The daily maximum temperatures (in °C) recorded in a city for 40 consecutive days are as follows:
21, 22, 23, 24, 24, 25, 25, 26, 26, 27,
27, 28, 28, 28, 29, 29, 30, 30, 30, 31,
31, 31, 32, 32, 33, 33, 33, 34, 34, 34,
35, 35, 36, 36, 37, 38, 39, 40, 42, 45
(i) Determine the range of the data.
(ii) Two different class widths that are multiples of 3 are to be chosen so that the number of classes lies between 4 and 8 inclusive. Identify both possible class widths and state the corresponding number of classes in each case.
(iii) For each class width obtained in part (ii), construct a grouped frequency distribution table with continuous intervals.
(iv) Comparing the two tables, state which class width gives a clearer picture of the distribution and give two reasons for your choice.