# Numerical Analysis-Interpolation Formulae (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 7 - 14 of 14

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## Question number: 7

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Use Simpson’s rule with five ordinates to compute an approximation to π with the help of the integration of the function (1 + x 2) -1 from 0 to 1.

### Explanation

T he rule of the integrand using Simpson’s rule for five ordinates is

where , n = 5

h= (1 - 0) /5 = 1/5

We divide the range 0 to 1 in five equal

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## Question number: 8

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

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Appeared in Year: 2012

Essay Question▾

### Describe in Detail

An unknown function u x has been tabulated below for some selected values of x. Use Newton’s divided difference formula on these to find an approximate value of u 3:

 x 0 2 5 10 u x 3 19 73 223

### Explanation

The Newton’s divided difference formula is used when the x-values not equally spaced. The Newton’s formula of divided difference for estimating u x corresponding to x is

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## Question number: 9

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2012

Essay Question▾

### Describe in Detail

Solve the equation f (x) = 0 by using a suitable interpolation formula on the following values:

 x 3 4 5 6 f (x) -2.8 -1.2 -0.3 1.8

### Explanation

To solve the equation f (x) = 0, using Lagrange’s inverse interpolation method

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## Question number: 10

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Fit the exponential curve y = a + bx to the following data

x: 0 2 4

y: 5.01 10 31.62

### Explanation

his is not exponential equation, it is a straight line y = a + bx

 S. no x y Xy x 2 1 0 5.01 0 0 2 2 10 20 4 3 4 31.62 126.48 16 Sum 6 46.63 146.48 20

The normal equations is

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## Question number: 11

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

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Appeared in Year: 2010

Essay Question▾

### Describe in Detail

Evaluate log e 7 by Simpson’s -1/3rd rule.

### Explanation

We get log e 7, when

So, the seven ordinates of the integrand using Simpson’s rule is

Where h = 1/6 (b-a) and y k =f (a + kh) for k = 1,2, 3,4, 5,6, 7

Here, b = 7,

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## Question number: 12

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

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Appeared in Year: 2010

Essay Question▾

### Describe in Detail

Estimate U 2 from the following table:

 x 1 2 3 4 5 U x 7 - 13 21 37

### Explanation

To find the missing value, we use binomial expansion method. Here 4 values are known, we would take fourth order finite difference zero. Thus,

Here for x = 1, U 0 =7, U 1 =? , U 2 =13, U 3 =21, U 4 =37

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## Question number: 13

» Numerical Analysis » Interpolation Formulae » Gauss

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Appeared in Year: 2009

Essay Question▾

### Describe in Detail

Find the value of

by taking 5 subintervals and using the Trapezoidal rule.

### Explanation

Let

First divided the interval into 5 subintervals

 x 0 1/4 1/2 3/4 1 y 1 16/17 4/5 16/25 ½

Here a = 0, b = 1, n = 4, h= (b-a) /n = 1/4

the Trapezoidal rule is

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## Question number: 14

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

By making use of difference table and a suitable interpolation formula, find the number of student who obtained less than 45 marks in an examination, from the following table

 Marks 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Number of students 31 42 51 35 31

### Explanation

Applying Newton-Gregory forward formula for interpolating the number of student who obtained less than 45 marks in an examination.

 Marks less than Number of student Difference ∆y 0 ∆ 2 y 0 ∆ 3 y 0 ∆ 4 y 0 x 0 =40 y 0 = 31 42 9 -25 37 50 y 1 =73 51 -16 60 y 2 =124 35 70 y 3 =159 12 80 y 4 =190 31 -4

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