Rainfall (in mm) recorded on 50 monsoon days at a Thrissur station:
0-20: 5, 20-40: f1, 40-60: 10, 60-80: f2, 80-100: 7, 100-120: 8.
The mean rainfall is 62.8 mm and the total is 50 days. Find f1.

The known frequencies total 30, so $f1+f2=20$. Class marks 10, 30, 50, 70, 90, 110 give $\sum f_i{x}_i=2060+30f_1+70f_2$, and the mean 62.8 forces $\sum f_i{x}_i=62.8\times 50=3140$, so $30f_1+70f_2=1080$. Substituting $f_1=20-f_2$ gives $600+40f_2=1080$, so $f_2=12$ and $f_1=8$. "12" is $f$2, the other unknown; "20" is $f1+f$2; "10" splits the 20 equally between the two classes without using the mean at all.