The marks obtained by 60 students in a Mathematics test are grouped in the following frequency distribution:
Class interval (marks): 0–10, 10–20, 20–30, 30–40, 40–50
Frequency: 5, 9, 15, 18, 13
a. (i) Calculate the arithmetic mean of the distribution.
b. (ii) Compute the variance and hence the standard deviation of the marks (take class mid-points).
c. (iii) Another section of 60 students wrote the same test; their mean mark was also 28 but their standard deviation was 4.2. Interpret, with justification, which section shows more consistency in performance.