IT2024-USER INTERFACE DESIGN Two Marks Questions With Answers 2014


Anna University, Chennai

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IT2024-USER INTERFACE DESIGN SYLLABUS

UNIT I INTRODUCTION 8

Human–Computer Interface – Characteristics Of Graphics Interface – Direct Manipulation

Graphical System – Web User Interface –Popularity –Characteristic & Principles.

UNIT II HUMAN COMPUTER INTERACTION 10

User Interface Design Process – Obstacles –Usability –Human Characteristics In Design – Human Interaction Speed –Business Functions –Requirement Analysis – Direct – Indirect Methods – Basic Business Functions – Design Standards – System Timings – Human Consideration In Screen Design – Structures Of Menus – Functions Of Menus– Contents Of Menu– Formatting – Phrasing The Menu – Selecting Menu Choice– Navigating Menus– Graphical Menus.

UNIT III WINDOWS 9

Characteristics– Components– Presentation Styles– Types– Managements– Organizations– Operations– Web Systems– Device– Based Controls Characteristics– Screen – Based Controls – Operate Control – Text Boxes– Selection Control– Combination Control– Custom Control– Presentation Control.

UNIT IV MULTIMEDIA 9

Text For Web Pages – Effective Feedback– Guidance & Assistance– Internationalization–

Accessibility– Icons– Image– Multimedia – Coloring.

UNIT V WINDOWS LAYOUT– TEST 9

Prototypes – Kinds of Tests – Retest – Information Search – Visualization – Hypermedia –

WWW– Software Tools.

TEXT BOOKS:

TOTAL: 45 PERIODS

1. Wilbent. O. Galitz ,“The Essential Guide To User Interface Design”, John Wiley& Sons,

2001.

2. Ben Sheiderman, “Design The User Interface”, Pearson Education, 1998.

REFERENCES:

Alan Cooper, “The Essential Of User Interface Design”, Wiley – Dream Tech Ltd., 2002.

TWO MARKS QUESTIONS & ANSWERS

CLASS: III - IT STAFF NAME: Mr. S.SARAVANAN

SEM:VI

UNIT-I PART- A

1. What is meant by Human-computer interaction?

It is the study, planning and design of how people and computer work together so that a person needs are satisfied in the most effective way.

2. What are the benefits of good design?

· To improve screen clarity and readability.

· It reduces decision making time.

clip_image009· Identifying and resolving problems during the design and development

3. What is meant by GUI?

GUI is a collection of techniques and mechanism to interact with pointing device of some

kind.

4. Mention any 2 advantages of graphical system?

· Symbols recognized faster than text.

The symbols can be recognized faster and more quickly than text and that graphical attributes quickly classifying the objects.

5. What are visually presented elements in a graphical system?

· Windows

· Menus.

· Icons.

· Screen based controls.

· Mouse point and cursor.

6. Define pick and click interaction?

Pick: To identify an element for a proposed action.

Click: The signal to perform an action.

7. Define Visualization.

It is a cognitive process that allows people to understand information that is difficult to perceive, because it is either too voluminous or too abstract.

8. What is an object and its types?

clip_image011Object is an entity. It can be manipulated as a single unit. Objects can be classified into 3 types.

(l) Data object. (2) Container object. (3) Device object.

9. Define property/attribute specification and explain its sequence.

· Property / attribute specification action establish or modify the attributes or properties of objects.

· Property / attribute specification sequence

(l) The user selects an object (ex) several words of text.

(2) The user then selects an action to apply to that object such as the action Bold.

10. Define concurrent performance of functions.

· Graphic system may do 2 or more things at one time.

· Multiple programs may run simultaneously.

11. What are the goals of web interface design?

· It is to build hierarchy of menus and pages tat well structured.

· It is graphically rich environment.

12. What is meant by web interface design?

It is essentially the design of navigation and the presentation of information. Proper interface design is matter of properly balancing the Structure and relationships of menus, content and other linked documents or graphics.

13. What are the similarities between GUI and web interface design?

· They are interactive.

· Both are used by people.

· Both are software design.

14. Write any 2 differences between GUI and Webpage design.

GUI design

Webpage design

Characteristics of interface such as monitor

and modem are well designed

The user device may range from handheld

mechanism to high end work station.

It navigate through structured menus ,lists

,screens dialogs and wizards.

It navigate through links, book marks and typed

URL’s.

clip_image01315. Write any 2 differences between Printed page versus Web pages?

Printed page

Web pages

Layout is precise

Layout is approximation

They are presented as complete entities and

their entire contents are available for reading or review immediately.

They are rendered slowly depending upon

transmission speeds and page content.

16. Differentiate the term Internet, Intranet and Extranet.

Intranet: Within organization internal network over a shared infrastructure using dedicate connections.

Internet: It is a huge network of computer networks.

Extranet: An extranet is a Special set of intranet that can be accessed by authorized persons from outside an organization or company.

17. Mention any 2 difference between Intranet versus the Internet?

Intranet

Internet

It is used for an organization every day activities.

It is used to find information

Need for cross-platform compatibility is

minimized

Need for cross-platform compatibility is

maximized

18. What is meant by transparency?

Permit the user to focus on the task or job without concern for the mechanics of the interface.

19. Define user interface? What are the components of user interface.

It is a collection of techniques and mechanisms to interact with something. It has two components Input & Output.

20 .What are the five ways to provide simplicity?

· Use progressive disclosure, hiding things until they are needed.

· Provide defaults.

· Minimize screen alignment points.

· Provide Uniformity & consistency.


UNIT-II PART - A

1. What are the common pitfalls in the design process?

The common pitfalls are.

· No early analysis and understanding of the user's needs and expectations

· Little or no creation of design element Prototypes

· No usability testing.

· Poor communication between members of the development team.

2. Define usability.

It describes the effectiveness of human performance. It can be defined as the capability to be used by humans easily and effectively.

3. What are the common usability problems?

1. Ambiguous menus and icons.

2. Highlighting and selection limitations.

3. Unclear Step sequence.

4. Complex linkage between and within an application.

5. Inadequate feedback and confirmation

4. Identify human characteristics in design?

The important human characteristics in design are perception, memory, visual and peripheral vision, sensory Storage, information processing & skill and individual differences.

5. Differentiate between short-term and long-term memory.

Short –term

Long-term

Contains limited amount of information

Contains unlimited amount of information

Receives information from either the

senses or long term memory

Receives information from short term through

learning process.

6. What is meant by visual activity?

The Capacity of the eye to resolve details is called visual activity. Visual activity is approximately halved at a distance of 2.5 degrees from the point of eye fixation.

7. What are the direct methods in requirement analysis?

The direct methods consist of

· Individual Face to Face interview.

· Telephone Interview or survey.

· Traditional Focus group.

· Facilitated team work group.

· Requirements Prototyping.

· Usability Laboratory testing.

8. What are the indirect methods in requirement analysis?

The indirect methods include

· Paper survey.

· Electronic survey.

· Electronic focus group

· Marketing and sales.

· Support Line.

· Email Of Bulletin Board.

· System Testing.

9. Define mental model.

It is an internal representation of a person's current conceptualization and understand of something. Mental model are gradually developed in order to understand, explain and do something.

10. What are the guidelines for designing conceptual model?

· Reflect the user's mental model.

· Provide proper and correct feedback.

· Provide action-response compatibility.

· Provide design consistency.

11. What are goals of interface design?

The goals in interface design are

· Reduce visual work.

· Reduce intellectual work.

· Reduce memory work.

· Reduce motor work.

12. What are the elements of screen?

Elements of a screen include control captions, data or information displayed on the screen

& headings and headlines.

13. What are the components of a statically graphic?

clip_image021They have at least 2 axes, 2 scales, an area to Present the data, title, legend and key.

14. What are System Training tools?

System training will be based on users needs, system conceptual design, system learning goals and System performance goals. Training may include tools such as video training, manuals, online tutorials, reference manuals, quick reference guides and online help.

15. What is test for a good design?

It simply involves the use of display techniques, consistent location of elements, the proper use of “white space” and groupings and an understanding of visually pleasing composition. The best interface makes everything on the screen easily seen.

16. How to achieve clarity?

Clarity is influenced by a multiple factors, such as consistency in design, visually pleasing composition, a logical and sequential ordering, the presentation of the proper amount of information, groupings and alignment of screen items.

17. What are the qualities in visually pleasing composition?

Visually pleasing composition contain following qualities such as Balance, Symmetry, Regularity, Predictability, Sequentially, economy, unity, proportion, simplicity and groupings.

18. What is known as Tabbing?

When a screen is first presented, the cursor must be positioned in the first field or control in which information can be entered. Tabbing order must then follow the flow of information as it is organized on the screen.

19. What is necessary for ordering?

Ordering is necessary to

· Facilitate search for an item.

· Provide information about the structure and relationship among items.

· Provide compatibility with the user’s mental model of the item structure.

20. Define pull down menu.

clip_image015[1]It is the first level menus used to provide access to common and frequently used application action that take on a wide variety of different windows.


UNIT-III PART -A

1. Define window.

A window is a area of the screen usually rectangular in shape, defined by a border that contains a particular view of some area of the computer. It can be moved and rendered independently on the screen.

2. What is known as split box?

A Window can split into 2 or more pieces or panes by manipulating a split box located above a vertical scroll bar or to the left of a horizontal scroll bar.

3. Define size grip?

A size grip is a Microsoft windows Special hand]e included in a window to permit it be resized. When the grip is dragged the window resizes following the same conventions as the sizing border.

4. What are the presentation styles of windows?

1. Tiled windows

2. Overlapping windows

3. Cascading windows

5. What are the advantages of Tiled windows?

Advantages of Tiled windows:·

The system usual]y allocates and positions windows for the user, eliminating the necessity to make positioning decisions.

· Open windows are always visible, eliminating the possibility of them being lost and forgotten.

· Every window is always completely visible, eliminating the possibility of information being hidden.

6. What is known as cascading window?

A special type of overlapping window has the window automatically arranged in a regular progression. Each window is slightly offset from others.

7. What are the different features, of tiled & over lapping window?

Tiled window used for

· Single task activities

· Data that needs to be seen simultaneously

· Tasks requiring little window manipulation

· Novice or inexperienced users overlapping windows used for:

· Switching between tasks

· Tasks necessitating a greater amount of window manipulation

· Except or experienced users

· Unpredictable display contents

clip_image021[1]8. What are the various types of windows?

1. Primary window: It is the one that appears on a screen when an activity or action is started.

2. Secondary window: They are supplemental windows. It may be dependent or independent of primary window.

9. Differentiate between cascading and unfolding.

· Cascading: A cascade is used when advanced options at a lower level in complex dialog must be presented. Present the additional dialog box in cascaded form.

· Unfolding: To provide advanced options at the same level in a complex dialog. Provide a command button with an expanding dialog symbol.

10. What are the various window management schemes?

1. Single document interface

2. Multiple document interfaces

3. Workbooks

4. Projects

SDI

MDI

Single document interface

Multiple document interface

A single primary windows with asset

of secondary windows

Managing set of windows

Object and window have simple one to

one relationship

To represent multiple occurrence of an

object.

12. What is meant by windows project?

A project is a similar to MDI, but does not visually contain child windows. The objects held within the project window can be opened in primary windows that are peers with the project window.

13. How window is organized?

· Organize windows to support user tasks.

· Support the most common tasks in the most efficient manner or fewest steps.

· Use primary windows to perform major interaction.

· Use secondary windows to obtain or display supplemental information Related to the primary windows.

14. What are the advantages of frames in web systems?

· They decrease the user's need to jump back and forth between screens, thereby reducing navigation related cognitive overhead.

They increase the user's opportunity to request, view and compare multiple sources of information.

· They allow content pages to be developed independently of navigation pages.

15. List some example for device based controls.

Device based controls called input devices are the mechanism through which people communicate their desires to the system.

Example: track ball, joystick, graphic tablet, light pen & touch screen

16. Differentiate the usage of keyboard with mouse?

Keyboard

Mouse

Keying process becomes fast and well

learned

Mouse is slower and it has tendency to

move about the desk.

It remains in the same spot. Its

location can be memorized.

Its location cannot be memorized

17. What is meant by graphic tablet?

A graphic tablet is a device with horizontal surface sensitive to pressure, heat, light or the blockage of light. It may lie on the desk or may be incorporated on a keyboard and is operated with fingers & light pen.

18. What is meant by spin box?

A spin box called spin button is a single field followed by 2 small vertically arranged buttons inscribed with up and down arrows. A selection entry is made by using the mouse to point at one of the directional buttons and clicking.

19. What is meant by slider?

A slider is a scale that exhibits the amount or degree of a quantity or quality. A slider incorporates the range of possible values and includes a shaft representing the range, the values with label and visual indication of the relative setting through the location of a sliding arm.

20. Differentiate between tooltip from balloon tips.

Tool tips

Balloon tips

It can be posted at any time only one

the last posted will be possible.

It is used for task bar for specified minimum

and maximum limits.

It has one or two words that identify

button action

It has a small pop up window that contain

information presented in a word balloon.


UNIT-IV PART – A

l. What type of words used in effective communication?

· Short familiar words

clip_image011[1]· Standard alphabetic characters

· Complete words

· Positive terms

· Simple action words

· Consistent words

2. What are the guidelines followed for sentence and message?

· Sentence and messages must be

· Brief and simple

· Directly and immediately usable

· An affirmative statement.

· In an active voice.

3. Define message? What are the types of messages?

Messages are communication provided on the screen to the screen viewer. A message should possess the proper tone and style and be consistent within it.

Types of message:

· System message

· Status message

· Informational message

· Warning message

· Critical message

· Question message

4. What is meant by instructional message?

Provide instructional information at the depth of detail needed by the user. Locate instruction at Strategic points on screen. Display instructions in a manner that visually differentiates from all other screen elements.

5. What is meant by response time?

Feed back to an user for an action must occur within certain time limits. System should match the speed and flow of human through processes.

6. What is the use of progress indicator?

A progress indicator is a long rectangular box that is initially empty but filled as the operation proceeds. Dynamically fill the bar with a color or shade of grey.

7. What is known as ear cons?

Sounds sometimes called ear cons, are useful for altering the user.

· To minor and obvious mistakes

When something unexpected happens

· When a long process is finished

8. Differentiate between slip and mistake?

Slip

Mistake

Can be reduced through proper

application of human factors in design.

Can be reduced by eliminating ambiguity from

design.

9. What are the ways to prevent errors?

Errors can be reduced in a number of ways

· Disable inapplicable choices.

· Design screen using selection controls instead of entry controls.

· Accept common misspelling whenever possible.

· Before an action is performed, permit it to be reviewed.

· Provide a common action mechanism.

l0. What is meant by contextual Help?

It provides information within the context of a task being performed or about a specific object being operated. Common kinds of contextual help command buttons, status bar messages and tool tips.

ll. What is the purpose of hints?

· To provide a few important contextual but specific items of information related to a displayed screen.

· It is more easily accessible and relevant to te current situation.

· The objective is quickly get the user back on track when confusion occurs.

l2. What is meant by internalization?

It is the process of isolating culturally specific elements form a product. The German text of a program developed in Germany for example is isolated from the program itself.

13. What is meant by localization?

Localization is the process of infusing a specific cultural context into previously internalized product.

Ex: Translating German Screen Components and message into English for American

users.

l4. What is meant by Accessibility?

Accessibility means a system must be designed to be usable by an almost unlimited range of people. It can be def1ned as providing easy access to a system for people with disabilities.

l5. What are the various types of disabilities?

Disabilities can be grouped into several categories.

· Visual

· Hearing

· Physical movement

· Speech or language impairments

· Cognitive disorders

· Seizure disorders

16. What is meant by icon?

Icons are used to represent objects and action with users can interact with or they can manipulate. It may be stand alone on a desktop or in a window. It is to reinforce important information a warning icon in a dialog message box.

17. What are the various kinds of icon?

· Symbolic - An abstract image representing something.

· Exemplar - An image illustrating an example or characteristic of something.

· Arbitrary - An image completely arbitrary in appearance whose meaning must be learned.

· Analogy - An image physically or semantically associated with something.

· Resemblance – An image that looks like what it means.

18. What is meant by dithering?

If pixels of different colors are placed next to each other, this tremor combines the 2 colors into a 3rd color. This is referred to dithering.

19. Mention the properties of a color.

· Hue: It is the spectral wavelength composition of a color.

· Chroma or Saturation: It is the purity of a color in a scale from gray to the most vivid version of the color.

· Value or Intensity: It is the relative lightness or darkness of a color in a range from black to white.

20) What is known as protanopia, deuteranopia and tritanopia.

Protanopia, Deuteranopia and Tritanopia are color viewing deficiencies.

· Red viewing deficiency is called protanopia.

· Green viewing deficiency is called deuteranopia.

· Blue viewing deficiency is called tritanopia.


UNIT-V PART - A

1.Differentiate control and section borders.

Control Border

Section Border

Incorporate a thin single line border

around the elements of selection control.

Incorporate a thicker single line border around

Group of related entry or the selection control elements.

2. What are the principles of good screen design?

· Present the proper amount of information on each screen.

· Providing an ordering that is logical, sequential and rhythmic to guide a person’s eye

through the display.

· Keep the proportion of the window devoted to information no more than 30 to 40 percent

of the window’s entire area.

Maintaining a top to bottom, left to right flow.

3. What is the purpose of usability testing?

Usability testing serves a two hold purpose.

· Testing is used to evaluate the product. It validates design decisions.

· It establishes a communication bridge between developers and users.

4. What is meant by cognitive walk through?

In a cognitive walk through developers walk through an interface in the context of representative user tasks. Individual task actions are examined and the evaluators try to establish a logical reason way the user would perform each examined action.

5. What is meant by think-aloud evaluation?

The users perform specific tasks while thinking out load. The objective is to get the user to talk continuously.

6. Define focus group.

In a focus group a small group of knowledgeable users and a moderator are brought together to discuss an interface design prototype or proposed design tasks.

7. Define transition diagram.

It has a set of nodes that represents system states and a set of links between the nodes that represents possible transitions. Each link is labeled with the user action that selects that link and possible computer responses.

8. What are importance of usability testing?

It is important for many reasons including the following.

· Developers and users possess different models.

· It is importance to predict usability from appearance.

· Design standards and guidelines are not sufficient.

· Informal feedback is inadequate.

9. What is meant by prototype?

A prototype is a simulation of an actual system tat can be quickly created. It is a vehicle for exploration, communication and evaluation.

10. What are the various searches used in the multimedia document?

· Photo search

· Map search

· Design or Diagram search

· Sound search

· Video search

· Animation search

11. What are the features of user-interface building tools?

· User interface independence

· Rapid prototyping

· Methodology and notation

12. List some software tools used for user interface design.

· User interface model can be created with slide show presentation such as Adobe persuasion, Microsoft-Power point.

· Apple hyper card, Macro Mind director or A Symmetric Tool Book used for creating multimedia applications.

· Visual programming tool paragraph provide direct manipulation

clip_image03713. What are the benefits of menu trees?

· They are powerful as a specification tool since they sow users, managers, implementers and other interested parties the complete and detailed coverage of the system.

· It shows high level relationships and low level details.

14. What are the ways to categorizing the web?

· Primary way of categorizing the web sites is by the originator’s identity.

· Second way of categorizing the web sites is by goals of the organization.

· Third way of categorizing the web sites is by the number of pages or amount of information is accessible.

· Fourth way of categorizing the web sites is by measure of success.

15. What are the various types of TTT?

· One dimensional linear data

· Two dimensional map data

· Three dimensional data

· Temporal data

· Multi dimensional data

· Tree data

· Network data

16. What is the four phase framework to clarify user interfaces for textual search?

· Formulation

· Action

· Results

· Refinement

17. Define www.

World website design is a matter of balancing the structure and relationship of menu or one pages and individual content pages or other linked graphics and documents.

18. Mention the types of prototypes.

· Hand sketches and scenarios

· Interactive paper prototype

· Programmed fa├žade.

MA1254 -STATISTICS AND NUMERICAL METHODS Two Marks Questions With Answers 2014


Anna University, Chennai

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SRINIVASAN ENGINEERING COLLEGE, PERAMBALUR

MA1254 -STATISTICS AND NUMERICAL METHODS

QUESTION BANK

PART –A

UNIT I

  1. Define standard error.

The S.D of a sampling distribution of a statistic is know as its standard error.

  1. Define null hypothesis.

For applying the test of significance, we first set up of a hypothesis a define statement about the population parameter. Such a hypothesis is usually a hypothesis of no difference .

  1. What is type I , type II error?
    1. Type I error : Reject null hypothesis , when it is true.
    2. Type II error : Accept null hypothesis, when it is wrong.

i.e) accept null hypothesis, when alternative hypothesis is true.

4. Define test statistics.

Z= t – E(t) / s E(t).

  1. Write the application of “ F” test and chi- square test.

F test - To test if two samples have come from the same population.

Chi square test – To test the significance of discrepancy between experimental values and the theoretical values.

  1. Write two applications of Chi square test.

Chi square is used to test whether differences between observed and expected frequencies are significances.

  1. Define a F – variance.

F = Greater variance / smaller variance.

8. When we use the large sample and what is the test we use for that?

When n > 30 we use z test.

  1. What are the tests we use in small samples?

t- test, F test and Chi square test.

10. What is the degrees of freedom of Chi square test?

Degrees of freedom = (r- 1) ( s -1).


UNIT – II

  1. Write the basic design of experiments.

Randomised blocks, replication and plan of an experiment.

  1. Define ANOVA.

Analysis of variance (ANOVA) is a technique that willenable us to test for the significance of the difference among more than two sample means.

According to R.A. Fisher, “ The separation of variance ascribable to one group of causes from the variance ascribable to other group.

  1. What are the basic steps in analysis of variance.

i) One estimate of the population variance from the variance among the sample means.

ii) Determine a second estimate of the population variance from the variance within the sample.

iii) Compare these two estimates if they are approximately equal in value, accept the null hypothesis.

  1. What are the technique of ANOVA ?

i) one way classficition

ii) two way classification separately

iii) Randomized block design

iv) Latin square.

  1. What are the advantages of C.R.D?

i) Easy to lay out.

ii) Allows flexibility

iii) Simple statistical analysis.

iv) The lots of information due to missing data is smaller than with any other design.

  1. State the advantages of Latin square over other design.

i) Latin square controls more of the variation than the completely randomized block design with a two way stratification.

ii) The analysis is simple.

iii) Even with missing data the analysis remains relatively simple.

  1. Write the differences between RBD and LSD.

RBD

i) Available for wide there is diagonal trend range of treatments’

ii) no restriction on the number of replications.

iii) Flexible and easier to mange.

iv) Can be accommodated in a field of any shape.

LSD.

i) More efficient when there is diagonal ternd of fertility.

ii) Suitable only in the special cases where the land exhibits marked trends in fertility.

iii) Suitable mainly for 5 or 10 treatments.

iv) Shape of the field should be approximately square or rectanglar.

  1. Define replication.

To estimate the magnitude of an effect in an experiment the principle of randomization and replication are applied. Randomisation by itself is not necessarily sufficient to yield a valid experiment. The replication or repetition of experiment or experimental unit is also necessary. Randomisation must be invariably accompanied by sufficient replication so as to ensure validity in an experiment.

  1. What is the degrees of freedom of LSD.

DOF = (n-1)(n -2)

  1. How can we find the F ratio.

F = MSC/ MSE.


UNIT – 3

1. Compare Gauss – Jacobi and Gauss –Seidal methods for solving linear systems of the form

AX =B.

Gauss elimination is direct method.

Gauss Seidal method is iterative method.

2. For solving a linear system, compare Gauss elimination method and Gauss – Jordan method.

In Gauss elimination method the given system is transformed system with upper – triangular coefficient matrix which can be solved by back substitution. In Gauss – Jordan method the coefficient matrix is reduced to an unit matrix and then directly we can find the unknowns.

3. State the two differences between direct and iterative methods for solving system of equations.

Direct Method

Iterative Method

It gives exact value

It gives only approximate solution

Simple, take less time

Time consuming and labourious

This method determine all the roots at the same time.

This method determine only one root at a time.

4. What is the condition for convergence of Gauss – Jacobi method of iteration?

The coefficient matrix should diagonally dominant.

5. What are the elementary transforms?

Elementary Transforms:

i) Interchange the i th and j th row ( or column)

ii) Multiply all the elements in the ith row by a number K.

iii) Adding the elements i n the i th row to the corresponding elements in the j th row multiply by a constant K.

6. Give the name of any 2 iteration method in numerical methods.

Gauss – Seidel method , Jacobi ‘s method.

7. In Gauss elimination method , the coefficient matrix is transformed to what form.

Upper triangular form.

8. What type of eigen value can be obtained using power method?

We can obtain dominant egien value of the given matrix.

9. State a sufficient condition for Gauss – Jacobi method to converge.

Let the given equations be

clip_image002

clip_image004

The sufficient condition is

clip_image006 clip_image008

clip_image010

10. State Newton’s Raphson iterative formula.

clip_image012 = clip_image014 where n = 0,1,2.....


UNIT 4

1. Construct a linear interpolating polynomial given the points (clip_image016(clip_image018

Y(x) = clip_image020 clip_image022 clip_image024

2.Form the divided difference table for the following data:

X

2

5

10

Y

5

29

109

Solution:

Divided difference table:

X

Y

I divided difference

II divided difference

2

5

8

16

1

5

29

10

109

3.Taking h to be the interval of differencing, find clip_image026.

clip_image028 = clip_image030

= clip_image032

= ( clip_image034) (clip_image036)

= clip_image038 .

4.When Newton’s backward interpolation formula is used?

To find the unknown values of ‘y’ for some ‘x’ which lies at the end of table of values, we use Newton’s backward formula.

5.Why is Trapezoidal rule is so called?

Since we approximate the given integral by the sum of ‘n’ Trapezoids we call it as Trapezoidal rule.

6.When does Simpson’s rule given exact result?

The Simpson’s rule will give exact result when we are decreasing the interval h.

7.Why Simpson’s 1/3 rule is called a closed formula?

Since the end point ordinates clip_image040 and clip_image042 are included in the Simpson’s 1/3 rule, it is called closed formula.

8.State Newton’s formula to find f’(x) using formula differenc es.

f’(x) = clip_image044

9.What is the order of error in Trapezoidal rule?

The order of error in Trapezoidal rule

E = - clip_image046

10.What is the order of the error in Simpson’s formula?

Two.


UNIT – 5

1. Where the Taylor series method of solving differential equation is powerful?

If it is possible to find the successive derivatives in a very easy manner , then only Taylor series method is powerful.

2. Write down the third order Taylor’s algorithm.

clip_image048

3. Write the merits and demerits of the Taylor method of solution.

Merits:

1. Taylor formula is easily derived for any order according to our interest.

2. The values of y(x) for any x are easily obtained.

Demerits:

This method suffers from the time consumed in calculating the higher derivatives.

4. Using Euler’s method , find y(0.1) if clip_image050 , y(0) = 0.

Given clip_image052 , h= 0.1

clip_image054

= 0 + 0.1 f(0,0)

= 0.1 (1) = 0.1.

5. In the derivation of fourth order Runge – kutta formula, why it is called fourth order.

The fourth order Runge – Kutta method agree with Taylor series solution upto the terms of clip_image056 . Hence it is called fourth order R.K method.

6. Compare Taylor series and R.K method.

a) The use of R.K ‘s method gives quick convergence to the solutions of the differential equations than Taylor’s series.

b) The labour involved in R.K’ s method is comparatively lesser.

c) In R.K’ s method , the derivatives of higher order are not required for calculation as in Taylor’s series method.

7. What are the advantages of R.K method over Taylor’s method?

The R.K method is desgined to give greater accuracy and they possess the advantage of requiring only the function values at some selected points on the sub intervals.

8. What do we mean by saying that a method is self starting? Not self – starting?

Iteration method is self starting since we can take value which lies in the given interval [a,b] in which the root lies. But Milne’s method is not self . Since we should know any 4 values prior to the value which we need.

9. State the Milne’s correction formula.

clip_image058

10. Define a difference quotient.

A difference quotient, is the quotient obtained by dividing the difference between two values of a function , by the difference between the two corresponding values of the independent variable.

MA1254 -STATISTICS AND NUMERICAL METHODS Questions Bank 2014


Anna University, Chennai

Anna_University,_Chennai_logo

SRINIVASAN ENGINEERING COLLEGE, PERAMBALUR

MA1254 -STATISTICS AND NUMERICAL METHODS

QUESTION BANK

PART – B

UNIT I

1.Car stereo manufacturer of A have mean life time of 1400 hrs with S.D of 200 hrs while those

of manufacturer B have mean lifetime of 1200 hrs with S.D of 100 hrs. If a random

sample of 120 stereos of each manufacturer are tested. i) What is the probability that the

manufacturer of A’s stereo’s will have a mean life time of at least 160 hrs more than the

manufacturer B’s stereo’s ii) and 250 hrs more than the manufacturer B stereo’s.

2. In a sample of 1000 people in Mumbai, 540 are rice eaters and the rest are wheat eaters. Can

we assume that both rice and wheat are equally popular in this state at 1% LOS?

3. In a test given of two groups of students the marks obtained were as follows.

I Group: 18 20 36 50 49 36 34 49 41

II Group: 29 28 26 35 30 44 46

Examine the significant difference between the means of marks secured by students of the above 2 groups.

4. The weight gains in pounds under two systems of feeding of calves of 10 pairs of identical

twins is given below.

Twin pair: 1 2 3 4 5 6 7 8 9 10

System A: 43 39 39 42 46 43 38 44 51 43

System B: 37 35 34 41 39 37 37 40 48 36.

Discuss whether the difference between the 2 systems of feeding is significant.

5.Two random samples gave the following results;

Sample

Size

Sample mean

Sum of squares of deviations from the mean

1

10

15

90

2

12

14

108

Test whether the samples come from the same normal population at 5% LOS.

6. 4 coins were tossed 160 times and the following results were obtained.

No of heads: 0 1 2 3 4

Observed Fr:17 52 54 31 6

Under the assumption that the coins are balanced, find the expected frequencies of getting

0, 1,2, 3,4 heads and test the goodness of fit.

7.A sample of 200 persons with a particular disease was selected. Out of these , 100 were given a

drug and the others were not given any drug. The result are as follows:

No of persons

Drug

No Drug

Total

Cured

65

55

120

Not cured

35

45

80

Total

100

100

200

Test whether the drug is effective or not.

  1. The following data relate to a random sample of government employees in 2 states of the Indian Union.

Sample

Size

Mean monthly income of the employees

Variance

1

16

440

40

2

25

460

42

Test whether the samples come from the same normal population

  1. A normal population has a mean of 6.48 and S.D of 1.5 . In a sample of 400 members mean is 6.75 .I s the difference significant?
  1. A simple sample of heights of 6400 English men has a mean of 170 cm and S. D of 6.4 cm, while a simple sample of heights of 1600 Americans has a mean of 172 cm and a S.D of 6.3 cm. Do the data indicate that Americans are, on the average , taller than the Englishmen?
  1. 1000 students at college level were graded according to their I.Q and their economic conditions. What conditions can U draw from the following data:

Economic conditions

I.Q level

High

Low

Rich

460

140

Poor

240

160


UNIT – II

1. The following are the number of mistakes made in 5 successive days by 4 technicians working for a photographic laboratory. Test whether the difference among the 4 sample means can be attributed to chance. LOS at 1%.

Technician

I

II

III

IV

6

14

10

9

14

9

12

12

10

12

7

8

8

10

15

10

11

14

11

11

2. Set up the analysis of variance for the following results of a Latin square design at 1% LOS.

A 12

C 19

B 10

D 8

C 18

B 12

D 6

A 7

B 22

D 10

A 5

C 21

D 12

A 7

C 27

B 17

3. To study the performance of 3 detergents and 3 different water temperatures, the whiteness readings were obtained with specially designed equipment.

Detergent

Water temp

A

B

C

Cold water

57

55

67

Warn water

49

52

68

Hot water

54

46

58

Perform a 2 way analysis of variance using 5 % LOS.

4. The following data are obtained from a clip_image002 factorial experiment blocked 3 times. Evaluate the sum of squares for all factorial effect by the contrast method. Draw conclusion.

Blocks

Treatment combination

I

II

III

(1)

12

19

10

k

15

20

16

p

24

16

17

kp

24

17

29

5.Perform two way ANOVA for the given below:

Treatments

Plots of land

A

B

C

D

I

38

40

41

39

II

45

42

49

36

III

40

38

42

42

6.Analyze the variance in LSD .

S122

P121

P123

Q122

Q124

R123

P122

S125

P120

Q199

S120

R121

R122

S123

Q121

P122

7. The following data are obtained from a clip_image002[1] factorial experiment blocked 3 times. Evaluate the sum of squares for all factorial effect by the contrast method. Draw conclusion.

Blocks

Treatment combination

I

II

III

IV

(1)

12

12.3

11.8

11.6

k

12.8

12.6

13.7

14

p

11.5

11.9

12.6

11.8

kp

14.2

14.5

14.4

15

8. Find ANOVA using CRD.

Samples

8

7

12

10

5

19

7

10

13

14

9

12

11

9

14

9. Perform two way ANOVA for the given below:

Water temp

Detergent A

Detergent B

Detergent C

Cold

57

55

67

Warm

49

52

68

Hot

54

46

58

10.Perform ANOVA for the given below using CBD method.

A6

C5

A8

B9

C8

A4

B6

C9

B7

B6

C10

A6


Unit 3

1. Solve the system of equations by Gauss Elimination method. 10 x- 2y +3z =23;

2 x+10 y -5z = - 33; 3x -4y +10 z =41.

2. Find the iterative formula for finding the value of clip_image004 where N is a real number , using Newton –

Raphson method also find 1/26.

3.Solve the following system of equations by Gauss – Jacobi method

27 x +6y –z =85; x + y +54 z =110; 6x +15 y +2z =72.

4.Using power method , find the eigen value of A =clip_image006

5. Solve the system of equations by Gauss Jordan method

3x+ y – z = 3; 2x – 8y + z = -5; x -2y + 9z = 8

6.Solve the following system of equations by Gauss – Seidel method

4x + 2y + z =14; x + 5y – z =10; x + y +8z =20.

7.Find the inverse of the matrix clip_image008

8.Find the dominant of eigen value and eigen vector of A =clip_image010

9.Compute the real root of x log x =1.2 using Newton’s Raphson method.

10. Find the inverse of clip_image012


Unit 4

1.The following table gives the population of a town during the last 6 census. Estimate using Newton’s

interpolation formula, the increase in the population during the period 1946 to 1948.

Year

1911

1921

1931

1941

1951

1961

Population(in 1000’s)

12

13

20

27

39

52

2.By dividing the range into 10 equal parts, evaluate clip_image014by using Simpson’s 1/3 rule.

3.Using the data given below find the value of clip_image016 by Trapezoidal rule.

X

1

2

3

4

5

6

7

8

9

Y

2.061

2.312

2.891

3.106

3.670

4.721

6.103

7.950

9.942

4.A rod is rotating in a plane about one of its ends. If the following table gives the angle clip_image018 radians through which the rod has turned for different values of time t seconds. Find it angular velocity and angular acceleration when t= 0.7 seconds.

t seconds

0.0

0.2

0.4

0.6

0.8

1.0

clip_image018[1]radians

0.0

0.12

0.48

1.10

2.0

3.20

5.Using Lagrange’s formula to calculate f(3):

x

0

1

2

4

5

6

F(x)

1

14

15

5

6

19

6..Find the cubic function from the following table:

x

0

1

3

4

F(x)

1

4

40

85

7.From the following table find clip_image020 at x = 43.

x

40

50

60

70

80

90

clip_image020[1]

184

204

226

250

276

304

8.Find the value of x = 2.5

x

0

1

2

3

4

y

7

10

13

22

43

9.Find the polynomial using Newton’s forward method.

x

4

6

8

10

y

1

3

8

16

10.Find the value of y’’ at the point x =0.96

X

0.96

0.98

1

1.02

1.04

F(x)

0.7825

0.7739

0.7651

0.7563

0.7473


Unit 5

1.Evaluate the values of y(0.1) given y’’ –clip_image022+clip_image024 =0 , y(0) =1, y’(0) =0 by using Taylor series

method.

2. Using Euler’s method solve y’ = x + y + xy, y(0) =1 . Compute y at x =0.1 by taking h =0.05

3. Using R.K method of 4th order solve clip_image026 with y(0) = 1 at x=0.2.

4. Consider the second order initial values problem y’’ -2y’ =clip_image028 sint with y(0)= -0.4 and

y’(0)= -0.6 using fourth order R.K method , find y(0.2)

5. Using Milne’s method find y(4.4) given 5xy’ + clip_image024[1]-2 = 0 given y(4) =1, y(4.1)=1.0049,

y(4.2) =1.0097 & y(4.3) = 1.0143

6. Solve the system equations clip_image030 with y(0) = 1, z (0) = 1 by taking h= 0.1 to get

y(0.1) and z(0.1) by Taylor series method.

7.Solve clip_image032 = 1- y , y(0) =0 by modified Euler’s method.

8.Using R.K method solve clip_image034 with y(0) = 1 at x= 0.2

9. Solve clip_image036 by

Milne’s method to find y(0.8) and y(1).

10. Using improved Euler’s method find y(0.2) and y(0.4) from y’ = x +y , y(0) = 1 with h =0.2.