Words in “index of coincidence” in relation to the Vigenère cipher
Here $f_i$ is simply the number of times the character $i$ appears in the ciphertext of length $N$ and where $Z$ is the alphabet size. 

If you had ciphertext ADCXU ZMDYZ DXZUM and which was derived from English plaintext then $N=15$  and $f_A=1,f_B=0,f_C=1, f_D=3,\ldots, f_Z=2.$