# Numerical Analysis-Interpolation Formulae (ISS 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)

Appeared in Year: 2011

### 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

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## Question number: 8

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

Appeared in Year: 2012

### 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 | 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

Appeared in Year: 2012

### 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

Appeared in Year: 2015

### 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 |

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

Appeared in Year: 2010

### 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

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## Question number: 12

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

Appeared in Year: 2010

### Describe in Detail

Estimate U _{2} from the following table:

x | 1 | 2 | 3 | 4 | 5 |

U | 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,

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## Question number: 13

» Numerical Analysis » Interpolation Formulae » Gauss

Appeared in Year: 2009

### 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)

Appeared in Year: 2015

### 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 | ∆ | ∆ | ∆ | ||

x | y | 42 | 9 |
-25… (178 more words) … |