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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