The daily rainfall (in mm) in a town was observed for 80 days during the monsoon season and grouped in the following frequency table, in which three frequencies are unknown.
Class interval (mm): 0–5, 5–10, 10–15, 15–20, 20–25, 25–30
Number of days: a, 3a, b, 12, b + 4, 8
Additional information:
(i) The total number of days is 80.
(ii) The cumulative frequency up to and including the 15–20 mm class is 50.
Answer the following.
(a) Form two independent equations using the given information and hence find the values of a and b.
(b) Complete the grouped frequency distribution table with the calculated frequencies.
(c) Draw a histogram for the completed data on graph paper, using an appropriate scale.
(d) Based on the histogram, comment briefly on the general distribution of rainfall amounts during the observation period.