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.
$15 - 20$
$3$
$20 - 25$
$8$
$25 - 30$
$9$
$30 - 35$
$10$
$35 - 40$
$3$
$40 - 45$
$0$
$45 - 50$
$0$
$50 - 55$
$2$

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.
$15 - 20$	$3$
$20 - 25$	$8$
$25 - 30$	$9$
$30 - 35$	$10$
$35 - 40$	$3$
$40 - 45$	$0$
$45 - 50$	$0$
$50 - 55$	$2$

Filo · Accepted Answer

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 + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) \times h

= 30 + (\frac{10 - 9}{2 ( 10 ) - 9 - 3}) \times 5

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

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

Mode

= 30.625 \equiv 30.6

for mean,

Mean,

\overset{x}{ˉ} = \frac{\sum f _{i} u _{i}}{\sum f _{i}}

\overset{x}{ˉ} = \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

.

Question Text	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.
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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