Intro to Engineering Study Sheet PDF

lOMoARcPSD|46133431 Copy of Intro-to-Eng-study-sheet Intro. to Engineering (University of Ontario Institute of Technology) Scan to open on Studocu Studocu is not sponsored or endorsed by any college or university Downloaded...

lOMoARcPSD|46133431 Copy of Intro-to-Eng-study-sheet Intro. to Engineering (University of Ontario Institute of Technology) Scan to open on Studocu Studocu is not sponsored or endorsed by any college or university Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Intro to Eng study sheet History of engineering Mesopotamians The land between Tigris and Euphrates Rivers o The first wheeled cart o Canals, temples and city walls o As early as 5500 BCE: astrolabe for astronomical observations o Galileo’s astrolabe was in Florence 1570 Code of Hammurabi 228- if a builder has built a house for a man, and has finished it, he shall pay him a fee of two shekels of silver for each SAR built on 229. If a builder has built a house for a man, and has not made his work sound, and the house he built has fallen, and caused the death of its owner, that builder shall be put to death. 230. If it is the owner's son that is killed, the builder's son shall be put to death. 231. If it is the slave of the owner that is killed, the builder shall give slave for slave to the owner of the house 232. If he has caused the loss of goods, he shall render back whatever he has destroyed. Moreover, because he did not make sound the house he built, and it fell, at his own cost he shall rebuild the house that fell. 233. If a builder has built a house for a man, and has not keyed his work, and the wall has fallen, that builder shall make that wall firm at his own expense. Canals and Irrigation The first aqueduct was built in 690 BC The water system of Nineveh eventually featured 150km of canals, aqueducts and other water works Although limited, Assyrian aqueduct pre-dated the more famous roman version by 500 years Baghdad Battery First battery? 250 bc o Resembles a galvanic cell o Believed to be used for electroplating in Mesopotamia Egyptians Experts in planning and construction Earliest known form of surveying Developed effective irrigation systems Built remarkable edifices (huge structures) out of stone o Frist pyramid was Step Pyramid at Sakkara o About 2980 BC Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Zoser’s strep pyramid o Six mastabas o 100,000 workers o 20 years to build India Indus valley: o Water reservoirs and canals o Drainage and sanitation systems Suspension bridges in the 4th century AD Greeks Harbor builders Built the first lighthouse in the world 280 BC Static electricity: Thales of Miletus (Greek) 600BC described a form of static electricity Romans Developing methods of construction Hydraulic cement Pile drivers, treadmill hoists, wooden bucket wheels Circus Maximus- for games and contests Roads Pantheon – a temple made in 17 BC (great architecture) The Alcantra Bridge: built in Spain in 98 AD six arches of dry stone Chinese Engineering Compass, gunpowder, papermaking, printing Matches, dry docks The great wall Middle ages the structures of Gothic cathedrals development of cannons and gunpowder mechanical clocks William gilbert coined the term “electricity” in 1600 Advancement of Science The term engineering, deriving from the word engineer, which itself dates back to 1325, when an engineer (literally, one who operates an engine) originally referred to “a constructor of military engines.” Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 In this context, now obsolete, an “engine” referred to a military machine, i. e., a mechanical contraption used in war (for example, a catapult). The word “engine” itself is of even older origin, ultimately deriving from the Latin ingenium (c. 1250), meaning “innate quality, especially mental power, hence a clever invention.” Leonardo da Vinci (1452-1519): conceptual designs and practical engineering works Nicolaus Copernicus (1473-1543): Modern astronomy Galileo (1564-1642): Formulated the scientific method of gaining knowledge Robert Boyle (1627-1691): compression and expansion of gases Robert Hooke (1635-1703): theory of elasticity Sir Isaac Newton (1642-1727): calculus, secrets of light and colour, theory of gravitation Thomas Newcomen (1663-1729): the first practical steam engine Leading up to the 20th century, great advancements in engineering occurred in Transportation o Canal systems : industrial revolution, Rideau canal o Road building o Steam engine and railroads: Pacific railroad, orient express, and Canadian pacific railroad Manufacturing o Steam engines supported: manufacturing, mining, transportation and textile industries Mining Electric power o Volta devises the first electric battery o Ohm quantifies the relationship between electric current and potential difference in a conductor o Humphrey Davy discovered electromagnetism and the arc light o Faraday demonstrated the process of magnetic induction o Edison invented the practical incandescent light bulb o Tesla secured patents for an induction motor and ac system o Westinghouse granted contract for first Niagara hydroelectric project. Early computer systems/communication o Pavel Schilling invents the first electric telegraph o Alexander graham bel patents the “acoustic telegraph” 20Th century Hydroelectric damns Nuclear power stations Cars Write flier Transistor Integrated circuit First cpu Moore’s law Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 The National Academy of Engineering List of the Challenges for Engineering in the 21st Century. 1) Make solar energy economical 2) Provide energy from fusion 3) Develop carbon sequestration methods 4) Manage the nitrogen cycle 5) Provide access to clean water 6) Restore and improve urban infrastructure 7) Advance health informatics 8) Engineer better medicines 9) Reverse-engineer the brain 10) Prevent nuclear terror 11) Secure cyberspace 12) Enhance virtual reality 13) Advance personalized learning 14) Engineer the tools of scientific discovery Roles of engineering society Ingenium (Latin) first used to describe those who had ability to invent/ operate weapons of war Engineering means different things: o England: People with practical skills o North America: Person who has received formal training to be an Engineer o Early American programs based on French engineering schools In Canada, the title “professional engineer” is restricted by law. o Only those persons who ▪ Have demonstrated competence ▪ Are licensed by professional licensing association (e.g., PEO, APEGS, etc.) An engineer is: A person who uses science, mathematics, experience, and judgment to create, operate, manage, control, or maintain devices, mechanisms, processes, structures, or complex systems Samuel Florman: “ To be human is to engineer” A typical technical team might consist of o Scientists o engineers o technologists o technicians o skilled workers Engineers provide the key link between theory and practical applications o Has theoretical background o Thinks creatively o Practical results o Able to lead multiple team members Education o Bachelors degree of engineering There are 74 different kinds of engineering across Canada Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Most common are: electrical, mechanical, civil, computer, chemical, and industrial Major Canadian engineering accomplishments Transcontinental railway o Canadian pacific railway linked Canada from coast to coast in 1885 o St. Lawrence Seaway opened up the great lakes to oceangoing ships in 1959 o Athabasca Oil Sands commercial oil sand o Nuclear power CANDU nuclear power system produced electric power using uranium fuel and heavy water cooling system o Very-high voltage transmission o Trans Canada Telephone Network 1958 o IMAX o Pacemaker developed by John A. Hopps in 1949 o Confederation bridge ▪ Longest bridge in the world crossing salt water subject to winter ice hazards ▪ Links PEI with New Brunswick ▪ Oct 1993 to May 31 1997 CN tower 1976 Blackberry Challengers for engineering Climate change o Cause intense weather reduce greenhouse gas emissions o New methods of conserving energy and reducing waste Role in society, need more engineers in upper roles in policy making Regulation of Engineering Purpose of regulation: o Prevent unqualified persons from practicing o Protect the public History of regulation o US was the first country to regulate engineering o Following Quebec’s bridge collapses in 1907 and 1916, Canada enacts regulations. o Engineering in Canada is self-regulated o Associations in provinces regulate engineering Case study: Quebec Bridge Tragedy Longest cantilevered span in the world Structure collapsed during construction in 1907 and again in 1916 75 workmen were killed Theodor Cooper (new York) was hired as consulting engineer Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Cooper and assistant worked from their office in new York Materials made in Pennsylvania Workmen assembled bridge under supervision od site engineers and inspectors Bridge was made from shores to middle Cooper was telegrammed when problems arose When problems were serious then cooper came to site Work was supposed to stop but a chief site engineer ordered work to continue There were serious errors in coopers design Cooper rarely visited site Communication problems Learned that: o Only competent ethical people should practice engineering o Laws were passed to license professional engineers Laws regulating engineering Associations are empowered to: o Monitor standards and professional practice o Discipline practitioners 1937, provincial associations created Canadian Council of Professional Engineers (CCPE) (renamed Engineers Canada in 2007) Roles of Engineers Canada Develops policies, guidelines, and position statements Result: Laws across Canada are similar Consistent laws enable engineers to move and practice across Canada Ontario – Professional Engineers of Ontario (PEO) Admission to Engineering Profession Study- get degree Register- apply to provincial association Work- gain engineering experience Write- professional practice examination Good character- submit character references Receive your engineering license. Provincial Associations Protect the public Structure makes engineering a well-organized profession Instill public confidence in the profession Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Learning and engineering approach Three major learning tasks in engineer’s lifetime: Successful completion of engineering education Obtain and profit from practical experience Maintain professional competence through continuing professional development (CPD) Professionalism and ethics Unprofessional behavior: Harms the public Reduces public confidence in engineering Can end a promising career Ex: supervising engineer accepts bribe to allow contractor to use substandard material o Illegal o Subject to disciplinary action of association Association codes of ethics: Each provincial licensing association publishes a code of ethics regulating engineers Main purpose: Protect the public Professional practice exam ensures engineers understand code of ethics Disciplinary actions are imposed on engineers who disregard code of ethics. The national code of ethics: Code of ethics imposes Duties ON Engineers to Conduct themselves in Honorable/ ethical Way: 1. public and THE Environment 2. competency clients or employers 3. advancement of the profession 4. Fairness toward others 5. Consequences of decisions 6. Report 7. Societal consequences 8. Equity Duty to public and environment The engineer Must consider his or her duty to society/ environment as most important duty Competency: Offer services, advise only in area of competency Practice in a carful and diligent manner Duty to clients or employers Professional engineer must: o Act as faithful agents to clients/employers o Keep employer/clients business confidential o Disclose any conflict of interest Engineer in private practice o Same duties to client as employee to employer Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Advancement of the Professionalism Keep selves informed to maintained competence Strive to advance body of knowledge Provide opportunities for growth of subordinate's Maintain dignity and prestige of profession o Must avoid dishonorable/ disgraceful conduct Fairness towards others Must act with equity fairness, courtesy and goodwill towards clients and colleagues Give credit where due Accept and give honest and fair professional criticism Must recognize rights Consequences of decisions Present clearly the consequences of engineering decisions are overrules or disregarded Duty to report Report to association any illegal or unethical engineering decisions by engineers or others Societal consequences: Be aware of ensure that clients/ employers are made aware of societal/environmental consequences of actions/projects Interpret engineering issues to public in objective and truthful manner Equity Treat equitably and promote the equitable Ethics in workplace Create productive / professional workplace Students not bound by code of ethics…but o Professional atmosphere important in student workplace o Professional behavior expected of students on work terms Teamwork essential for successful completion projects Ethics in the workplace Ethical problems Code of ethics can serve as a guide Resolving disputes o Settle disputes through courteous, direct communication o Full review of dispute will lead to solution Whistle Blowing Last resort when all internal avenues exhausted Licensing Association may mediate mostly Illegal activities must be reported if public health/welfare involved Failure to act may be considered professional misconduct or even complicity Although whistle-blowing is rare, several Associations have defined reporting procedures Procedure: o Get facts and identify urgency o Consider/ propose solution o Speak to key person Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 o Go higher o Blowing the whistle (association may act as a mediator) Enforcement activities of associations Protect the public Action depends on whether complaint concerns licensed or unlicensed person Common professional complaints Conflict of interest Breach of standards Proper use of engineer’s seal The act of signing and sealing a document o Documents completely prepared o Plans are approved for construction Should not seal preliminary documents Professional misconduct to seal a document that was neither prepared Iron ring Ceremony- Ritual of Calling of an Engineer Participants in ceremony wear an iron ring on little finger of working hand Society vs association Society o Membership is voluntary o Advocate on behalf of members Association o Need a license to practice (membership is mandatory) o Must protect the public Role of engineering societies Focus on a discipline, industry or specialization Their activities have an impact on the engineering profession Licensing laws in other countries less comprehensive in Canada History of engineering societies Industrial revolution created a need to disseminate technical information In Britain the first engineering society was established- Institute of civil engineers 1818 IEEE 1963 AIEE and IRE merged to create: Institute of Electrical and Electronics Engineers (IEEE) Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Some ethical Systems Rule Based ethics o Apply a set of rules to make all decisions Conditional Rule-Based Ethics o Rules apply (or not) depending on conditions Utilitarian Ethics o Produce the greatest good for the most people Main ethical duties: PEO code of ethics Duty to Society (major) Duty to Employers Duty to Clients Duty to Colleagues Duty to Employees and Subordinates Duty to the Engineering Profession Duty to Oneself Occupational health and safety The engineer needs a methodical procedure for recognizing hazards and reducing them Engineers should know o Safety responsibilities o Guidelines and principles for recognizing and controlling hazards o Applicable safety codes and standards Safety Responsibilities of the engineer Engineers maybe responsible for managing tasks that are potentially dangerous Health and safety hazards may be encountered in construction, manufacturing and maintenance Failure of engineer to act to correct a potentially dangerous situation or follow codes and standards is professional misconduct Principles of hazard recognition and control Identify and asses hazard Try to prevent/ eliminate need for creating hazard Assessing Hazards Assess capabilities and limitations of users Anticipate common errors and failure modes Evaluate designs for safety and health Provide adequate instructions and warnings Design a safe tooling and workstations Consider maintenance needs Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Reasons for recall Analysis reveals presence of a potential hazard that can result in serious incidents. Reports are received of unsafe conditions, unsafe incidents, or unsafe product characteristics. An incident reveals previously unforeseen product deficiency. Government standard or regulation has been violated. Product does not live up to advertised claims with regard to safety. Standards Documents describing rules or methods that serve as models of professional practice Following a standard in design is evidence that work and been conducted to a professional level of competence. Codes and regulations Parts of statutes, by laws, by which a national or local government requires specific practices to be followed, including adherence to particular standards Performance – based or objective based codes start by specifying objectives Prescriptive codes specify physical characteristics to be satisfied Evaluating Risk in Design Risk factors must be considered when evaluating alternatives at every design stage Answering risk-related questions leads to study of risk management Risk management: Risk analysis o Identify hazards/ consequences and estimate probability of occurrence o Risk evaluation: alternatives to reduce risk are generated, costs/ benefits are calculated o Management decision: select the risks that will be managed and implement the decisions Analytical Methods: Methods to identify hazards and evaluate risks o Checklists o Hazard and operability (HZAOP) studies o Failure modes and effects analysis (FMEA) ▪ List all components or subsystems. ▪ Identify each component by part name and number. ▪ Describe each component and its function. ▪ List all ways (modes) in which each component can fail. ▪ Determine effect of failure on other components and on unit. ▪ Describe how to detect each failure mode. Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 ▪ Indicate action needed to eliminate hazards and identify person responsible for that action. ▪ Assess criticality of each failure mode and its probability of occurrence. o Fault – tree analysis Case study Challenges High injury frequencies Increasing workers compensation costs Frequent H&S work refusals Incidents occupying excessive time New H&S legislation (Bill 208) List 4 most important H&S changes at Oshawa Truck Assembly Center in 1990’s o Culture change o Policies and procedures o Core safety elements Engineering and Environmental science Defining Sustainability “Sustainable development is development that meets the needs of the present, without compromising the ability of future generations to meet their own needs.” Achieving Sustainability Two questions to be answered: o What kind of planet do we want for our children? o What kind of planet can we get? Engineers, scientists, and economists can solve technical problems However, they must balance with societal commitment to accept major lifestyle changes Importance of sustainable living Welfare of future generations threatened by: o Careless disposal of waste o Excessive consumption of resources Emissions from burning fossil fuels contribute to global warming and climate change But massive societal change is possible with minimal effect on standard of living as next figure bears out Process of Global Warming Gas emission Greenhouse effect Global Warming Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Climate change The solar balance The greenhouse effect is essential to human life, but small deviations in earth’s solar energy balance can produce large effects leading to global warming or cooling Consequences of Climate change Human cause: worldwide atmospheric concentrations GHGs at levels which greatly exceed pre-industrial values Temperature will rise 0.3-4.8 C over the next century Sea level rise (due to decrease in ice volume) Present observations o Changes in arctic temperatures, ocean salinity, wind patterns, extreme weather conditions Other consequences: flooding, drought, plagues, bleaching of corals Feedback Irreversibility Ethical Implications of Climate Change Economic loss caused by climate change will affect poorest nations the most Is it ethical or fair? How will industrialized nations respond to the millions of climate change refugees Guidelines for Environmental Practice Understand/monitor environmental/sustainability issues. Use specialists in environmental sustainability when needed. Apply professional and responsible judgment. Environmental planning/management should be integrated into all activities likely to have any adverse effects. Include costs of environmental protection when evaluating the economic viability of projects. Recognize value of environmental efficiency/sustainability; consider full lifecycle assessment… Solicit input from stakeholders and strive to respond to environmental concerns in a timely fashion. Comply with regulatory requirements; disclose information necessary to protect public safety to authorities. Work actively to improve environmental understanding and sustainability practices. What can we do: Engineering for sustainability Engineers can assist society by o Promoting energy efficiency o Encouraging research into alternative energy sources o Molding alternatives o Showing the environmental consequences of design decisions Modelling Life cycle analysis Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 o Evaluates environmental impact of a product from source material to disposal Multi-disciplinary engineering and systems thinking o Engineers must bridge gap between science and economics to arrive at good solutions Some environmental Concerns Global Regional Local Global Climate change Acid precipitation Groundwater degradation Ozone depletion Herbicide and pesticide use Hazardous wastes disposals Habitat and biodiversity reductions Soil degradation Oil spills Surface water chemistry depredation Smog Visibility degradation Toxins in sediments and sludge Radionuclides Thermal pollution Some environmental issues where engineers can help Feed growing population more effectively Develop more economic ways to make products/services and recycle Find best ways to avoid pollution of fresh water and oceans Manage aquifer water levels – relative to food production Prevent soils from becoming depleted of nutrients Mine/extract without destroying landscape or causing pollution Avoid extinction of broad array of species; preserve habitats Manage forests/plant life variety; foster natural CO2sequestration Develop economic to manage the environment Create efficient technology (homes, heating, cooling, transportation, manufacturing, etc.) Capture/transform/store energy and distribute effectively Units, significant figures Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 SI Unit System Absolute system Mass is a fundamental unit Newton’s second law (force= mass * Acceleration) is invoked to derive force due to gravity FPS system Gravitational System Force is a fundamental unit Mass is derived from Newton’s Second law Distance, force, and time are fundamental dimensions, measured in units of feet, pounds and seconds. Systematic Errors Consistent deviation from the true value Error has same magnitude and sign when repeated measurements are made under the same conditions Can be detected by Calibration Comparison with results obtained independently Three types of systematic errors Natural Error From environmental effects Instrument error Called offset Caused by imperfections in adjustment or construction of instrument. Personal Result from habits of the observer Can be reduced by proper training Random Errors Result of small variations in measurements Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Random errors do not bias measurement If several measurements are made, their mean is normally a better estimate of true value than any single measurement Source of random errors: Technical specifications of instrument Reading errors Precision, Accuracy and bias Terms often misused or considered synonyms Precision refers to repeatability Accuracy refers to closeness to true value Bias is a non-random, systematic error Fixed notation Ordinary decimal notation 30140.0 Scientific notation 3.014*104 Engineering Notation Exponent of 10 is a multiple of 3 to correspond to SI prefixes 30.14*103 Significant digits Determine the precision of the number Are identified as follows All non-zeroes are significant All zeroes between significant figures are significant Leading zeroes are not significant Trailing zeroes are significant in fractional part Energy conservation and conversion Energy is the ability to do work Work is done when a force caused an object to move in the direction of the force. Work is a transfer of energy Energy and work are expressed in units of joules (J) – SI unit Kinetic Energy Kinetic energy is the energy of motion, all moving objects have kinetic energy. The amount of kinetic energy that an object has depends on its mass and velocity. Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 KE= mass*velocity2/2 Potential Energy The energy an object has because of its position The amount of gravitational potential energy that an object has depends on its weight and its height GPE= m*g*h Mechanical Energy The total energy of motion and positon of an object. Both kinetic and potential energy are types of mechanical energy ME=PE+KE Other forms of energy Thermal energy: all of the kinetic energy due to random motion of the particles that make up an object All matter has thermal energy Chemical energy: a form of potential energy because it depends on the position and arrangement of the atoms in a compound Electrical energy: the energy of moving electrons Sound energy: caused by an objects vibrations, they transmit some kinetic energy to the air particles which also vibrate. Light energy: produced by the vibrations of electrically charged particles Nuclear energy: is the energy that comes from changes in the nucleus of an atom Can be produced when nuclei are joined in fusion reaction or when nucleus is split in a fission reaction Car engine and energy conversions Electrical energy produces a spark The thermal energy of the spark releases the chemical energy in the fuel The fuel’s chemical energy n turn becomes thermal energy Thermal energy is converted into mechanical energy used to move the car, and to electrical energy to produce more sparks Energy is conserved within a closed system Energy transfers only to each of the objects The law of conservation of energy states that energy cannot be created or destroyed Energy can be converted from one form to another, but always adds up to the same amount of total energy In every energy conversion head is always generated, so there will always be thermal energy Non-renewable resources Cannot be replaced ( or replaces much more slowly than they are used) Fossil fuels are non-renewable energy resources that formed from the remains of organisms that lived long ago. Oil, natural gas and coal are the most common fossil fuels. Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Electric generators convert the chemical energy in fossil fuels into electrical energy by the process shown below. Renewable Resources Are naturally replaces more quickly than they are used Sunlight can be changed into electrical energy through solar cells Solar cells can be used in devices such as calculators, rooftops, etc. Potential energy of water in a reservoir can be changed into kinetic energy as the water flows through a dam. Wind turbine Geothermal energy: caused by the heating of the Earth’s crust Engineering and empirical model, statistics and curve fits Definitions Observation: measured value Parent population: complete set of all the possible observations of variable Sample: observations consisting of one or more measurements taken from parent population (subset of parent population Sample distribution: description of frequencies with which values of observations in a given sample occur Histogram or cumulative probability function Parent distribution: description of frequencies with which values of observations from parent population occur Continuous or discrete function Error: difference between measured value and true value of variable Statistic: calculated value that characterizes data in presence of random uncertainties Descriptive statistics: used to describe complex data simply Inferential Statistics: used to estimate or predict properties if parent population from sample Histogram Type of graph used to display distributions Occurrences of grades (out of 20) on past tests Sample mean Common central value measures are mean, median and mode Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Sample mean is defined by฀ For a population containing N elements, the population mean is given by฀ Median Median is the middle value when the data is ordered (half are greater/half are less than) Mode The values that is most frequent in the sample Effect of skew A distribution has a negative skew when it has a tail that tends toward the lower values than the central value. The ratio mean/median determines skew Mean > median , positive skew Mean < median, negative skew a) Unimodal and symmetric, no skew b) Unimodal and negatively skewed c) Bimodal and positively skewed Range: interval bounded by extreme (lowest/ highest) observations Mean square deviation (MSD): population mean may not be known, using measured data we can express the variance as Sample variance: Last observation, xn is dependent on previous observations and sample mean Result: MSD underestimates population variance Variance: measure of deviation of observations from central value Standard deviation: variance is the measure of deviation but units from math those of mean, median. To permit the comparison with the central values, standard deviation is the square root of variance Downloaded by Furqan Ahmad Arif ([email protected])  lOMoARcPSD|46133431 Spread sheet analysis Scientific computing & Matlab Downloaded by Furqan Ahmad Arif ([email protected])