# The following table shows the ages of the patients admitted in a hospital during a year:

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency

**Solution:**

We will find the mean by the direct method.

Mean, (x) = a + Σf_{i}d_{i}/Σf_{i}

Modal Class is the class with the highest frequency

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

Here,

- Class size, h
- The lower limit of modal class, l
- The Frequency of model 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 that, class mark, x_{i} = (Upper-class limit + Lower-class limit)/2

From the table it can be observed that, Σf_{i} = 80 and Σf_{i}x_{i} = 2830

Mean, (x) = a + Σf_{i}d_{i}/Σf_{i}

= 2830/80

= 35.37

To find mode, we know that modal class is the class with the highest frequency

From the table, it can be observed that the maximum class frequency is 23, belonging to class interval 35 − 45.

Therefore, Model class = 35 − 45

Class size, h = 10

Lower limit of model class, l = 35

Frequency of model class, f_{1} = 23

Frequency of class preceding model class, f_{0} = 21

Frequency of class succeeding the model class, f_{2} = 14

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

= 35 + [(23 - 21)/(2 × 23 - 21 - 14)] × 10

= 35 + 2/(46 - 35) × 10

= 35 + 2/11 × 10

= 35 + 1.8

= 36.8

So, the model age is 36.8 years which means the maximum number of patients admitted to the hospital are of age 36.8 years.

Mean age is 35.37 and the average age of the patients admitted is 35.37 years.

**Video Solution:**

## The following table shows the ages of the patients admitted in a hospital during a year: Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency

### NCERT Solutions for Class 10 Maths - Chapter 14 Exercise 14.2 Question 1:

The following table shows the ages of the patients admitted in a hospital during a year: Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency

The mode and the mean of the data showing the ages of the patients admitted in a hospital during a year are 36.82 years and 35.37 years respectively. This implies that the maximum number of patients admitted to the hospital are of age 36.82 years and the average age of the patients admitted is 35.37 years.