The marks obtained by students in a 100-mark examination were grouped as follows. One class frequency is missing.
Marks
0–20
20–40
40–60
60–80
80–100
Frequency
8
f
20
12
5
The median mark of the distribution is 53.
(a) Determine the missing frequency f.
(b) Using the completed table, calculate the mode of the distribution.
(c) State which of the three measures—mean, median or mode—is necessarily the largest for this distribution and give a brief reason for your answer.