Question

Find out mode of the following frequency distribution:

Marks (More than)	0	10	20	30	40	50	60	70	80
No. of Students	40	38	33	25	15	7	5	2	0

Answer 1

Class Interval	Number of students (c.f.)	Frequency (f)
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80 80 − 90	40 38 33 25 15 7 5 2 0	2(=40-38) 5(=38-33) 8(=33-25) (f0) 10(=25-15) (f1) 8(=15-7) (f2) 2(=7-5) 3(=5-2) 2(=2-0) 0

By inspection, we can say that the modal class is (30 – 40) as it has the highest frequency of 10.
$$\begin{gathered} \mathrm{Mode}\left(Z\right)=l_1+\frac{f_1-f_0}{2f_1-f_0-f_2}\times i \\ \mathrm{or},Z=30+\frac{10-8}{2\left(10\right)-8-8}\times 10 \\ \mathrm{or},Z=30+\frac{2}{4}\times 10 \\ \mathrm{or},Z=30+5=35 \\ \mathrm{Hence},\mathrm{mode}\left(Z\right)\mathrm{is}35. \end{gathered}$$