# 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) = Σfᵢxᵢ/Σfᵢ

Modal Class is the class with the highest frequency

Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h

Here,

- Class size is h
- The lower limit of modal class is l
- The Frequency of modal class is f₁
- Frequency of class preceding modal class is f₀
- Frequency of class succeeding the modal class is f₂

To find Mean, we know that, class mark, xᵢ = (Upper-class limit + Lower-class limit)/2

From the table it can be observed that, Σfᵢ = 80 and Σfᵢxᵢ = 2830

Mean, (x) = Σfᵢxᵢ/Σfᵢ

= 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 modal class, f₁ = 23

Frequency of class preceding modal class, f₀ = 21

Frequency of class succeeding the modal class, f₂ = 14

Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × 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 modal 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.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 14

**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

**Summary:**

The following table shows the ages of the patients admitted in a hospital during a year: The median and mode of the data given are 35.37 and 36.2 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.

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