The heights of 90 young saplings were recorded and grouped in classes of width 10 cm. In both ‘less than’ and ‘more than’ cumulative frequency tables several entries are missing.
(i) ‘Less than’ cumulative frequencies
Upper height limit (cm): 10 20 30 40 50 60
Cumulative frequency (<): 7 23 — — 79 90
(ii) ‘More than’ cumulative frequencies
Lower height limit (cm): 0 10 20 30 40 50
Cumulative frequency (>): 90 83 — 40 — 11
It is further known that the number of saplings whose heights lie between 30 cm and 40 cm is equal to the number whose heights lie between 10 cm and 20 cm.
(a) Complete both cumulative frequency tables.
(b) Hence obtain the frequency of every class interval.
(c) Draw a histogram for the completed frequency distribution and state the modal class.