The following table gives the heights of 100 students of a school, but the class intervals are not in ascending order. Arrange the classes in the proper order and answer the questions that follow.
Class interval (cm)
160–165
145–150
170–175
150–155
140–145
165–170
155–160
175–180
Number of students
15
12
10
18
5
12
20
8
(a) Re-write the distribution with class intervals arranged in ascending order and construct the corresponding ‘less than’ cumulative frequency table.
(b) On a graph sheet, choose an appropriate scale and draw the ‘less than’ cumulative frequency curve for the data.
(c) Using the curve, estimate the median height of the students.
(d) With the help of the graph, determine approximately how many students have a height exceeding 160 cm.