# 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

**Solution:**

We will find the mean by direct method

Mean, (x) = a + Σf_{i}x_{i}/Σf_{i}

Modal Class is the class with the highest frequency

Mode = l + (f_{1} - f_{0})/(2f_{1} - f_{0} - f_{2}) × h

Here,

Class size, h

Lower limit of modal class, l

Frequency of modal class, f_{1}

Frequency of class preceding modal class, f_{0}

Frequency of class succeeding the modal class, f_{2}

To find mean, we know Class mark, x_{i} = (Upper class limit + Lower class limit)/2

Class size, h = 500

Taking assumed mean, a = 32.5

Mean, (x) = Σf_{i}x_{i}/ Σf_{i}

= 1022.5/35

= 29.2

From the table, it can be observed that the maximum class frequency is 10, belonging to class interval 30 − 35

Therefore, modal class = 30 − 35

Class size, h = 5

Lower limit of modal class, l = 30

Frequency of modal class, f_{1} = 10

Frequency of class preceding modal class, f_{0} = 9

Frequency of class succeeding the modal class, f_{2} = 3

Mode = l + (f_{1} - f_{0})/(2f_{1} - f_{0} - f_{2}) x h

= 30 + [(10 - 9)/(2 × 10 - 9 - 3) × 5

= 30 + 1/(20 - 12) × 5

= 30 + 5/8

= 30 + 0.625

= 30.625

**≈** 30.6

The modal teacher-student ratio is 30.6 and mean teacher-student ratio is 29.2.

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

**Video Solution:**

## The following data gives the state-wise, teacher-student ratio in higher secondary schools of India. Find the mode and mean of the data and interpret the two

### NCERT Solutions for Class 10 Maths - Chapter 14 Exercise 14.2 Question 4:

The following data gives the state-wise, teacher-student ratio in higher secondary schools of India. Find the mode and mean of the data and interpret the two.

The mode and mean of the state-wise teacher-student ratio in higher secondary schools of India are 30.6 and 29.2 respectively