Question

Use Lagrange’s formula and estimate from the following data the number of workers getting income not exceeding Rs. 26 per month.

Income not exceeding (Rs.)	15	25	30	35
No. of workers	36	40	45	48

Answer 1

Let x represent the income per month and y denote the number of workers. 

From the given data, 

x₀ = 15, y₀ = 36 

x₁ = 25, y₁ = 40 

x₂ = 30, y₂ = 45 .

x₃ = 35, y₃ = 48 

We have to find the value of y at x = 26 

By Lagrange’s interpolation formula,

The different value are given in the table below

y = -0.432 + 31.68 + 11.88 – 2.112

y = 41.016 

Thus the number of workers getting income not exceeding Rs.26 per month is 42

Comments

Why 42?

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Because if total workers are 41 or less than 41 then their income exceeds Rs. 26 but workers are 42 than their income less than Rs. 26