Question

Find the mean, mode and median of the following data:

Classes	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	5	10	18	30	20	12	5

• A. mean=35.60, median=35.667, mode=35.4545
• B. mean=35.60, median=35.667, mode=34.4545
• C. mean=33.60, median=35.667, mode=36.4545
• D. mean=35.60, median=33.666, mode=35.12

Answer 1

The correct option is A mean=35.60, median=35.667, mode=35.4545

To find the mean, mode and median of the following data

Classes	0-10	10-20	20-30	30-40	40-50	50-60	60-70
mid points	5	15	25	35	45	55	65
Frequency	5	10	18	30	20	12	5
$x_i{f}_i$	25	150	450	1050	900	660	325
CF	5	15	33	63	83	95	100

$\sum f_i{x}_i=3560$
Total frequency $=100$

$\therefore N=\frac{100}{2}=50$,

Mean$=\frac{3560}{100}=35.60$,
Median class is $30-40$
Median$=l+\frac{\frac{N}{2}-m}{f}.c$,
$=30+\frac{\frac{100}{2}-33}{30}.10$
$=30+\frac{17}{3}=30+5.6667=35.6667$
mode$=l+\frac{c{\Delta }_1}{{\Delta }_1+{\Delta }_2}$
${\Delta }_1=30-18=12,{\Delta }_2=30-20=10$
mode$=l+\frac{c{\Delta }_1}{{\Delta }_1+{\Delta }_2}$
$=30+\frac{10\left(12\right)}{22}=30+5.4545=35.4545$