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# The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure

**Solution:**

We will find the mean by step-deviation method

Mean, (x) = a + (Σfᵢdᵢ/Σfᵢ) × h

Modal Class is the class with the highest frequency

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

Here,

Class size, h

Lower limit of modal class, l

Frequency of modal class, f₁

Frequency of class preceding modal class, f₀

Frequency of class succeeding the modal class, f₂

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

Taking assumed mean, a = 2750

Class size, h = 500

From the table, we obtain, Σfᵢ = 200 and Σfᵢuᵢ = - 35

Mean, (x) = a + (Σfᵢuᵢ/Σfᵢ) × h

= 2750 + (- 35/200) × 500

= 2750 - 175/2

= 2750 - 87.5

= 2662.5

From the table, it can be observed that the maximum class frequency is 40, belonging to class interval 1500 − 2000

Therefore, modal class = 1500 − 2000

Class size, h = 500

Lower limit of modal class, l = 1500

Frequency of modal class, f₁ = 40

Frequency of class preceding modal class, f₀ = 24

Frequency of class succeeding the modal class, f₂ = 33

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

= 1500 + [(40 - 24)/(2 × 40 - 24 - 33)] × 500

= 1500 + 16/23 × 500

= 1500 + 347.83

= 1847.83

The modal monthly expenditure of the families is ₹ 1847.83 and the mean monthly expenditure of the families is ₹ 2662.50

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

**Video Solution:**

## The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.2 Question 3

**Summary:**

The following data gives the distribution of total monthly household expenditure of 200 families of a village. The modal and mean monthly household expenditure of the families are ₹ 1847.83 and ₹ 2662.50 respectively.

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