and try.
