Question

Find mode from the following grouped frequency distribution table:

Number of Trees Planted	Number of Students
$0-10$	$30$
$10-20$	$60$
$20-30$	$50$
$30-40$	$70$
$40-50$	$40$

• A. $34$ trees
• B. $35$ trees
• C. $38$ trees
• D. $36$ trees

Answer 1

Answer: (A)

$N=30+60+50+70+40=250$

$⟹\frac{N}{2}=125$

Since, the highest frequency of students is $70$. So, $30-40$ is the modal group.

$⟹L=30$

Also, $f_0=50$, frequency of the group before the modal group

$f_1=70$, frequency of the modal group

$f_2=40$, frequency of the group after modal group.

$h=10$, width of the group

Then, Mode $=L+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

$=30+\frac{70-50}{140-50-40}\times 10$

$=30+\frac{20}{50}\times 10$

$=30+4=34$

Hence, mode is $34$ trees.