Podcast
Questions and Answers
When solving a system of linear equations using the Gauss-Jordan method, which operation is NOT typically allowed?
When solving a system of linear equations using the Gauss-Jordan method, which operation is NOT typically allowed?
- Adding a multiple of one row to another row.
- Taking the logarithm of all elements in a row. (correct)
- Swapping two rows.
- Multiplying a row by a non-zero constant.
When fitting an exponential curve of the form $Y = ab^x$ to a given dataset, what is a common first step in determining the parameters a and b?
When fitting an exponential curve of the form $Y = ab^x$ to a given dataset, what is a common first step in determining the parameters a and b?
- Taking the natural logarithm of both sides of the equation. (correct)
- Plotting the data on a linear scale and estimating the slope.
- Performing a linear regression directly on the original data.
- Averaging the _x_ and _y_ values to find the centroid.
Which of the following is a key assumption when using Newton's forward interpolation method?
Which of the following is a key assumption when using Newton's forward interpolation method?
- The data points are evenly spaced. (correct)
- The data points are randomly distributed.
- The data points follow a perfect polynomial relationship.
- The data points exhibit exponential growth.
Which measure of dispersion is most sensitive to extreme values in a dataset?
Which measure of dispersion is most sensitive to extreme values in a dataset?
When calculating the median from grouped data, what does the cumulative frequency represent?
When calculating the median from grouped data, what does the cumulative frequency represent?
In the context of fitting a parabola using the method of group averages, what is the primary goal of dividing the data into groups?
In the context of fitting a parabola using the method of group averages, what is the primary goal of dividing the data into groups?
Which type of error is primarily caused by the limitations in the precision of computer arithmetic?
Which type of error is primarily caused by the limitations in the precision of computer arithmetic?
What distinguishes numerical methods from numerical analysis?
What distinguishes numerical methods from numerical analysis?
When fitting a second-degree polynomial to data, increasing the degree of the polynomial generally leads to:
When fitting a second-degree polynomial to data, increasing the degree of the polynomial generally leads to:
What is the purpose of interpolation?
What is the purpose of interpolation?
Flashcards
Types of Errors
Types of Errors
Discrepancies between computed, observed, or measured values & true or theoretically correct values. Includes Round-off, Truncation, and Human Errors.
Numerical Methods
Numerical Methods
Algorithms to approximate numerical problems, especially when analytical solutions are difficult or impossible to obtain.
Gauss-Jordan Method
Gauss-Jordan Method
A method for solving systems of linear equations by performing row operations to obtain a reduced row echelon form.
Exponential Curve
Exponential Curve
A curve where y changes exponentially with x, defined by the equation Y = abˣ.
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Interpolation Method
Interpolation Method
Estimating values between known data points using a polynomial that passes through those points.
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Measures of Dispersion
Measures of Dispersion
Statistics that describe the spread of data around a central value. Examples include variance and standard deviation.
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Mean vs. Median
Mean vs. Median
A 'mean' is the average value. A 'median' is the central value when observations are ordered.
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Second Degree Polynomial
Second Degree Polynomial
A polynomial of degree two, represented by the equation y = ax² + bx + c.
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Method of Group Averages
Method of Group Averages
A method to fit curves by dividing data into groups, averaging within groups, and solving for parameters.
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- B.Sc. (Information Technology) 2nd Semester exam covers Numerical Methods & Statistical Techniques (Paper-III).
- The exam duration is three hours, with a maximum score of 75.
- The question paper is divided into four sections, each containing two questions.
- Students must attempt five questions in total, selecting at least one from each section.
- All questions carry equal marks.
Section A
- Question 1(a) asks to list the different types of errors.
- Question 1(b) asks you to define Numerical Methods and differentiate them from Numerical Analysis.
- Question 2 requires solving a system of linear equations using the Gauss Jordan Method:
- x + y - x = 2
- 2x + 3y + 5z = -3
- 3x + 2y - 13z = 6
Section B
- Question 3 requires fitting an exponential curve of the form Y = abˣ to the provided data set.
- Question 4 asks to find the value of y when x = 218 using Newton's forward interpolation method, given a data set of x and y values.
Section C
- Question 5 involves explaining various measures of dispersion and providing an example of each.
- Question 6 requires calculating the mean and median from the frequency distribution data provided.
Section D
- Question 7 asks to fit a second-degree polynomial to the data presented in the table.
- Question 8 provides corresponding values of x and y
- It asks to fit a parabola of the form y = a + bx + cx² using the method of group averages.
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