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.

No. of students per teacher	No. of state/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

• A. $Mode=43.6$ and $Mean=21.2$
• B. $Mode=39.6$ and $Mean=24.2$
• C. $Mode=35.6$ and $Mean=27.2$
• D. $Mode=30.6$ and $Mean=29.2$
  

Answer 1

The correct option is D $Mode=30.6$ and $Mean=29.2$

Answer:- $x_i=\frac{\text{lower limit + upper limit}}{2}$

No. of students per teacher	$x_i$	No. of state ($f_i$)	$x_i\times f_i=x_i{f}_i$
15-20	17.5	3	52.5
20-25	22.5	8	180
25-30	27.5	9	247.5
30-35	32.5	10	325
35-40	37.5	3	112.5
40-45	42.5	0	0
45-50	47.5	0	0
50-55	52.5	2	105
		$\Sigma f_i=35$	$\Sigma f_i{x}_i=1022.5$

$\therefore Mean=\frac{\Sigma x_i{f}_i}{\Sigma f_i}=\frac{1022.5}{35}=29.2$

Here, maximum frequency ${}^{\prime }{10}^{\prime }$ is of classs interval ${}^{\prime }30-{35}^{\prime }$.

$\therefore Modalclass=30-35$.

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

where

L $=$ Lower limit of modal class $=30$

$f_1$ = frequency of modal class $=10$

$f_0$ = frequency of previoous class $=9$

$f_2$ = frequency of next class $=3$

h = width of class $=35-30=5$

$\therefore Mode=30+\frac{10-9}{2\left(10\right)-9-3}\times 5=30+\frac{1}{8}\times 5=30.625$

$\therefore$ D) Mode $=30.625$ $\&$ Mean $=29.2$.