This document discusses statistical analysis of experimental data. It outlines concepts like accuracy, precision, error, and data rejection. Accuracy refers to how close a measurement is to the true value, while precision refers to the agreement between multiple measurements. There are different types of errors like systematic and random errors. Various statistical metrics are presented for evaluating accuracy and precision, including mean, standard deviation, percent error and Gaussian distributions. Guidelines for identifying and rejecting outlier data points using the Q-test are also provided.
IB Chemistry on Acid Base Indicator and Salt HydrolysisLawrence kok
This document provides a tutorial on acid-base indicators and their use in titration. It discusses the properties of common acid-base indicators including their pKa values and color changes in acidic and basic solutions. Examples of titration curves are shown for strong acid with strong base and weak acid with strong base reactions. The key points are:
- Indicators change color at their pKa value within a pH range of about 1-2 units.
- The indicator used must change color within the pH range encountered at the equivalence point of the titration.
- The equivalence point and end point of the titration (when the indicator changes color) must coincide.
Test method of ferrous sulfate heptahydrateRech Chemical
This document provides a method for testing the iron content of ferrous sulfate heptahydrate. The method involves weighing 1g of the sample and dissolving it in water with sulfuric acid and phosphoric acid. The solution is then titrated with potassium permanganate until it turns pink for 30 seconds. The iron content is calculated based on the volume of potassium permanganate used and its concentration. The difference between two test results should be no more than 0.4% for the results to be valid.
The document discusses Karl Fischer titration (KFT) techniques for determining water content. It describes two common methods - volumetric KFT, which uses a burette to dispense Karl Fischer reagent, and coulometric titration, which generates iodine electrochemically. The key reaction involves iodine oxidizing an intermediate alkylsulfite to alkylsulfate, consuming water. Factors like solvent choice, water content, pH, and kinetics are discussed. The document also outlines how volumetric and coulometric titrators function and how the endpoint is detected.
Redox titrations involve adjusting the oxidation state of the analyte using an auxiliary oxidizing or reducing agent so that it can be titrated. Common reagents used in redox titrations include potassium permanganate, sodium thiosulfate, cerium sulfate, and potassium dichromate. Redox titrations are used to determine various analytes like ascorbic acid, hydrogen peroxide, iron, and calcium compounds. The document discusses the principles and procedures of important redox titrations like permanganometry, iodimetry, cerimetry, and dichrometry. It also describes the determination of water using the Karl Fischer reagent and reaction.
Gravimetric analysis is a technique for determining the amount of an analyte by converting it into a solid product whose mass can be easily measured. There are two main types of gravimetric analysis: combustion analysis and precipitation analysis. Combustion analysis involves burning a sample to convert carbon and hydrogen into gases like CO2 and H2O whose masses are then measured. Precipitation analysis involves adding a reagent to convert the analyte into a solid precipitate. The mass of the solid precipitate is then measured to calculate the original amount of analyte. Key factors that affect precipitation analysis include the solubility, filterability, and purity of the solid product. Gravimetric analysis is an accurate and inexpensive analytical technique
1. Analytical chemistry deals with identifying, separating, and quantifying chemical substances through both qualitative and quantitative analysis.
2. Classical methods involve isolating analytes through operations like precipitation and distillation for qualitative analysis. Titrimetric and volumetric analysis quantify amounts of substances through measurement of titrant volumes in reactions. Gravimetric analysis determines mass.
3. Standard solutions of known concentration are used to determine concentrations of other substances. Primary standards like oxalic acid are highly pure and stable, while secondary standards like sodium hydroxide are standardized against primary standards for specific analyses.
The document discusses various topics related to chemical kinetics including:
- Rate of reaction is defined as the change in concentration of reactants or products over time. Rate laws relate the rate of reaction to the concentrations of reactants.
- Reaction order refers to the sum of powers in the rate law. Molecularity is the actual number of reacting species. Pseudo-orders occur when one reactant is in excess.
- Rate constants have different units for different reaction orders. Integrated rate laws and the half-life method can be used to determine the order of a reaction experimentally.
- Collision theory states that molecules must collide with sufficient energy and correct orientation to react. Physical factors like temperature, solvent, and
1. Conductometry involves measuring the electrical conductivity of an electrolyte solution during a chemical reaction to determine the quantity of a substance present.
2. The conductivity of a solution depends on the number of ions present - strong electrolytes conduct well while weak electrolytes and non-electrolytes conduct poorly or not at all.
3. During a conductometric titration, the replacement of one ion with another affects the overall conductivity as the titration progresses, allowing the equivalence point to be identified from a graph of conductivity versus titrant volume.
IB Chemistry on Acid Base Indicator and Salt HydrolysisLawrence kok
This document provides a tutorial on acid-base indicators and their use in titration. It discusses the properties of common acid-base indicators including their pKa values and color changes in acidic and basic solutions. Examples of titration curves are shown for strong acid with strong base and weak acid with strong base reactions. The key points are:
- Indicators change color at their pKa value within a pH range of about 1-2 units.
- The indicator used must change color within the pH range encountered at the equivalence point of the titration.
- The equivalence point and end point of the titration (when the indicator changes color) must coincide.
Test method of ferrous sulfate heptahydrateRech Chemical
This document provides a method for testing the iron content of ferrous sulfate heptahydrate. The method involves weighing 1g of the sample and dissolving it in water with sulfuric acid and phosphoric acid. The solution is then titrated with potassium permanganate until it turns pink for 30 seconds. The iron content is calculated based on the volume of potassium permanganate used and its concentration. The difference between two test results should be no more than 0.4% for the results to be valid.
The document discusses Karl Fischer titration (KFT) techniques for determining water content. It describes two common methods - volumetric KFT, which uses a burette to dispense Karl Fischer reagent, and coulometric titration, which generates iodine electrochemically. The key reaction involves iodine oxidizing an intermediate alkylsulfite to alkylsulfate, consuming water. Factors like solvent choice, water content, pH, and kinetics are discussed. The document also outlines how volumetric and coulometric titrators function and how the endpoint is detected.
Redox titrations involve adjusting the oxidation state of the analyte using an auxiliary oxidizing or reducing agent so that it can be titrated. Common reagents used in redox titrations include potassium permanganate, sodium thiosulfate, cerium sulfate, and potassium dichromate. Redox titrations are used to determine various analytes like ascorbic acid, hydrogen peroxide, iron, and calcium compounds. The document discusses the principles and procedures of important redox titrations like permanganometry, iodimetry, cerimetry, and dichrometry. It also describes the determination of water using the Karl Fischer reagent and reaction.
Gravimetric analysis is a technique for determining the amount of an analyte by converting it into a solid product whose mass can be easily measured. There are two main types of gravimetric analysis: combustion analysis and precipitation analysis. Combustion analysis involves burning a sample to convert carbon and hydrogen into gases like CO2 and H2O whose masses are then measured. Precipitation analysis involves adding a reagent to convert the analyte into a solid precipitate. The mass of the solid precipitate is then measured to calculate the original amount of analyte. Key factors that affect precipitation analysis include the solubility, filterability, and purity of the solid product. Gravimetric analysis is an accurate and inexpensive analytical technique
1. Analytical chemistry deals with identifying, separating, and quantifying chemical substances through both qualitative and quantitative analysis.
2. Classical methods involve isolating analytes through operations like precipitation and distillation for qualitative analysis. Titrimetric and volumetric analysis quantify amounts of substances through measurement of titrant volumes in reactions. Gravimetric analysis determines mass.
3. Standard solutions of known concentration are used to determine concentrations of other substances. Primary standards like oxalic acid are highly pure and stable, while secondary standards like sodium hydroxide are standardized against primary standards for specific analyses.
The document discusses various topics related to chemical kinetics including:
- Rate of reaction is defined as the change in concentration of reactants or products over time. Rate laws relate the rate of reaction to the concentrations of reactants.
- Reaction order refers to the sum of powers in the rate law. Molecularity is the actual number of reacting species. Pseudo-orders occur when one reactant is in excess.
- Rate constants have different units for different reaction orders. Integrated rate laws and the half-life method can be used to determine the order of a reaction experimentally.
- Collision theory states that molecules must collide with sufficient energy and correct orientation to react. Physical factors like temperature, solvent, and
1. Conductometry involves measuring the electrical conductivity of an electrolyte solution during a chemical reaction to determine the quantity of a substance present.
2. The conductivity of a solution depends on the number of ions present - strong electrolytes conduct well while weak electrolytes and non-electrolytes conduct poorly or not at all.
3. During a conductometric titration, the replacement of one ion with another affects the overall conductivity as the titration progresses, allowing the equivalence point to be identified from a graph of conductivity versus titrant volume.
I hope You all like it. I hope It is very beneficial for you all. I really thought that you all get enough knowledge from this presentation. This presentation is about materials and their classifications. After you read this presentation you knowledge is not as before.
Non-aqueous titration is used when reactants are insoluble or reactive with water, or are very weak acids or bases that do not fully dissociate. Water is replaced by other solvents like perchloric acid. Non-aqueous titration can estimate weak acids and bases that cannot be easily titrated in water due to its amphoteric nature. Common types of non-aqueous titration include acidimetry, using acidic solvents and perchloric acid as the titrant to estimate weak bases, and alkalimetry, using basic solvents and sodium methoxide as the titrant to estimate weak acids.
This document summarizes key concepts in chemical kinetics including:
1. Chemical kinetics deals with the rates of chemical reactions and factors that affect rates. Rates can be expressed in terms of changes in concentrations over time.
2. Reaction rates depend on temperature, catalysts, and concentrations as expressed in rate laws. Rate constants are measures of reaction speeds.
3. Reactions can have different orders depending on which concentrations influence the rate. Pseudo-order reactions appear higher order but actually follow lower order kinetics.
Chem 2 - Chemical Kinetics III - Determining the Rate Law with the Method of ...Lumen Learning
This document discusses determining the rate law for a chemical reaction through initial rate experiments. It explains that the rate of reaction depends on reactant concentrations and describes how to find the orders of each reactant by comparing how the rate changes with concentration changes. The orders are used to define the rate law expression. Experimental data is then used to calculate the numeric rate constant.
This document provides an overview of chemical nomenclature and naming conventions for different types of chemical compounds. It discusses naming rules for ionic compounds, molecular compounds, acids, and bases. For ionic compounds, it describes how to name binary ionic compounds and polyatomic compounds based on the cation and anion present. It also addresses naming metal ions with different oxidation states. For molecular compounds, it outlines using prefixes to indicate the number of each type of atom. The document concludes with sections on naming simple acids based on replacing the nonmetal element ending with "-ic acid" and an overview of oxoacids and bases.
This document outlines the key concepts and learning objectives for Chapter 17, which covers solubility equilibria and complex-ion equilibria. The chapter will examine how to determine solubility product constants (Ksp) and use them to calculate solubility. It will also explore how the common ion effect and pH can impact solubility. The chapter will then discuss the formation of complex ions and how they relate to solubility and precipitation. It concludes by looking at applications to qualitative metal ion analysis.
1. This document discusses various oxidation-reduction titration methods including those using ceric ammonium sulfate, potassium iodate, potassium bromate, and titanous chloride as titrants.
2. Preparation and standardization procedures are provided for 0.1N ceric ammonium sulfate, 0.05M potassium iodate, 0.1N potassium bromate, and titanous chloride solutions.
3. Examples of titrations discussed include assays of ferrous fumarate, acetomenaphthone, ferrous gluconate tablets using ceric ammonium sulfate; assays of benzalkonium chloride and hydralazine hydrochloride using potassium iodate; and assays
This document provides a summary of key concepts for predicting products in chemical reactions on the AP Chemistry exam. It defines common reaction types like precipitation and acid-base reactions. It outlines the steps to take to determine the molecular, complete ionic, and net ionic equations for different reaction types. These include double replacement, acid-base, decomposition, combustion, redox, and complex ion formation reactions. Solubility rules are also summarized to predict if a compound will precipitate out of solution. The document concludes with guidance on how to convert word problems into balanced chemical equations.
Infrared spectroscopy is a technique used to identify chemical functional groups in molecules by detecting the vibrational transitions of bonds between atoms. It works by measuring how infrared radiation is absorbed by a sample based on the vibrational frequencies of the chemical bonds present. The main components of an IR spectrometer are an infrared radiation source, a sample holder, a detector, and a recorder. Factors like electronic effects, hydrogen bonding, and bond angles can affect the vibrational frequencies observed in IR spectra. Infrared spectroscopy has many applications including structure elucidation and identification of organic compounds.
This document discusses selecting chromatography columns. It begins by outlining factors to consider like retention, resolution, selectivity and efficiency. It then discusses the popularity of C18 columns but notes other phases like C8, phenyl and HILIC may be better depending on the analytes. The document explores improvements in column technology over time through smaller particle sizes and core-shell designs. It highlights how different column phases provide unique selectivities that can better separate similar compounds. In the end, it recommends evaluating needs and considering alternative columns and vendors beyond the typical C18.
Potassium permanganate is being standardized by titrating it against a primary standard of sodium oxalate. Sodium oxalate is dissolved in sulfuric acid, and then titrated with potassium permanganate solution. The reaction causes the purple permanganate solution to become colorless. When the titration is complete, one extra drop of permanganate causes the solution to turn pink, indicating the endpoint of the reaction. The experiment is repeated three times and the average volume of permanganate used is calculated to determine its molarity.
Acid-base titration is a technique used to determine the concentration of an acid or base by neutralizing a solution of unknown concentration with a solution of known concentration. The reaction is monitored using an indicator that changes color at the endpoint of the titration. The document outlines the basic procedure which involves transferring a sample of the solution of unknown concentration into a flask, adding an indicator, and then titrating with the solution of known concentration until the endpoint is reached as indicated by the color change of the indicator. The volume added is used to calculate the concentration of the original unknown solution.
This document discusses acid-base equilibria and titrations. It defines pH and pOH and their relationships to hydrogen and hydroxide ion concentrations. It describes the differences between strong acids, weak acids, and buffer solutions. It provides examples of preparing acidic and basic buffer solutions, such as an acetic acid-sodium acetate buffer. It also discusses acid-base indicators and their use in titrations, giving examples like methyl orange and phenolphthalein. Finally, it mentions the use of metallochromic indicators like Eriochrome Black T in titrations involving EDTA.
The document is a slide presentation on chapter 1 of a general chemistry textbook. Chapter 1 covers fundamental topics like the properties and states of matter, measurement units, and dimensional analysis. It defines physical and chemical properties, classifies matter as elements, compounds, and mixtures, and discusses techniques for separating mixtures. Key concepts explained include significant figures, temperature scales, volume, density, and unit conversions. The presentation concludes with sample end-of-chapter questions.
Distillation is a process used to separate mixtures by heating the mixture so that its components boil at different temperatures and can be collected separately by condensation. The document discusses using distillation to separate salt from water by boiling a saltwater solution, allowing the water to evaporate and condense separately from the salt. Fractional distillation is also mentioned as a method to separate mixtures of liquids by taking advantage of differing boiling points. Safety precautions are outlined to prevent burns from hot equipment during the distillation demonstration.
Adhesion forces are the attraction between oil and water molecules, while cohesion forces are the attraction between oil molecules. The work of adhesion (Wa) is calculated as the surface tension of oil plus water minus the oil-water interaction, while the work of cohesion (Wc) is twice the surface tension of oil. By taking the difference of these works, the spreading coefficient (S) can be derived as the surface tension of water minus the difference between the oil-water interaction and the surface tension of oil.
The document outlines rules for graphing and linear regression. It discusses key aspects of graphing such as properly labeling axes, selecting appropriate scales, and drawing lines smoothly through data points. It then covers linear regression, defining the linear equation and describing how to calculate the slope and y-intercept by minimizing the sum of the deviations between observed and calculated data points. Formulas for determining the slope and y-intercept using linear regression are provided.
The document discusses accuracy and precision in measurement. It defines accuracy as how close a measurement is to the actual value, which depends on the person measuring. Precision refers to how finely tuned or close together measurements are, which depends on the measuring tool. Accuracy and precision are demonstrated through shooting at a target, where accuracy is hitting the bullseye and precision is a tight grouping of shots. Exact numbers come from counting or defined relationships, while measured numbers use a measuring tool and require estimation.
I hope You all like it. I hope It is very beneficial for you all. I really thought that you all get enough knowledge from this presentation. This presentation is about materials and their classifications. After you read this presentation you knowledge is not as before.
Non-aqueous titration is used when reactants are insoluble or reactive with water, or are very weak acids or bases that do not fully dissociate. Water is replaced by other solvents like perchloric acid. Non-aqueous titration can estimate weak acids and bases that cannot be easily titrated in water due to its amphoteric nature. Common types of non-aqueous titration include acidimetry, using acidic solvents and perchloric acid as the titrant to estimate weak bases, and alkalimetry, using basic solvents and sodium methoxide as the titrant to estimate weak acids.
This document summarizes key concepts in chemical kinetics including:
1. Chemical kinetics deals with the rates of chemical reactions and factors that affect rates. Rates can be expressed in terms of changes in concentrations over time.
2. Reaction rates depend on temperature, catalysts, and concentrations as expressed in rate laws. Rate constants are measures of reaction speeds.
3. Reactions can have different orders depending on which concentrations influence the rate. Pseudo-order reactions appear higher order but actually follow lower order kinetics.
Chem 2 - Chemical Kinetics III - Determining the Rate Law with the Method of ...Lumen Learning
This document discusses determining the rate law for a chemical reaction through initial rate experiments. It explains that the rate of reaction depends on reactant concentrations and describes how to find the orders of each reactant by comparing how the rate changes with concentration changes. The orders are used to define the rate law expression. Experimental data is then used to calculate the numeric rate constant.
This document provides an overview of chemical nomenclature and naming conventions for different types of chemical compounds. It discusses naming rules for ionic compounds, molecular compounds, acids, and bases. For ionic compounds, it describes how to name binary ionic compounds and polyatomic compounds based on the cation and anion present. It also addresses naming metal ions with different oxidation states. For molecular compounds, it outlines using prefixes to indicate the number of each type of atom. The document concludes with sections on naming simple acids based on replacing the nonmetal element ending with "-ic acid" and an overview of oxoacids and bases.
This document outlines the key concepts and learning objectives for Chapter 17, which covers solubility equilibria and complex-ion equilibria. The chapter will examine how to determine solubility product constants (Ksp) and use them to calculate solubility. It will also explore how the common ion effect and pH can impact solubility. The chapter will then discuss the formation of complex ions and how they relate to solubility and precipitation. It concludes by looking at applications to qualitative metal ion analysis.
1. This document discusses various oxidation-reduction titration methods including those using ceric ammonium sulfate, potassium iodate, potassium bromate, and titanous chloride as titrants.
2. Preparation and standardization procedures are provided for 0.1N ceric ammonium sulfate, 0.05M potassium iodate, 0.1N potassium bromate, and titanous chloride solutions.
3. Examples of titrations discussed include assays of ferrous fumarate, acetomenaphthone, ferrous gluconate tablets using ceric ammonium sulfate; assays of benzalkonium chloride and hydralazine hydrochloride using potassium iodate; and assays
This document provides a summary of key concepts for predicting products in chemical reactions on the AP Chemistry exam. It defines common reaction types like precipitation and acid-base reactions. It outlines the steps to take to determine the molecular, complete ionic, and net ionic equations for different reaction types. These include double replacement, acid-base, decomposition, combustion, redox, and complex ion formation reactions. Solubility rules are also summarized to predict if a compound will precipitate out of solution. The document concludes with guidance on how to convert word problems into balanced chemical equations.
Infrared spectroscopy is a technique used to identify chemical functional groups in molecules by detecting the vibrational transitions of bonds between atoms. It works by measuring how infrared radiation is absorbed by a sample based on the vibrational frequencies of the chemical bonds present. The main components of an IR spectrometer are an infrared radiation source, a sample holder, a detector, and a recorder. Factors like electronic effects, hydrogen bonding, and bond angles can affect the vibrational frequencies observed in IR spectra. Infrared spectroscopy has many applications including structure elucidation and identification of organic compounds.
This document discusses selecting chromatography columns. It begins by outlining factors to consider like retention, resolution, selectivity and efficiency. It then discusses the popularity of C18 columns but notes other phases like C8, phenyl and HILIC may be better depending on the analytes. The document explores improvements in column technology over time through smaller particle sizes and core-shell designs. It highlights how different column phases provide unique selectivities that can better separate similar compounds. In the end, it recommends evaluating needs and considering alternative columns and vendors beyond the typical C18.
Potassium permanganate is being standardized by titrating it against a primary standard of sodium oxalate. Sodium oxalate is dissolved in sulfuric acid, and then titrated with potassium permanganate solution. The reaction causes the purple permanganate solution to become colorless. When the titration is complete, one extra drop of permanganate causes the solution to turn pink, indicating the endpoint of the reaction. The experiment is repeated three times and the average volume of permanganate used is calculated to determine its molarity.
Acid-base titration is a technique used to determine the concentration of an acid or base by neutralizing a solution of unknown concentration with a solution of known concentration. The reaction is monitored using an indicator that changes color at the endpoint of the titration. The document outlines the basic procedure which involves transferring a sample of the solution of unknown concentration into a flask, adding an indicator, and then titrating with the solution of known concentration until the endpoint is reached as indicated by the color change of the indicator. The volume added is used to calculate the concentration of the original unknown solution.
This document discusses acid-base equilibria and titrations. It defines pH and pOH and their relationships to hydrogen and hydroxide ion concentrations. It describes the differences between strong acids, weak acids, and buffer solutions. It provides examples of preparing acidic and basic buffer solutions, such as an acetic acid-sodium acetate buffer. It also discusses acid-base indicators and their use in titrations, giving examples like methyl orange and phenolphthalein. Finally, it mentions the use of metallochromic indicators like Eriochrome Black T in titrations involving EDTA.
The document is a slide presentation on chapter 1 of a general chemistry textbook. Chapter 1 covers fundamental topics like the properties and states of matter, measurement units, and dimensional analysis. It defines physical and chemical properties, classifies matter as elements, compounds, and mixtures, and discusses techniques for separating mixtures. Key concepts explained include significant figures, temperature scales, volume, density, and unit conversions. The presentation concludes with sample end-of-chapter questions.
Distillation is a process used to separate mixtures by heating the mixture so that its components boil at different temperatures and can be collected separately by condensation. The document discusses using distillation to separate salt from water by boiling a saltwater solution, allowing the water to evaporate and condense separately from the salt. Fractional distillation is also mentioned as a method to separate mixtures of liquids by taking advantage of differing boiling points. Safety precautions are outlined to prevent burns from hot equipment during the distillation demonstration.
Adhesion forces are the attraction between oil and water molecules, while cohesion forces are the attraction between oil molecules. The work of adhesion (Wa) is calculated as the surface tension of oil plus water minus the oil-water interaction, while the work of cohesion (Wc) is twice the surface tension of oil. By taking the difference of these works, the spreading coefficient (S) can be derived as the surface tension of water minus the difference between the oil-water interaction and the surface tension of oil.
The document outlines rules for graphing and linear regression. It discusses key aspects of graphing such as properly labeling axes, selecting appropriate scales, and drawing lines smoothly through data points. It then covers linear regression, defining the linear equation and describing how to calculate the slope and y-intercept by minimizing the sum of the deviations between observed and calculated data points. Formulas for determining the slope and y-intercept using linear regression are provided.
The document discusses accuracy and precision in measurement. It defines accuracy as how close a measurement is to the actual value, which depends on the person measuring. Precision refers to how finely tuned or close together measurements are, which depends on the measuring tool. Accuracy and precision are demonstrated through shooting at a target, where accuracy is hitting the bullseye and precision is a tight grouping of shots. Exact numbers come from counting or defined relationships, while measured numbers use a measuring tool and require estimation.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help boost feelings of calmness, happiness and focus.
This document describes a wheelchair navigation system based on voice commands for physically challenged individuals. The system uses voice recognition to understand commands spoken by the user to navigate around their home. It contains several modules including voice capture, voice recognition, motor control, and security. The voice capture module receives the user's spoken commands and the recognition module matches them to pre-recorded commands to move the wheelchair forward, backward, left, or right. It can also activate emergency services if the user feels unsafe. The system aims to give physically challenged people more independence and mobility within their home through a low-cost voice-controlled wheelchair navigation system.
Ofertas de viajes que incluyen un viaje de 4 días y 2 noches por $2000, un tour de 5 días y 3 noches en Montañita por $650, y un tour de 1 día al Cementerio de Tulcán por $50, así como un tour de 2 días y 1 noche a Las Peñas por $250.
This document provides a literature review that compares experiences with community policing and community safety policies and strategies in rural Britain and Finland. It examines how national policies in both countries emerged and how subsequent strategies developed from an inter-agency approach focused on crime and disorder to a more holistic vision of community concerns. The review finds that while policy formations were similar, the strategies diverged due to differing societal contexts. It concludes that greater attention must be paid to unique social structures and processes within different contexts for strategies to effectively improve rural security.
This document proposes a design for an optical transceiver section for wireless sensor nodes that uses visible light communication instead of radio frequency. It describes a cubic transceiver section with light emitting diodes and photodiodes arranged on the faces to allow full duplex communication in all directions. The design uses low-power, high-luminosity LEDs and analyzes the optical link between nodes to ensure sufficient illumination and a signal-to-noise ratio above the threshold for error-free communication. Simulation results show the design provides over 450 lux of illumination across an indoor area and a signal-to-noise ratio above 19.6 dB between nodes up to 2 meters apart.
TireAngel provides complete tire pressure monitoring solutions for commercial vehicles and passenger automobiles. Their flagship product is the SecuTireTM TM Link, a programmable TPMS ECU that receives wireless transmissions from TPMS sensors. It filters and buffers sensor data and transmits tire status information to display monitors, telematics devices, and mobile apps. This allows fleet managers to remotely monitor tire pressure and integrate TPMS data into their telematics systems. TireAngel aims to connect TPMS to the Internet of Things by developing solutions that are easy to use, reliable, economical, and can globally integrate tire data monitoring into telematics networks.
This document discusses digital image processing and image encryption techniques. It provides an overview of digital image processing, describing how images are defined and processed digitally. It then discusses various purposes of image processing like visualization, sharpening, recognition, and encryption. The document outlines different categories of image encryption methods, including position permutation, value transformation, and position-substitution techniques. It provides examples of specific encryption algorithms that fall under each category, such as Arnold transform and digital signatures. Finally, it discusses using XOR operations and affine transforms for image encryption.
Jeshua Christos loves you and want to give it all to you, Ephesians 1:19-23 oh, the utter extravagance of his work in us who trust him--endless energy, boundless strength! All this energy issues from Christ: God raised him from death and set him on a throne in deep heaven, in charge of running the universe, everything from galaxies to governments, no name and no power exempt from his rule. And not just for the time being, but forever. He is in charge of it all, has the final word on everything. At the center of all this, Christ rules the church. The church, you see, is not peripheral to the world; the world is peripheral to the church. The church is Christ's body, in which he speaks and acts, by which he fills everything with his presence.
Prince of Shalom
משׁיח
This document describes the development of an internet-based geographic information system (GIS) for real estate marketing. It discusses developing the software in three stages: planning system functions, designing the interface, and applying it to a case study region. Various tools and functions of the GIS software are described, including searching properties, generating reports, reserving units online, and testing the software. The GIS integrates data on properties, environmental features, and allows users to remotely search and choose properties for sale.
Derivation and Application of Six-Point Linear Multistep Numerical Method for...IOSR Journals
A six-step Continuous Block method of order (5, 5, 5, 5, 5, 5) T is proposed for direct solution of the second (2nd) order initial value problems. The main method and additional ones are obtained from the same continuous interpolant derived through interpolation and collocation procedures. The methods are derived by interpolating the continuous interpolant at 𝑥 = 𝑥𝑛+𝑗 , 𝑗 = 6 and collocating the first and second derivative of the
continuous interpolant at 𝑥𝑛+𝑗 , 𝑗 = 0 and 𝑗 = 2, 3, … 5 respectively. The stability properties of the methods are discussed and the stability region shown. The methods are then applied in block form as simultaneous numerical integrators. Two numerical experiments are given to illustrate the efficiency of the new methods.
Using Kentico EMS to optimize the B2B sales processJames Williamson
The document discusses using Kentico EMS to optimize the B2B sales process. It covers how B2B sales has changed with buyers now more informed and less reliant on salespeople. It then outlines how to implement a managed sales process in Kentico EMS, including developing value propositions, content modeling, buyer personas, marketing automation based on the buyer journey, and personalizing content. The implementation is demonstrated through an example commercial irrigation systems company.
Madcom analyzes the need for broadband in eastern paRich Frank
This document analyzes the need for broadband in rural Eastern Pennsylvania and proposes a public-private partnership to expand access. It finds that while wireless is available to most areas, wired broadband is still lacking and is key to economic growth. Securing support from institutions, economic groups, and potential private investors is important to make the case for a broadband build that could utilize federal funding and benefit schools, libraries, and telemedicine initiatives. Data on local businesses and infrastructure is presented to illustrate the business case.
This document reviews techniques for classifying news articles based on their content. It discusses the typical workflow for news classification, which includes collecting news articles, preprocessing the text through steps like tokenization and stemming, selecting informative features, and applying classification algorithms like Naive Bayes, support vector machines, neural networks or decision trees. The document analyzes the strengths and limitations of different feature selection methods and classifiers. It concludes that combining algorithms may improve classification efficiency and that these techniques could be tested on larger datasets.
Lord Jeshua Christos biggest wish for you is prosperity, peace, divine health and recovery. Our prayers for you are always spilling over into thanksgivings. We can't quit thanking God our Father and Jesus our Messiah for you!
This document provides an overview of key concepts in statistics that will be covered in the CHM 235 course, including:
- The normal distribution and how it relates to sampling from populations. Parameters like the mean, standard deviation, and normal curve shape sampling distributions.
- Common statistical tests like confidence intervals, comparing a measured value to a known value, and comparing means of two data sets using t-tests. These tests rely on assumptions of normal distributions and comparing calculated t values to statistical tables.
- Additional concepts like variance, relative standard deviation, average deviation, and F-tests to compare standard deviations before applying t-tests. An example takes the reader through each of these statistical calculations and tests.
This document provides an overview of key concepts in statistics for quantitative analysis, including:
- Statistics are mathematical tools used to describe and make judgments about data. The type of statistics discussed assumes data has a normal (bell-shaped) distribution.
- The normal distribution is characterized by a mean (μ) and standard deviation (σ or s). Standard deviation quantifies the spread of data around the mean.
- Common statistical tests covered include confidence intervals, comparing a measured value to a known value using a t-test, and comparing means of two data sets using an F-test and t-test.
- The F-test determines if the standard deviations of two data sets are significantly different before using
The document discusses the use of statistics in analytical chemistry. It provides definitions and explanations of key statistical concepts used to analyze chemical data, including:
- Mean, median, standard deviation, and variance as measures of central tendency and spread of data.
- The normal distribution and how it relates to accuracy and precision.
- Confidence intervals and how they are used to estimate the uncertainty around a measured value based on the standard deviation.
- How the size of data sets affects the confidence interval and uncertainty of results.
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.3: Estimating a Population Standard Deviation or Variance
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.3: Estimating a Population Standard Deviation or Variance
This document provides an overview of basic statistics concepts. It defines statistics as mathematical tools used to describe and make judgments about data. It discusses key assumptions in parametric statistics, such as data having a normal distribution. It also defines important statistical terms like mean, standard deviation, variance, standard error, and different ways to express variability in data like relative standard deviation and relative average deviation. Finally, it briefly mentions some common statistical tests like constructing confidence intervals and comparing means that make use of the Student's t-distribution.
Ch3_Statistical Analysis and Random Error Estimation.pdfVamshi962726
Here are the steps to solve this example:
(a) Compute the sample statistics:
Mean (x̅) = (Σxi)/n = (56.13)/10 = 5.613 cm
Standard deviation (s) = √[(Σ(xi - x̅)2)/(n-1)] = 0.6266 cm
(b) The interval over which 95% of measurements should lie is:
x̅ ± t0.025,9s = 5.613 ± 2.262(0.6266) = 5.613 ± 1.417 cm
(c) The estimated true mean value at 95% probability is:
μx = x
This document discusses various statistical tests used to analyze dental research data, including parametric and non-parametric tests. It provides information on tests of significance such as the t-test, Z-test, analysis of variance (ANOVA), and non-parametric equivalents. Key points covered include the differences between parametric and non-parametric tests, assumptions and applications of the t-test, Z-test, ANOVA, and non-parametric alternatives like the Mann-Whitney U test and Kruskal-Wallis test. Examples are provided to illustrate how to perform and interpret common statistical analyses used in dental research.
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Chapter 3: Describing, Exploring, and Comparing Data
3.2: Measures of Variation
This document discusses various measures of dispersion used to quantify how spread out or varied values in a data set are. It defines dispersion as the difference or deviation of values from the central value. Measures of dispersion described include range, standard deviation, quartile deviation, mean deviation, variance, and coefficient of variation. Both absolute measures, which use numerical variations, and relative measures, which use statistical variations based on percentages, are examined. Relative measures allow for comparison between different data sets.
This document defines variance and standard deviation and provides formulas and examples to calculate them. It states that variance is the average squared deviation from the mean and measures how far data points are from the average. Standard deviation tells how clustered data is around the mean and is the square root of the variance. It provides step-by-step instructions to find variance and standard deviation, including calculating the mean, deviations from the mean, summing the squared deviations, and taking the square root. Worked examples are shown to find the variance and standard deviation of students' test scores and people's heights in a room.
This document discusses standard deviation and related statistical concepts. It defines standard deviation as a measure of variability around the mean and explains how to calculate it from both ungrouped and grouped data. It also defines related terms like variance, standard error of the mean, and confidence limits of the mean. Standard deviation is calculated using the formula that sums the squared deviations from the mean, divided by n-1. Standard error is the standard deviation divided by the square root of the sample size, and confidence limits refer to ranges around the mean within which we can be certain the population mean falls.
Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdfRavinandan A P
Biostatistics, Unit-I, Measures of Dispersion, Dispersion
Range
variation of mean
standard deviation
Variance
coefficient of variation
standard error of the mean
1) Statistics are important in analytical chemistry to objectively analyze experimental data, communicate significance, and optimize experimental design.
2) Key statistical terms include mean, median, population, sample, standard deviation, and accuracy vs precision.
3) Spreadsheet software can be used to calculate statistical values like standard deviation and perform regressions for calibration curves.
This document discusses key statistical concepts used in analytical chemistry, including accuracy, precision, standard deviation, probability distributions, and significance testing. It explains how statistics are applied to evaluate experimental data quality and validate analytical methods. Spreadsheets and linear regression are also summarized as tools for statistical data analysis.
This document discusses measures of central tendency and variation for numerical data. It defines and provides formulas for the mean, median, mode, range, variance, standard deviation, and coefficient of variation. Quartiles and interquartile range are introduced as measures of spread less influenced by outliers. The relationship between these measures and the shape of a distribution are also covered at a high level.
Quantitative Analysis for Emperical ResearchAmit Kamble
Overview for Approach Methods for quantitative analysis; which includes
1) Planning of Experiments
2) Data Generation
3) presentation of report
some numerical approach methods; data modeling; hypothesis methods
1. The document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, standard deviation, coefficient of variation, and coefficient of quartile deviation.
2. It provides definitions and formulas for calculating each measure. For example, it states that range is defined as the difference between the maximum and minimum values, while standard deviation is the square root of the average of the squared deviations from the mean.
3. The document also compares absolute and relative measures of dispersion. Absolute measures use numerical variations to determine error, while relative measures express dispersion as a proportion of the mean or other measure of central tendency.
This document discusses various measures of dispersion used to describe the spread or variability in a data set. It describes absolute measures of dispersion, such as range and mean deviation, which indicate the amount of variation, and relative measures like the coefficient of variation, which indicate the degree of variation accounting for different scales. Common measures discussed include range, variance, standard deviation, coefficient of variation, skewness and kurtosis. Formulas are provided for calculating many of these dispersion statistics.
This document discusses various statistical tools used in decision making, including regression analysis, confidence intervals, comparison tests, and analysis of variance. It provides examples of how regression analysis can be used to determine correlations and unknown parameters. It also explains how confidence intervals are calculated and used to determine how reliable a sample statistic is in estimating an unknown population parameter. Comparison tests are outlined as a method to determine if one process or supplier is better than another.
This document is a lecture summary from Henry R. Kang on January 2010 about molecules, ions, and ionic compounds. It begins by defining substances, elements, compounds, atoms, molecules, and ions. It then discusses molecular compounds and their molecular, empirical, and structural formulas. Ionic compounds are made of cations and anions that combine to form a neutral compound. Examples of ionic formulas and how to determine the charges on monatomic and polyatomic ions are provided.
This document provides an overview of concepts related to mass and moles in chemistry, including:
- Atomic mass is the mass of an atom measured in atomic mass units (amu), with 1 amu defined as 1/12 the mass of one carbon-12 atom.
- Average atomic mass accounts for the fact that elements contain different isotopes by taking a weighted average of isotopic masses based on their abundances.
- Molecular and formula masses are the sums of atomic masses for all atoms in a molecule or formula unit, respectively.
- A mole is defined as the amount of a substance containing the same number of entities (atoms, molecules, etc.) as there are atoms in exactly 12 grams of carbon
This document provides an overview of atomic structure and theory from a general chemistry lecture. It discusses early atomic philosophers like Democritus and Dalton's atomic theory. Key concepts covered include the subatomic particles that make up atoms (protons, neutrons, electrons), experimental evidence for their existence from scientists like Thomson, Rutherford, and Millikan. The document also explains models of the atom including Thomson's "raisin pudding" model and Rutherford's nuclear model. Other topics summarized are the law of conservation of mass, isotopes, and the periodic table.
This document provides an overview of scientific notation, significant figures, and dimensional analysis. It discusses the rules and procedures for writing numbers in scientific notation, performing arithmetic operations using scientific notation, and determining the number of significant figures. Examples are provided to illustrate how to use dimensional analysis to convert between different units through factor-label methods. Problem solving techniques are also outlined, such as reading the problem carefully, identifying the appropriate conversion equation, checking the answer, and evaluating if the answer is reasonable.
This document summarizes key concepts about measurement from a general chemistry lecture, including:
- SI base units for length, mass, time, temperature and others. Prefixes are used to modify the units.
- Derived SI units are composed from multiple base units, like area, volume, density and more.
- English units are also discussed and converted to metric units.
- Concepts like mass vs weight, temperature scales, density, and the problematic "lb" unit are explained. Examples are provided to demonstrate calculations and conversions between units.
This document discusses different types of matter including substances, elements, compounds, and mixtures. It defines substances as having a definite composition and distinct properties that cannot be separated into other types of matter by physical processes. Elements are substances that cannot be broken down further by chemical means, while compounds are composed of two or more elements chemically bonded together in fixed proportions. Mixtures are combinations of substances that retain their identities and can be separated by physical means. The document also covers the three physical states of matter - solid, liquid, and gas - and how physical and chemical changes can alter matter.
This document proposes and tests a fractional-pixel averaging method for de-screening images that were scanned from halftoned prints. It presents the formulation of fractional-pixel averaging, which involves dividing pixels into sub-pixels, assigning values to sub-pixels, and using resolution conversion to average sub-pixel values. The method was tested on an IS&T NIP16 test target scanned at 600 dpi, which exhibited moiré patterns due to interaction between the offset print screen and scanner resolution. Results showed that fractional-pixel averaging was effective at removing moiré patterns by smoothing textures while retaining intensity.
This document describes a new method for designing digital filters using fractional-pixel sums. The method involves converting an image between two resolutions and using the pixel values from the intermediate resolution to generate directional masks. These masks can then be combined linearly to form different types of digital filters, such as moving-average filters. The filters produced by this method were tested on inverted bi-level images and shown to effectively remove blocking artifacts when compared to original continuous-tone images. The quality of inverted images was found to improve with higher resolution.
Chemistry is the study of matter and its properties, as well as the changes matter undergoes. It is a central science that is essential to our way of life and many other disciplines. Chemistry has many applications including in health, medicine, energy, material development, technology, food and agriculture, and the environment. It both enables advancements in these areas through new materials and technologies, but can also damage the environment through pollution, waste, and other impacts that chemistry aims to address through alternative and more sustainable approaches.
This document discusses the scientific method and different levels of interpretation in chemistry. It explains that the scientific method involves making observations and measurements, developing hypotheses to explain phenomena, designing experiments to test hypotheses, and using the results to interpret observations. The three levels of interpretation are hypotheses, which are tentative explanations; laws, which describe consistent relationships; and theories, which unify laws and evidence into explanatory frameworks. The document provides examples like the Big Bang theory to illustrate these concepts.
1. Henry R. Kang (1/2010)
General Chemistry
Lecture 5
Statistical Data
Analysis
2. Henry R. Kang (7/2008)
Outlines
• Fundamental Statistics
• Accuracy and Precision
• Data Rejection
3. Henry R. Kang (1/2010)
Accuracy & Precision
• Accuracy
Accuracy is a measure of the closeness of a
measured quantity to the true value.
• Precision
How close two or more measurements of the
quantity agree with one another.
Precision is a measure of the agreement of
replicate measurements.
5. Henry R. Kang (7/2008)
Errors
• All Measurements Contain Errors.
• Types of Errors
Systematic errors
One-sided errors (either positive or negative)
• Usually from a single source
• Resulting data are consistently high or low
Results may be precise but inaccurate
• Examples: Balance is incorrectly zeroed. Use incorrect constant for
calculations.
Random errors
Randomly occurred
Positive and negative deviations occur with equal frequency and size.
• A bell shape curve (Gaussian or normal distribution)
The source of the error is usually not known
6. Henry R. Kang (7/2008)
Gaussian Distribution
• Gaussian distribution gives the distribution of data points with respect to the
true value. It gives a bell-shaped curve as shown in the figure.
The closer to the true value, the higher the probability.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-3 -2 -1 0 1 2 3
Standard Deviation
Probability
7. Henry R. Kang (7/2008)
Measuring Accuracy
• Percent Error
If the true value is known
• Part Per Thousand (PPT)
• Part Per Million (PPM)
• Unfortunately, the true value is often not known.
% error =
| true value – experimental value |
| True value |
× 100
PPT =
| true value – experimental value |
| true value – experimental value |
| True value |
| True value |
× 1000
× 106
PPM =
8. Henry R. Kang (7/2008)
Measuring Precision
• Mean (or Average)
• Deviation and Absolute Deviation
• Absolute Average Deviation
• Relative Deviation
• Relative Average Deviation (RAD)
• Standard Deviation
• Relative Standard Deviation
9. Henry R. Kang (7/2008)
Mean (Average)
• For multiple measurements of a given quantity,
we have numerical values x1, x2, x3, - - - -, xn, where
n is the number of measurements.
• Sum is defined as
Sum = x1 + x2 + x3 + - - - + xn = ∑ xi
• Mean xavg is defined as
∑ xiSum
n n=xavg =
10. Henry R. Kang (7/2008)
Deviation & Absolute Deviations
• Deviation is the difference (or variation) of a single measurement,
xi, away from the mean value, xavg.
d1 = x1 – xavg
d2 = x2 – xavg
d3 = x3 – xavg
-- - -- -- - -- --
-- - -- -- - -- --
dn = xn – xavg
• Absolute deviation is always positive.
d1 = | x1 – xavg|
d2 = | x2 – xavg|
d3 = |x3 – xavg|
-- - -- -- - -- --
-- - -- -- - -- --
11. Henry R. Kang (7/2008)
Absolute Average Deviation
• Absolute average deviation, davg, is the arithmetic
mean of individual absolute deviations, di.
d1 = | x1 – xavg|
d2 = | x2 – xavg|
d3 = | x3 – xavg|
--------- ---
--------- ---
dn = | xn – xavg| ∑ di
n=davg
12. Henry R. Kang (7/2008)
Relative Deviation
• Relative deviation, Di, is the ratio of
individual absolute deviations, di, to the
mean value, xavg.
D1 = d1 / xavg = | x1 – xavg| / xavg
D2 = d2 / xavg = | x2 – xavg| / xavg
D3 = d3 / xavg = | x3 – xavg| / xavg
------------
Di = di / xavg = | xi – xavg| / xavg
------------
13. Henry R. Kang (7/2008)
Relative Average Deviation
• Relative average deviation (RAD) is the
absolute average deviation relative to
the mean xavg
A precision of 3 ppt or less is considered
very good.
RAD (ppt) = × 1000
davg
xavg
14. Henry R. Kang (7/2008)
Standard Deviation
• Standard deviation (σ) is useful in estimating data points
distribution in the form of the Gaussian distribution (a
bell-shaped curve).
(xavg ± σ) incorporates 68.3% of the data points.
(xavg ± 3σ) incorporates 99.7% of the data points.
The smaller the σ, the less spread of data points.
d1 = x1 – xavg
d2 = x2 – xavg
d3 = x3 – xavg
------------
dn = xn – xavg
∑ di
2
n – 1
=σ
√ =
√
d1
2
+ d2
2
+ d3
2
+ - - - - + dn
2
n – 1
15. Henry R. Kang (7/2008)
Relative Standard Deviation
• Relative standard deviation (σr) is the standard
deviation relative to the mean value.
d1 = x1 – xavg
d2 = x2 – xavg
d3 = x3 – xavg
--------- ---
dn = xn – xavg
where n is the number of measurements
∑ (di /xavg)2
n – 1
=σr
√ =
√ D1
2
+D2
2
+D3
2
+ - - - - +Dn
2
n – 1
or σr (ppt) = (σ / xavg ) × 1000
16. Henry R. Kang (7/2008)
Gaussian Distribution
• Gaussian distribution gives the
distribution of data points with
respect to the true value. It gives a
bell-shaped curve as shown in the
figure.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-3 -2 -1 0 1 2 3
Standard Deviation
Probability
• The Gaussian equation is
P(x) = [(2π)1/2
σ]–1
exp[-(x – X)2
/(2σ2
)]
where σ is the standard deviation and X is the true value.
The closer to the true value, the higher the probability.
The area under the curve (or the integration of the Gaussian function)
(xture ± σ) incorporates 68.3% of the data points.
(xture ± 3σ) incorporates 99.7% of the data points.
(xture ± 3.8901σ) incorporates 99.99% of the data points.
(xture ± 4.4172σ) incorporates 99.999% of the data points.
(xture ± 6σ) incorporates nearly 100% of the data points.
17. Henry R. Kang (7/2008)
Standard Deviation & Data Distribution
• The smaller the σ, the less spread of data points.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-4 -3 -2 -1 0 1 2 3 4
Standard Deviation
Probability
σ = 0.5
σ = 1.0
σ = 2.0
18. Henry R. Kang (7/2008)
Approximation of Standard Deviation
• The computational cost for standard deviation is pretty
high; therefore, there exists a good approximation to
compute standard deviation with much less
computational cost.
• š = Ř/√N
Ř is the range of data points from the lowest value to the
highest value
Ř = xmax – xmin
N is the number of data points.
• For a small number of measurements the approximation
is accurate enough to replace the formal standard
deviation.
20. Henry R. Kang (1/2010)
Accuracy & Precision of Measurements
• Accuracy is a measure of the closeness of a measured quantity to
the true value.
• Precision is a measure of the agreement of replicate
measurements.
• Measurements can be precise but not accurate or accurate but not
precise or neither. The best result is, of course, accurate and
precise.
Accurate &
precise
Precise but
not accurate
not accurate
& not precise
accurate but
not precise
21. Henry R. Kang (1/2010)
Example 1 of Accuracy and Precision
• Measured %S values in H2SO4 are 28.72%, 28.40%, and 28.57%,
where the true value is 32.69%. Determine the accuracy and
precision.
• Answer:
Mean = (28.72% + 28.40% + 28.57%) / 3 = 28.60%
Estimated precision by using the approximation: š = Ř / √N
š = (28.72 – 28.40)% / 31/2
= 0.32% / 1.732 = 0.18 %
Relative standard deviation: sr = š / xM
sr = 0.18% / 28.60% = 0.0063
Accuracy = |X − xM| = | 32.69% − 28.60% | = 4.09%
Relative accuracy = Accuracy / True value
= 4.09% / 32.69% = 0.125
• These result indicate that the data are precise but inaccurate.
22. Henry R. Kang (1/2010)
Example 2 of Accuracy and Precision
• Measured %S values in H2SO4 are 28.89%, 32.56%, and 36.64%,
where the true value is 32.69%. Determine the accuracy and
precision.
• Answer:
Mean = (28.89% + 32.56% + 36.64%) / 3 = 32.70%
Estimated precision by using the approximation: š = Ř / √N
š = (36.64 – 28.89)% / 31/2
= 7.75% / 1.732 = 4.47 %
Relative standard deviation: sr = š / xM
sr = 4.47% / 32.70% = 0.137
Accuracy = |X − xM| = | 32.69% − 32.70% | = 0.01%
Relative accuracy = Accuracy / True value
= 0.01% / 32.69% = 0.0003
• These result indicate that the data are imprecise but accurate.
23. Henry R. Kang (1/2010)
Example 3 of Accuracy and Precision
• Measured %S values in H2SO4 are 25.62%, 33.56%, and 27.93%,
where the true value is 32.69%. Determine the accuracy and
precision.
• Answer:
Mean = (25.62% + 33.56% + 27.93%) / 3 = 29.04%
Estimated precision by using the approximation: š = Ř / √N
š = (33.56 – 25.62)% / 31/2
= 7.94% / 1.732 = 4.58 %
Relative standard deviation: sr = š / xM
sr = 4.58% / 29.04% = 0.158
Accuracy = |X − xM| = | 32.69% − 29.04% | = 3.65%
Relative accuracy = Accuracy / True value
= 3.65% / 32.69% = 0.112
• These result indicate that the data are imprecise and inaccurate.
25. Henry R. Kang (7/2008)
Data Rejection
• Replicate measurements of a given quantity are usually
scattered.
Some values are closer than others.
• Which values to keep (or which values to discard)
If a single result differs greatly from the others that is caused
by a particular error of the experimenter, then this result
should be discarded.
If a result is significantly “off”, but there is no error in the
experiment, then the result, in general, should be kept.
• If in doubt, use the rejection coefficient Q test.
• Do not discard any result just to get “good precision”.
26. Henry R. Kang (7/2008)
Q Test
• Q test is used to test the extreme values (the highest and lowest
values)
• Procedure
Calculate the range
Range = xmax – xmin
Calculate the difference between the extreme value with its nearest
neighbor
dhi = xmax – xnbor,hi; dlo = | xmin – xnbor,lo |
Calculate the ratio (Q value) between the difference and the range
Qhi = dhi / Range ;Qlo = dlo / Range
• Compare the resulting Q value with the rejection table at 90%
confidence level (or other selected confidence level)
If the calculated Q value is greater than the Q value given in the table, then
reject the value.
27. Henry R. Kang (7/2008)
Rejection Q Tables
Number
of Data
Q90 Q96 Q99
3 0.94 0.98 0.99
4 0.76 0.85 0.93
5 0.64 0.73 0.82
6 0.56 0.64 0.74
7 0.51 0.59 0.68
8 0.47 0.54 0.63
9 0.44 0.51 0.60
10 0.41 0.48 0.57
28. Henry R. Kang (7/2008)
Q Test - Example
• Data: 35.00, 35.05, 35.10, 35.80
• Calculate the range
Range = xmax – xmin= 35.80 – 35.00 = 0.80
• Calculate the difference between the extreme value with its
nearest neighbor.
dhi = xmax – xnbor,hi = 35.80 – 35.10 = 0.70
dlo = xmin – xnbor,lo = | 35.00 – 35.05 | = 0.05
• Calculate Q values between the difference and the range.
Qhi = dhi / Range = 0.70 / 0.80 = 0.88
Qlo = dlo / Range = 0.05 / 0.80 = 0.063
• Compare the resulting Q value with the rejection table at 90%
confidence level.
For 4 samples, the Q value in the table is 0.76
Qhi > 0.76; therefore, the highest value 35.80 can be dropped
Once the value is dropped, it is no longer in the data set and should not
be used for the calculations of mean and various deviations.
#Data Q90
3 0.94
4 0.76
5 0.64
6 0.56
7 0.51
8 0.47
9 0.44
10 0.41
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