As there are #16# members with age less than #10# and #33# members with age less than #20#, we have #33-16=17# members between age of #10# and #20#. This way we can derive actual frequency from cumulative frequency, which is as given below:
Age #color(white)(XXXXXXX)#Cum. Frequency#color(white)(XXX)#Frequency
#0-10color(white)(XXXXXXXX)16color(white)(XXXXXXXXXX)16#
#10-20color(white)(XXXXXXxx)33color(white)(XXXXXXXXXX)17#
#20-30color(white)(XXXXXXxx)53color(white)(XXXXXXXXXX)20#
#30-40color(white)(XXXXXXxx)78color(white)(XXXXXXXXXX)25#
#40-50color(white)(XXXXXXxx)96color(white)(XXXXXXXXXX)18#
#50-60color(white)(XXXXXXX)110color(white)(XXXXXXXXXX)14#
#60-70color(white)(XXXXXXX)125color(white)(XXXXXXXXXX)15#
As the highest frequency is #f_m=25#, whose modal class is #30-40# and class interval is #i#; the frequency just before is #f_(m-1)=20# and frequency just after is #f_(m+1)=18#.
Formula for Mode is #Mode=L_1+(f_m-f_(m-1))/(2f_m-f_(m-1)-f_(m-2))xxi#
#.:Mode=30+(25-20)/(2xx25-20-18)xx10#
= #30+5/12xx10=30+4.166~=34.17#
