The 'extern' declarations should go in the header;
The actual definitions (with initialisations) should go in the 'C' file.

header.h

// Note that the array sizes are not needed here
extern code unsigned int x_data[]; 
extern code unsigned int y_data[];

mainfile.c

#include <headerfile.h> // This is included here so that the compiler can warn
                        // if the 'extern' declarations don't match the actual definitions!

code unsigned int x_data[10]={0,1,2,3,4,5,6,7,8,9};
code unsigned int y_data[10]={10,11,12,13,14,15,16,17,18,19};
etc

otherfile.c

#include <headerfile.h> // This gives access to the 'extern' declarations

If you had the definitions in the header, as you originally showed, you would get Linker errors complaining about Multiple Definitions