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Use standard deviation to estimate the amount of error in a set of related data.

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Independent sample_t-test

Independent sample_t-test

Gelombang

Gelombang

Domanda iscrizione-scuola-musica-2012-13

Domanda iscrizione-scuola-musica-2012-13

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Independent sample_t-test

This presentation is about t-test

Domanda iscrizione-scuola-musica-2012-13

filippocarrega filippo carrega filippocarrega97@gmail.com indirizzo numeor telefono

CS201- Introduction to Programming- Lecture 07

Virtual University
Course CS201- Introduction to Programming
Lecture No 07
Instructor's Name: Dr. Naveed A. Malik
Course Email: cs201@vu.edu.pk

Unit2 planet earth

1 ESO Science, unit 2 planet earth

CS201- Introduction to Programming- Lecture 40

Virtual University
Course CS201- Introduction to Programming
Lecture No 40
Instructor's Name: Dr. Naveed A. Malik
Course Email: cs201@vu.edu.pk

Iglesia de Filadelfia

ESTUDIO BIBILICO APOCALIPSIS MENSAJE A LAS SIETE IGLEISIAS - IGLESIA FILADELFIA

21 High-quality programming code construction part-ii

High-quality programming code construction part 2

Independent sample_t-test

Independent sample_t-test

Gelombang

Gelombang

Domanda iscrizione-scuola-musica-2012-13

Domanda iscrizione-scuola-musica-2012-13

CS201- Introduction to Programming- Lecture 07

CS201- Introduction to Programming- Lecture 07

Unit2 planet earth

Unit2 planet earth

CS201- Introduction to Programming- Lecture 40

CS201- Introduction to Programming- Lecture 40

Iglesia de Filadelfia

Iglesia de Filadelfia

21 High-quality programming code construction part-ii

21 High-quality programming code construction part-ii

equilibrio químico y velocidades de reacción

equilibrio químico y velocidades de reacción

demand

demand

demand

demand

equilibrio ácido-base

equilibrio ácido-base

Archivo de Excel

Archivo de Excel

Grade 12 U0-L2-Error

This document provides instruction on calculating errors in measurement for basic math operations. It reviews the concepts of accuracy, precision, systematic and random error. It then demonstrates how to calculate the error when adding, subtracting, multiplying and dividing measurements. For addition and subtraction, the errors are simply added. For multiplication and division, the relative uncertainties of each term are added before converting back to an error value. Examples are provided for addition/subtraction and multiplication/division of measurements with given errors. Students are directed to practice these calculations in their workbook.

Grade 12 U0-l1-ReviewofSigDig

This document provides instruction on basic skills for dimensional analysis, significant figures, and arithmetic operations involving measurements with uncertainty. It includes examples of performing calculations with significant figures and scientific notation, rounding numbers according to rules, and using dimensional analysis to determine if a hypothesized relationship between physical quantities is correct. Practice questions are provided at the end for students to test their understanding.

Grade 11, U4 L1-Vibrations

1) The document discusses vibrations and waves, defining key terms like amplitude, period, frequency, and phase. It describes the motion of a pendulum and how its frequency is related to its length.
2) Resonance is defined as occurring when energy is added to a vibrating system at the same frequency and phase as the natural frequency, potentially causing a continuous increase in the system's energy over time.
3) Examples of periodic and simple harmonic motion include a pendulum and mass attached to a spring. The document provides links to videos demonstrating resonance and vibration concepts.

Grade 11, U4 L4-Standing waves

When two identical waves move toward each other on a string, they form a standing wave with the same wavelength and double the amplitude. Standing waves have nodes where the string does not move and antinodes where it moves the most. If the string's length is shortened, the fundamental frequency increases and wavelength decreases, while the wave speed remains constant according to the wave equation.

Grade 11, U4 L3-Superposition of Waves

This document discusses waves at boundaries and wave superposition. When a wave encounters a boundary between two media, it is partially transmitted and partially reflected. Special cases like free ends and walls are also examined. When two waves of equal wavelength and amplitude but opposite phase overlap, they cancel out in destructive interference. Overlapping waves of the same phase results in constructive interference and a doubling of amplitude. Superposition of waves involves both destructive and constructive interference combining waves of different shapes. Practice questions apply these concepts to pulses moving between springs with different wave speeds.

Grade 11, U4 L2-Waves

This document discusses properties of mechanical waves, including:
- Mechanical waves require a medium and examples are water and sound waves. Electromagnetic waves do not require a medium.
- A mechanical wave transfers energy through a medium. Water waves move outward from where a rock hits a pond.
- The speed of a wave depends on the medium, not the amplitude or size of the wave. Sound waves travel at the same speed regardless of volume.
- A wave's shape is typically sinusoidal and characterized by amplitude, wavelength, crest, and trough. The fundamental wave equation relates speed, frequency, and wavelength.

Grade 11 U2 L9-Power and Efficiency

This document discusses power and efficiency. It defines power as the rate at which work is done or energy is transferred, and gives the equation for calculating power. An example is provided where power is calculated for two men pushing a box up a ramp. Efficiency is also defined as a ratio of output to input energy or work. Examples of efficiency ratings are given for various devices like heaters, power plants, and light bulbs. Practice questions are listed from the textbook for further studying power and efficiency concepts.

Grade 11 U2 L5B Cons and Non-Cons Forces

This document discusses conservative and non-conservative forces and how they relate to energy transformations. It provides examples of how work done by conservative forces, like gravity, depends only on start and end points, not the path taken. However, work done by non-conservative forces, like friction, does depend on the path. It gives examples of objects moving under gravity and friction to illustrate these concepts. The document concludes by defining conservative and non-conservative forces and providing an example problem calculating work done by non-conservative forces on a skydiver.

Grade 11, U2 L5A-Conservation of Energy

The document discusses the concept of conservation of energy, explaining that energy cannot be created or destroyed, only changed in form. It defines different types of systems and provides examples of how to use the law of conservation of energy to solve mechanics problems involving changes in gravitational potential energy and kinetic energy. Practice problems are provided to help reinforce understanding and application of energy conservation concepts.

Grade 11, U2 L1-Energy & Work

The document discusses the concepts of energy, work, and power, defining kinetic energy as the energy of motion and potential energy as stored energy due to position or condition. It explains that work is done when a force causes an object to move, and can be calculated using the work equation W = Fd, where work is measured in joules. Examples are provided to illustrate calculating work from applying forces and interpreting force-position graphs.

Grade 11, U2-L2-Work

Work can be positive or negative depending on the direction of force and displacement. Positive work is done when force and displacement are in the same direction, such as when a weight is lifted, gaining gravitational potential energy. Negative work is done when force and displacement are in opposite directions, as when a weight is lowered and gravitational potential energy is lost. The equation for work, W = Fcosθ x Δd, produces a negative number when the force and displacement are at 180 degrees to each other, indicating negative work has been done.

Grade 11, U2 L3-Kinetic Energy

This document discusses kinetic energy and the work-energy theorem. It provides explanations and examples of how kinetic energy is gained when a force is applied to an object, causing it to move. It also derives the work-energy theorem that states the work done on an object is equal to the change in its kinetic energy. The document concludes with practice problems for students to work through related to these concepts.

Grade 11, U2 L4-Eg

Lesson 4 discusses gravitational potential energy (Eg). Eg depends on mass and height measured from a reference datum. Eg can be calculated using the equation Eg = mgh, where m is mass in kg, g is 9.81 m/s2, and h is height in meters. Examples are provided to demonstrate calculating changes in Eg based on changes in height when work is done lifting or lowering objects. Practice questions are also included to test understanding of calculating Eg for objects at different heights.

Grade 11, U4 L6-Air Columns

Standing waves can form in air columns when they are excited by a sound source. The document discusses standing waves in air columns that are closed at one end or open at both ends. It provides the equations to calculate the fundamental frequency and higher harmonics or overtones based on the length of the air column and speed of sound. Examples are given of different instruments that function as air columns, and practice problems are provided to apply the concepts.

Grade 11, U4 L7-Sound Intensity

This document provides information about sound and hearing:
- Noise lacks a consistent pitch or repeating waveform, while music has sounds that are whole number multiples of the lowest frequency.
- Loudness is subjective, while sound intensity is measured in watts per square meter (W/m2) or decibels (dB), using a logarithmic scale. Common sound intensities are given.
- Echolocation allows bats and dolphins to detect objects using sound wave reflections, while sonar determines underwater distances by timing sound wave echoes.
- The typical human hearing range is 20 Hz to 20,000 Hz, but it decreases with age. Tests can check one's hearing range.
- Practice questions review concepts like

Grade 11, U4 L5-Wave Characteristics

This document covers various characteristics of waves including:
1) All waves transmit energy, diffract, reflect, refract, and exhibit constructive and destructive interference.
2) Diffraction is the spreading out of waves as they pass through an opening, like sound waves spreading through a doorway.
3) Refraction occurs when waves change speed as they pass into a new medium, like water waves bending as they enter shallow water.
4) Pitch is a sound wave's frequency, determining if it is high or low. Pure tones have one frequency while complex tones have multiple frequencies.
5) When waves of slightly different frequencies overlap, beats occur and disappear when the sources are in tune.

Grade 12 U0-L2-Error

Grade 12 U0-L2-Error

Grade 12 U0-l1-ReviewofSigDig

Grade 12 U0-l1-ReviewofSigDig

Grade 11, U4 L1-Vibrations

Grade 11, U4 L1-Vibrations

Grade 11, U4 L4-Standing waves

Grade 11, U4 L4-Standing waves

Grade 11, U4 L3-Superposition of Waves

Grade 11, U4 L3-Superposition of Waves

Grade 11, U4 L2-Waves

Grade 11, U4 L2-Waves

Grade 11 U2 L9-Power and Efficiency

Grade 11 U2 L9-Power and Efficiency

Grade 11 U2 L5B Cons and Non-Cons Forces

Grade 11 U2 L5B Cons and Non-Cons Forces

Grade 11, U2 L5A-Conservation of Energy

Grade 11, U2 L5A-Conservation of Energy

Grade 11, U2 L1-Energy & Work

Grade 11, U2 L1-Energy & Work

Grade 11, U2-L2-Work

Grade 11, U2-L2-Work

Grade 11, U2 L3-Kinetic Energy

Grade 11, U2 L3-Kinetic Energy

Grade 11, U2 L4-Eg

Grade 11, U2 L4-Eg

Grade 11, U4 L6-Air Columns

Grade 11, U4 L6-Air Columns

Grade 11, U4 L7-Sound Intensity

Grade 11, U4 L7-Sound Intensity

Grade 11, U4 L5-Wave Characteristics

Grade 11, U4 L5-Wave Characteristics

Sample and sample Techniques

Statistics

Amplitude modulation Simulation

Amplitude Modulation Simulation in MATLAB

Research event iao prof. comhaire

Op 2 oktober vond op de campus van The International Academy of Osteopathy (IAO) te Gent een wetenschappelijke avond plaats. Het research team van de IAO, onder leiding van Prof. Dr. Frank Comhaire, heeft op dit event de meest interessante onderzoeksresultaten en onderzoeksplannen toegelicht. De meer dan dertig deelnemers waren heel enthousiast en het research team was heel tevreden over het verloop van de avond. De IAO draagt wetenschappelijk onderzoek hoog in het vaandel. Vorig jaar investeerden ze in het DIERS formetric 4D toestel. Dit toestel brengt op een niet-invasieve manier de wervelkolom van de patiënt in beeld en is uniek in de osteopathie wereld. Het DIERS toestel speelt dan ook een belangrijke rol in de diverse onderzoekslijnen die momenteel op de IAO campus te Gent actief zijn.

Chapter 2 - Assignment Analyzing Transactions

This will be up for the weekend please update your note packets for a grade on MONDAY

Microwave Spectroscopy

Introduction to microwave spectroscopy

Lung cancer screening

review of lung cancer screening guidelines

Night vision Technology

night vision technology

01 termoqu%e dmica

termodina

Solving linear equations (chapter 2)

Basic Algebra. Including Solving Linear Equation and Inequalities.Combining Like Terms, Ratios and inequalities.

Chapter 6 testbench

digital communication ,proakis

13089861

arquitectura del computador historia y evolucion

Fluid & electrolytes & acid base

for pathophysiology

Complicaciones agudas de DM II 2

Complicaciones agudas de DMII

Reliability-based design of pile foundations

Reliability based design (RBD) refers to any design methodology that are based on a rigorous reliability analysis. RBD is the only methodology available to date that can ensure self-consistency from both physical and probabilistic requirements and is compatible with the theoretical basis underlying structural design (Kulhawy & Phoon, 2002). It is considered as fundamental theoretical basis for all Load and Resistance Design (LRFD) and is capable of mitigating numerous logical inconsistencies inherent in current geotechnical design.

Training methods

DETAIL ACCOUNT OF TRAINING METHODS

Formula1 presentation

Presentación técnica sobre coches de Fórmula 1

Resumen termoquimica1

Termoquimica

CS201- Introduction to Programming- Lecture 10

Virtual University
Course CS201- Introduction to Programming
Lecture No 10
Instructor's Name: Dr. Naveed A. Malik
Course Email: cs201@vu.edu.pk

Sample and sample Techniques

Sample and sample Techniques

Amplitude modulation Simulation

Amplitude modulation Simulation

Research event iao prof. comhaire

Research event iao prof. comhaire

Chapter 2 - Assignment Analyzing Transactions

Chapter 2 - Assignment Analyzing Transactions

Microwave Spectroscopy

Microwave Spectroscopy

Lung cancer screening

Lung cancer screening

Night vision Technology

Night vision Technology

01 termoqu%e dmica

01 termoqu%e dmica

Solving linear equations (chapter 2)

Solving linear equations (chapter 2)

Chapter 6 testbench

Chapter 6 testbench

Dielectrics lect28

Dielectrics lect28

13089861

13089861

Fluid & electrolytes & acid base

Fluid & electrolytes & acid base

Complicaciones agudas de DM II 2

Complicaciones agudas de DM II 2

Reliability-based design of pile foundations

Reliability-based design of pile foundations

Training methods

Training methods

Formula1 presentation

Formula1 presentation

08 relationships among variables

08 relationships among variables

Resumen termoquimica1

Resumen termoquimica1

CS201- Introduction to Programming- Lecture 10

CS201- Introduction to Programming- Lecture 10

Topics for math test 2018

This document outlines the topics that will be covered on a math test for an academic physics course. It lists various grade 10 math concepts that students are expected to understand, such as the Pythagorean theorem, trigonometric ratios, solving linear and quadratic equations, graphing, slopes, and angles. The test will count towards students' term marks, so mastery of these prerequisite math skills is necessary to succeed in the grade 11 physics course. Students are advised to study by doing practice problems and reviewing old tests and textbook sections.

Grad12, U3-L2A-HorizPM-R

Horizontal projectile motion involves motion in two dimensions: up-down and horizontal. This document focuses on horizontal projectile motion, where the initial velocity only has a horizontal component. It examines how the horizontal velocity does not affect the rate of falling, but must be considered along with vertical motion to determine the total velocity and range of the projectile. The range of a projectile is calculated using the formula R = (2h/g)1/2v1, where h is the initial height, g is the acceleration due to gravity, and v1 is the initial horizontal velocity.

Grade9, L11-U3Habitat loss and fragmentation

Farmland, settlements and highways have replaced much of Ontario's deciduous forest. Habitat loss and fragmentation are threats, with loss most extreme in conversion to farmland and urban development. This divides ecosystems and exposes more habitat to pollution. To protect sustainability, conservation aims to maintain large, connected areas with low external influences. Threats also impact aquatic ecosystems through activities like shoreline development, dredging, sedimentation and wetland drainage.

Grade 9, U3-L10 pesticides and biomagnification

This document discusses pesticides and their environmental impacts. It describes how monocultures create ideal conditions for pest populations to thrive. Pesticides are commonly used to control pests, but they can harm non-target species and accumulate in organisms through bioaccumulation and biomagnification. Long-term pesticide use can also lead to pest resistance. The document advocates for alternative pest control methods like those used in organic farming to reduce pesticide dependence.

Grade 9-U3-L9-Invasive species

This document discusses invasive species, which are introduced species that spread rapidly and negatively impact the environment. It provides examples of invasive species in Canada like zebra mussels, European earwigs, and carp. Introduced species often lack natural predators and can outcompete native species, allowing their populations to grow unchecked. This can significantly damage ecosystems and cost the economy billions. The document outlines different methods to control invasive species populations, including pesticides, physical removal, and biological controls like introducing predators. However, prevention of accidental introductions is the most effective approach.

Grade 9,U3-L7 population ecology

The document discusses factors that affect population size and growth rates, including births and deaths, as well as immigration and emigration. It notes that population change equals births minus deaths plus immigration minus emigration. Density-dependent factors like competition for resources and disease can control populations. Density-independent factors like environmental conditions also impact populations. An example calculates the population change for a town based on births, deaths, immigration, and emigration to show that the population increased.

Grade9,U3-L6 Ecological Succession

Ecological succession describes how communities of plants and animals change over time following a disturbance of an area. It can be primary succession, which occurs in areas without previous life like after a volcanic eruption, or secondary succession, which follows a disruption but not destruction of a community like after a forest fire. Succession proceeds as hardier species first colonize an area, gradually changing the environment to allow less hardy species to establish themselves until a stable community forms, though it may take a hundred years to fully recover from severe disturbances. Aquatic and coastal ecosystems like bogs and sand dunes also undergo successional changes as vegetation grows and transforms the landscape over long periods.

Grade9, U3-L5 biotic and abiotic factors

This document discusses biotic and abiotic factors that influence ecosystems and populations. Abiotic factors like temperature, light, water, and soil determine where species can survive based on their tolerance ranges. Within tolerance ranges, optimal conditions allow populations to flourish while stress near limits can reduce health. Biotic factors like competition, predation, and mutualism also influence species success. As populations increase in size, resource demands increase until the ecosystem reaches its carrying capacity, or maximum sustainable population.

Grade 9, U3-L4 Cycles

The document discusses several biogeochemical cycles that move essential elements through ecosystems. It explains that the water cycle moves water through evaporation and precipitation, the carbon cycle exchanges carbon between the atmosphere and organisms through photosynthesis and respiration, and most carbon is stored long-term in deposits like fossil fuels. The nitrogen cycle converts nitrogen from the atmosphere into usable forms through nitrogen fixation by bacteria and returns it through denitrification. These cycles continuously circulate critical nutrients and are essential to sustaining life.

Grade 9, U3-L3 Food Chains and Food Webs

This document discusses ecological niches, food webs, and ecological pyramids. It defines key concepts like producers, consumers, herbivores, carnivores, omnivores, and describes trophic levels. Food chains are simplified representations of feeding relationships, while food webs show complex and interconnected feeding relationships in an ecosystem. Ecological pyramids illustrate the transfer of energy and biomass between trophic levels, with higher levels containing less energy and fewer individuals than lower levels due to energy loss at each transfer.

Grade9, U3-L2, Energy flow in ecosystems

All organisms require energy, which primarily comes from sunlight through photosynthesis. During photosynthesis, producers like plants use sunlight to convert carbon dioxide and water into oxygen and energy-rich sugars. Producers and consumers then undergo cellular respiration, using the sugars and oxygen to produce energy, carbon dioxide, and water. This cycle of photosynthesis and cellular respiration allows energy from the sun to flow through ecosystems and be used by all organisms.

Grade 9, U3-L1-Life on planet earth

The document discusses Earth's atmosphere and how it sustains life. It describes the atmosphere as a thin gaseous layer made up of 78% nitrogen and 21% oxygen that surrounds the planet. The atmosphere moderates temperatures, blocks ultraviolet light, and prevents excessive heating and cooling, maintaining an average surface temperature of 15°C. Without the atmosphere, most species would be unable to survive on Earth.

Grade9, U2-L7-Power generation, efficiency and cost of electricity

Electricity is generated at power stations from various energy sources like hydroelectric, nuclear, coal, wind, solar and natural gas. Generators transform this input energy into alternating current (AC) electrical energy, which is more efficient for long distance transmission than direct current (DC). Efficiency is a measure of the energy output versus input. Common rates for electricity are charged per kilowatt-hour, with time-of-use rates accounting for supply and demand. Calculating the cost to operate devices uses the power used, operating time and rate charged. An example compares the lower cost of a 13W CFL bulb versus a 60W incandescent bulb over 3 hours using time-of-use rates. Homework questions

Grade 9, U2-L6-Circuits

The document provides an overview of electric circuits and potential difference for a grade 9 science class. It introduces series and parallel circuits, defines electric potential difference, and discusses how to measure potential difference in series and parallel circuits. Key points covered include the relationships between voltages in series and parallel circuits and equations relating voltage, energy, charge, and work. Students are directed to practice questions and supplemental video resources are provided.

Grade 9, U2-L5 Equivalent Resistance and Complex CCT's

This document discusses circuits with resistance in series and parallel configurations. It explains that the total resistance (Req) of resistors in series can be calculated as the sum of the individual resistances (R1 + R2 + ... + Rn). For parallel resistors, the total resistance is calculated as the reciprocal of the sum of the reciprocals of the individual resistances (1/R1 + 1/R2 + ... + 1/Rn)-1. Complex circuits contain both series and parallel components, making them more difficult to solve for total resistance and current/voltage values. An example complex circuit is worked out on the chalkboard to demonstrate the analysis process.

Grade 9, U2-L4-Electrical quantities

This document defines and provides examples of key electrical quantities including electric charge, current, potential difference, resistance, and power. It explains that electric charge is measured in coulombs and is equal to the charge of approximately 6.2 x 1018 electrons. It also gives formulas for calculating current from charge and time, potential difference from energy and charge, and resistance from potential difference and current using Ohm's Law. Examples are provided for calculating charge, current, potential difference, resistance, and power.

Grade 9, U2-L3-Current electricity

The document defines key concepts in electric circuits including that electricity is the controlled flow of electrons through a conductor. An electric circuit provides a continuous path for electrons to flow and includes a power source, loads, and pathways that can be connected in series or parallel. Common circuit components are defined such as batteries, switches, resistors, motors, and their standard symbols.

Grade 9, U2-L2, Charging and Discharging Objects

An electroscope is used to test if an object is charged. It has a metal ball, rod, and leaves that allow electrons to move easily. When charged, the leaves separate. Charging can occur through contact or induction. Induction charges an object without direct contact by redistributing its electrons due to a nearby charged object. Lightning is a large-scale example of electrical discharge through induction in storm clouds.

Grade 9-U2-L1-Static electricity

This document introduces the topics of static electricity, current electricity, and power generation. It discusses what causes static electricity, such as walking across carpet and touching something to get a shock. Static electricity occurs when electrons are not moving along a path but rather build up as they move between atoms. The document also covers electric charge, conductors, insulators, and tools for detecting electric charge like electroscopes.

Grade 9, U1-L13-Molecular Compounds

This document defines molecular compounds and provides examples. It discusses that molecular compounds are composed of non-metal elements that are chemically bonded through covalent bonds where atoms share electron pairs. Examples of common molecular compounds are given such as gases, hydrocarbons, alcohols, carbohydrates, and biological molecules. Methods for drawing and naming molecular compounds such as Lewis dot diagrams and structural formulas are also outlined.

Topics for math test 2018

Topics for math test 2018

Grad12, U3-L2A-HorizPM-R

Grad12, U3-L2A-HorizPM-R

Grade9, L11-U3Habitat loss and fragmentation

Grade9, L11-U3Habitat loss and fragmentation

Grade 9, U3-L10 pesticides and biomagnification

Grade 9, U3-L10 pesticides and biomagnification

Grade 9-U3-L9-Invasive species

Grade 9-U3-L9-Invasive species

Grade 9,U3-L7 population ecology

Grade 9,U3-L7 population ecology

Grade9,U3-L6 Ecological Succession

Grade9,U3-L6 Ecological Succession

Grade9, U3-L5 biotic and abiotic factors

Grade9, U3-L5 biotic and abiotic factors

Grade 9, U3-L4 Cycles

Grade 9, U3-L4 Cycles

Grade 9, U3-L3 Food Chains and Food Webs

Grade 9, U3-L3 Food Chains and Food Webs

Grade9, U3-L2, Energy flow in ecosystems

Grade9, U3-L2, Energy flow in ecosystems

Grade 9, U3-L1-Life on planet earth

Grade 9, U3-L1-Life on planet earth

Grade9, U2-L7-Power generation, efficiency and cost of electricity

Grade9, U2-L7-Power generation, efficiency and cost of electricity

Grade 9, U2-L6-Circuits

Grade 9, U2-L6-Circuits

Grade 9, U2-L5 Equivalent Resistance and Complex CCT's

Grade 9, U2-L5 Equivalent Resistance and Complex CCT's

Grade 9, U2-L4-Electrical quantities

Grade 9, U2-L4-Electrical quantities

Grade 9, U2-L3-Current electricity

Grade 9, U2-L3-Current electricity

Grade 9, U2-L2, Charging and Discharging Objects

Grade 9, U2-L2, Charging and Discharging Objects

Grade 9-U2-L1-Static electricity

Grade 9-U2-L1-Static electricity

Grade 9, U1-L13-Molecular Compounds

Grade 9, U1-L13-Molecular Compounds

- 1. Basic Skills – Lesson 3 Introduction to Standard Deviation and Error Estimation MMeeaann DDeevviiaattiioonn SSttaannddaarrdd DDeevviiaattiioonn ffoorr:: a.) AA ppooppuullaattiioonn b.) AA ssaammppllee ooff tthhee ppooppuullaattiioonn
- 2. When measurements are taken (and eexxppeerriimmeennttaall ddaattaa iiss oobbttaaiinneedd)) tthhee ddaattaa wwiillll uussuuaallllyy tteenndd ttoo vvaarryy ffrroomm tthhee mmeeaann oorr aavveerraaggee vvaalluuee.. {{IInnddiivviidduuaall vvaalluueess wwiillll tteenndd ttoo bbee both ggrreeaatteerr tthhaann aanndd lleessss tthhaann tthhee mmeeaann}}.. FFoorr eexxaammppllee,, iiff tthhee ddiiaammeetteerr ooff 110000 ssiimmiillaarr sstteeeell bbaallll bbeeaarriinnggss aarree mmeeaassuurreedd,, tthhee vvaalluueess wwoouulldd lliikkeellyy nnoott aallll bbee tthhee ssaammee iiff aa hhiigghh pprreecciissiioonn mmeeaassuurriinngg ddeevviiccee iiss uusseedd ((ssuucchh aass aa ddiiggiittaall ccaalliippeerr)) TThhee vvaarriiaattiioonn ((oorr ddiissppeerrssiioonn)) ooff tthhee ddaattaa ffrroomm tthhee mmeeaann vvaalluuee ccaann bbee tthhoouugghhtt ooff aass tthhee eerrrroorr tthhaatt iiss pprreesseenntt iinn tthhee mmaannuuffaaccttuurriinngg pprroocceessss uusseedd ttoo mmaakkee tthhee sstteeeell bbaallll bbeeaarriinnggss.. TThheerree aarree vvaarriioouuss wwaayyss ttoo qquuaannttiiffyy tthhiiss eerrrroorr,, tthhee mmoosstt ccoommmmoonn bbeeiinngg standard deviation.. IInn oorrddeerr ttoo uunnddeerrssttaanndd ssttaannddaarrdd ddeevviiaattiioonn,, wwee mmuusstt hhaavvee aa bbaassiicc uunnddeerrssttaannddiinngg ooff aa normal distribution.. TThhiiss ccaann bbee sseeeenn iinn tthhee ffoolllloowwiinngg ddiiaaggrraamm::
- 3. Normal Distribution ((IInnttrroo ttoo SSttaattiissttiiccss)) TThhee nnoorrmmaall ddiissttrriibbuuttiioonn iiss sshhoowwnn ttoo bbee ssyymmmmeettrriiccaall aanndd rreesseemmbblleess aa bbeellll.. WWiitthhiinn ±± 11 ssaammppllee ssttdd.. ddeevv.. ooff tthhee mmeeaann,, 6688%% ooff tthhee ddaattaa (( oorr mmeemmbbeerrss ooff tthhee ssaammppllee ppooppuullaattiioonn)) aarree ffoouunndd WWiitthhiinn ±± 22 ssaammppllee ssttdd.. ddeevv.. 9955%% ooff tthhee ddaattaa iiss ffoouunndd.. 9 5 % o f s a m p l e p o p u l a t i o n x + 1 s + 2 s - 1 s - 2 s Frequency of Occurrence N o r m a l D i s t r i b u t i o n ( A B e l l C u r v e ) 6 8 % o f s a m p l e p o p u l a t i o n
- 4. Sample Population and Population AA sample population iiss uusseedd wwhheenn iitt iiss impossible ttoo mmeeaassuurree tthhee eennttiirree ppooppuullaattiioonn.. FFoorr eexxaammppllee;; tthhee ddiiaammeetteerr ooff 220000 bbaallll bbeeaarriinnggss aarree rraannddoommllyy mmeeaassuurreedd ffrroomm aa ppooppuullaattiioonn ooff 110000 000000.. TThhee sample population hhaass aa ssiizzee ooff 220000.. WWhheenn tthhee ssttdd.. ddeevv.. ffoorr aa ssaammppllee iiss ccaallccuullaatteedd,, aa ssmmaallll “s” iiss uusseedd ttoo rreepprreesseenntt tthhiiss vvaalluuee.. IIff aallll tthhee mmeemmbbeerrss ooff tthhee ppooppuullaattiioonn ((110000 000000)) ccaann bbee mmeeaassuurreedd,, tthhee ssyymmbbooll ffoorr ssiiggmmaa ((ϭ )) iiss uusseedd ttoo rreepprreesseenntt tthhee vvaalluuee ffoorr ssttdd.. ddeevv.. TThhee ccaallccuullaattiioonn ffoorr ssttdd.. ddeevv.. iiss slightly ddiiffffeerreenntt ffoorr ss aanndd ϭϭ ..
- 5. CCaallccuullaattiioonn ooff ss aanndd ϭϭ TToo ccaallccuullaattee tthhee ssttdd ddeevv ffoorr aa ssaammppllee ppooppuullaattiioonn ooff ““n”” mmeemmbbeerrss:: ss == ((((((xx11--xxMMEEAANN))22 ++ ((xx22--xxMMEEAANN))22 ++……++ ((xxnn--xxMMEEAANN))22 ))//(n-1) ))00..55 TToo ccaallccuullaattee tthhee ssttdd ddeevv ffoorr aann eennttiirree ppooppuullaattiioonn,, ooff ““n”” mmeemmbbeerrss:: ϭϭ== ((((((xx11--xxMMEEAANN))22 ++ ((xx22--xxMMEEAANN))22 ++……++ ((xxnn--xxMMEEAANN))22 ))//((n)) ))00..55 Your calculator will (likely) have these equations already preprogrammed, however, it may be a challenge to use them.
- 6. Mean Deviation Mean deviation (DD)) iiss aannootthheerr mmeetthhoodd ooff eexxpprreessssiinngg tthhee ddiissppeerrssiioonn ffrroomm tthhee mmeeaann.. TToo ccaallccuullaattee:: DD == ((||xx11--xxMMEEAANN|| ++ ||xx22--xxMMEEAANN|| ++……++ ||xxnn -- xxMMEEAANN||))//nn WWhheenn eexxpprreessssiinngg eexxppeerriimmeennttaall ddaattaa aass aa ssiinnggllee rreessuulltt ((wwiitthh eerrrroorr)) wwee ccaann uussee tthhee ffoolllloowwiinngg:: XX == xxMMEEAANN ±± ΔΔxx,, wwhheerree ΔΔxx == ss,, oorr ΔΔxx == ϭϭ oorr ΔΔxx == DD YYoouurr hhoommeewwoorrkk qquueessttiioonnss wwiillll iinnddiiccaattee wwhhiicchh vvaalluuee iiss ttoo bbee ccaallccuullaatteedd..
- 7. Practice Questions WWoorrkkbbooookk:: PPaaggee 55,, QQ##44,, 55aa Listed below are the diameters (in mm) of 5 steel ball bearings taken from a population of 25: 3.45, 3.62, 3.50, 3.44, 3.54 Express the data a single value including error. Use standard deviation to calculate the error.. AAnnsswweerr ggiivveenn nneexxtt ccllaassss
- 8. AAnnsswweerr:: 33..5511 ±± 00..0077 mmmm