Two historians of the school athletics team compared the distributions of race-completion times (in seconds) of Boys and Girls in a 100 m sprint trial. Both distributions were shown on the same pair of axes as adjoining histograms having identical class intervals of width 2 seconds from 12–14, 14–16, 16–18, 18–20 and 20–22.
• For Boys the frequencies are proportional to the bar heights 6 cm, 10 cm, 14 cm, 8 cm and 2 cm.
• For Girls the frequencies are proportional to the bar heights 2 cm, 6 cm, 16 cm, 12 cm and 4 cm.
• On both histograms the vertical scale is 1 cm = 1 athlete.
Each group had the same total number of athletes.
(a) Complete separate frequency tables for Boys and Girls.
(b) For each group, identify the modal class.
(c) Using the tables, find which group has the greater number of athletes finishing the race in less than 18 seconds, and by how many.
(d) Comment, with a reason, on which group shows a greater concentration of times around its mode.