Question

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacher	Number of states/U.T.
$15-20$	$3$
$20-25$	$8$
$25-30$	$9$
$30-35$	$10$
$35-40$	$3$
$40-45$	$0$
$45-50$	$0$
$50-55$	$2$

Answer 1

Mode: The class which have highest frequency.

In this case, class interval $30-35$ is the modal class.

Now,

Lower limit of modal class, $l=30,h=5,f_1,=10,f_0=9,f_2=3$

We know that,

Mode =$l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$$=30+\left(\frac{10-9}{2\left(10\right)-9-3}\right)\times 5$

$=30+\left(\frac{1}{20-12}\right)5$

$=30+\frac{1}{8}\times 5$

Mode $=30.625\equiv 30.6$

for mean,

Mean, $\overline{x}=\frac{\sum f_i{u}_i}{\sum f_i}$

$\overline{x}=\frac{1022.5}{35}=29.2$

Therefore,

Most states/U.T. have a student teacher ratio of $30.6$ and on an average, the ratio is $29.2$.