The following table shows the distribution of marks (out of 10) obtained by 20 students. Two frequencies are missing.
Marks (x): 1 2 3 4 5
Frequency (f): 2 f1 6 f2 4
The arithmetic mean of the distribution is 3.2 and the standard deviation is 1.25.
(i) Using the given mean and the fact that the total number of students is 20, obtain one linear equation in f1 and f2.
(ii) Using the given standard deviation, obtain a second equation in f1 and f2.
(iii) Solve the simultaneous equations to find the values of f1 and f2.