The mid-points and corresponding frequencies for the time (in minutes) taken by a group of commuters to reach their college are given below:
Mid-point (minutes) 10 20 30 40 50
Frequency 5 9 12 8 6
Using the information above, answer the following questions.
(i) Determine the arithmetic mean commute time.
(ii) Calculate the variance and the standard deviation of the commute times (correct to one decimal place).