Business statestics formullas
•Download as PPTX, PDF•
1 like•122 views
This document provides an overview of various statistical concepts including measures of central tendency (mean, median, mode), measures of dispersion (range, quartile deviation, standard deviation), correlation, regression, and time series analysis. It defines formulas and methods for calculating common statistical measures such as the arithmetic mean, weighted mean, median, mode, range, quartile deviation, standard deviation, correlation coefficients, regression coefficients, and time series trend line. Examples are given for calculating these measures using both individual/discrete and continuous data series.
Report
Share
Report
Share
Recommended
Business statestics formullas
This document provides an overview of various statistical concepts including measures of central tendency (mean, median, mode), measures of dispersion (range, quartile deviation, mean deviation, standard deviation), correlation, regression, and time series analysis. Key topics covered include calculating and applying arithmetic mean, weighted mean, combined mean, median, mode, range, quartile deviation, mean deviation, standard deviation, correlation coefficients, regression coefficients, and least squares regression for time series forecasting. Formulas and methods for computing each concept are presented.
Fluid Mechanics
This example uses Buckingham's Pi theorem to relate the time taken (T) for a car to travel a distance (D) at a velocity (V). There are 3 variables (T, D, V) and 2 fundamental units (time, length), so there is 1 dimensionless parameter. Applying the theorem, it is shown that the time taken is equal to the distance divided by the velocity. So if a car travels 200 km at 100 km/hr, the time taken is 200/100 = 2 hours.
Dimensionless analysis & Similarities
This document discusses dimensional analysis and dimensionless numbers that are important in fluid mechanics. It defines Reynolds number, Froude number, Euler number, Weber number, and Mach number. It explains how dimensional analysis can help reduce the number of variables in experimental investigations. It also discusses similitude and the different types of model testing including undistorted and distorted models. The key uses and advantages of model testing are outlined.
Similitude and Dimensional Analysis -Hydraulics engineering
This document discusses similitude and dimensional analysis for model testing in hydraulic engineering. It introduces key concepts like similitude, prototype, model, geometric similarity, kinematic similarity, dynamic similarity, dimensionless numbers, and model laws. Reynolds model law is described in detail, which states that the Reynolds number must be equal between the model and prototype for problems dominated by viscous forces, such as pipe flow. An example problem demonstrates how to calculate the velocity and flow rate in a hydraulic model based on given prototype parameters and Reynolds model law.
A 1 D Breakup Model For
Finite element method analytical understanding was implemen ted to simulate the 1-dimensional break up model fot a jet spray . Programming was done in MATLAB
Dimensional analysis
This presentation will be useful to understand how dimensional analysis can be used to develop scale up correlation
Sumit[1]
This document provides formulas for various statistical concepts including measures of central tendency, dispersion, correlation, regression, and time series analysis. It defines formulas for calculating the mean, median, mode, standard deviation, quartiles, correlation coefficients, regression coefficients, and time series forecasting using least squares. Various methods for weighted averages and index numbers are also summarized.
Buckingham's theorem
Buckingham's Π theorem is a method of dimensional analysis that arranges variables in a physical problem into dimensionless groups (Π terms) to reduce the number of variables. It works when the total number of variables (n) is greater than the number of fundamental dimensions (m) involved. The example problem applies the method to determine the drag force (FD) on a sphere moving through a fluid based on variables like sphere diameter (D), velocity (V), fluid density (ρ), and viscosity (μ). Following steps of listing variables, determining n and m, forming Π groups, and solving for exponents to satisfy dimensionality, two dimensionless groups Π1 = FD/(ρV2D2) and
Recommended
Business statestics formullas
This document provides an overview of various statistical concepts including measures of central tendency (mean, median, mode), measures of dispersion (range, quartile deviation, mean deviation, standard deviation), correlation, regression, and time series analysis. Key topics covered include calculating and applying arithmetic mean, weighted mean, combined mean, median, mode, range, quartile deviation, mean deviation, standard deviation, correlation coefficients, regression coefficients, and least squares regression for time series forecasting. Formulas and methods for computing each concept are presented.
Fluid Mechanics
This example uses Buckingham's Pi theorem to relate the time taken (T) for a car to travel a distance (D) at a velocity (V). There are 3 variables (T, D, V) and 2 fundamental units (time, length), so there is 1 dimensionless parameter. Applying the theorem, it is shown that the time taken is equal to the distance divided by the velocity. So if a car travels 200 km at 100 km/hr, the time taken is 200/100 = 2 hours.
Dimensionless analysis & Similarities
This document discusses dimensional analysis and dimensionless numbers that are important in fluid mechanics. It defines Reynolds number, Froude number, Euler number, Weber number, and Mach number. It explains how dimensional analysis can help reduce the number of variables in experimental investigations. It also discusses similitude and the different types of model testing including undistorted and distorted models. The key uses and advantages of model testing are outlined.
Similitude and Dimensional Analysis -Hydraulics engineering
This document discusses similitude and dimensional analysis for model testing in hydraulic engineering. It introduces key concepts like similitude, prototype, model, geometric similarity, kinematic similarity, dynamic similarity, dimensionless numbers, and model laws. Reynolds model law is described in detail, which states that the Reynolds number must be equal between the model and prototype for problems dominated by viscous forces, such as pipe flow. An example problem demonstrates how to calculate the velocity and flow rate in a hydraulic model based on given prototype parameters and Reynolds model law.
A 1 D Breakup Model For
Finite element method analytical understanding was implemen ted to simulate the 1-dimensional break up model fot a jet spray . Programming was done in MATLAB
Dimensional analysis
This presentation will be useful to understand how dimensional analysis can be used to develop scale up correlation
Sumit[1]
This document provides formulas for various statistical concepts including measures of central tendency, dispersion, correlation, regression, and time series analysis. It defines formulas for calculating the mean, median, mode, standard deviation, quartiles, correlation coefficients, regression coefficients, and time series forecasting using least squares. Various methods for weighted averages and index numbers are also summarized.
Buckingham's theorem
Buckingham's Π theorem is a method of dimensional analysis that arranges variables in a physical problem into dimensionless groups (Π terms) to reduce the number of variables. It works when the total number of variables (n) is greater than the number of fundamental dimensions (m) involved. The example problem applies the method to determine the drag force (FD) on a sphere moving through a fluid based on variables like sphere diameter (D), velocity (V), fluid density (ρ), and viscosity (μ). Following steps of listing variables, determining n and m, forming Π groups, and solving for exponents to satisfy dimensionality, two dimensionless groups Π1 = FD/(ρV2D2) and
Hydraulic similitude and model analysis
The document discusses dimensional analysis, similitude, and model analysis. It provides background on how dimensional analysis and model testing are used to study fluid mechanics problems. Dimensional analysis uses the dimensions of physical quantities to determine which parameters influence a phenomenon. Model testing in a laboratory allows measurements to be applied to larger scale systems using similitude. Buckingham's π-theorem is introduced as a way to non-dimensionalize variables when there are more variables than fundamental dimensions. Rayleigh's and Buckingham's methods are demonstrated on an example of determining the resisting force on an aircraft.
Application of vector integration
This document discusses the application of vector integration in various domains. It begins by defining vector calculus concepts like del, gradient, curl, and divergence. It then presents several theorems of vector integration. Next, it explains how vector integration can be used to find the rate of change of fluid mass and analyze fluid circulation, vorticity, and the Bjerknes Circulation Theorem regarding sea breezes. It also discusses using vector calculus concepts in electricity and magnetism.
Dimensional analysis - Part 1
1. Dimensional Analysis definition necessity
2. Fundamental quantities- Primary Dimensions
3. Non Primary Dimensions
4. Secondary derived Dimensions
5. Dimensionless quantities
6. Necessity and objectives of Dimensional Analysis
7. Dimensional Homogeneity
8.Methods of Dimensional Analysis
9. Rayleigh's Method of dimensional analysis
10. Numerical Problem on Rayleigh's Method of dimensional analysis
REYLEIGH’S METHOD,BUCKINGHAM π-THEOREM
This document discusses two methods of dimensional analysis: Rayleigh's method and Buckingham π-theorem. Rayleigh's method expresses dependent variables as an exponential function of independent variables. It is useful for problems with 3-4 variables but difficult above that. Buckingham π-theorem states that variables can be grouped into dimensionless π terms, with the number of terms equal to the total variables minus the number of fundamental dimensions. This allows problems with many variables to be solved through grouping and repeating variables. Both methods involve setting up equations using dimensional homogeneity to solve for exponent values.
Sdarticle 2
This document summarizes a numerical simulation of flow between two rotating coaxial frustum cones. The simulation found that the fluid does not flow directly out of the outlet, but flows upward to a certain height, generating a vortex area with large velocity and pressure. This reflux area moves upward as the Reynolds number increases. For small frustum inclinations, the flow becomes unstable with very large velocity and pressure, even at small rotation rates. The study compares the flow properties to Taylor-Couette flow between rotating cylinders.
Shelf life calculation of drugs
This document discusses the calculation of shelf life for drug products. Shelf life is defined as the time when one can be 95% confident that a product contains not less than 90% of the active drug ingredient. Data from stability studies of three batches over 18 months was analyzed. A linear regression analysis found the degradation rate constant to be 0.267 mg/month. Using this, the time for the drug concentration to reach 90% of the initial concentration was calculated to be 25.5 months. The lower 95% confidence interval for this time was determined to be 19.8 months.
Free Ebooks Download
1. Dimensional analysis and the concept of similitude allow experiments using scale models to be used to study full-scale systems. Dimensional analysis uses Buckingham pi theorem to determine the minimum number of dimensionless groups needed to describe a phenomenon in terms of the variables involved.
2. For a model to accurately simulate a prototype system, the dimensionless pi groups that describe the phenomenon must be equal between the model and prototype. This establishes the modeling laws or similarity requirements that a model must satisfy.
3. Common dimensionless groups in fluid mechanics include the Reynolds number, Froude number, Strouhal number, and Weber number. These groups arise frequently in analyzing experimental data from fluid mechanics problems.
Dimensional analysis
Dimensional analysis is a mathematical technique used to establish relationships between physical quantities in fluid phenomena. It involves considering the dimensions of quantities and grouping dimensionless parameters to better understand flows. Dimensional analysis provides guidance for experimental work by indicating important influencing factors. It is applied to develop equations, convert between units, reduce experimental variables, and enable model studies through similitude. The key concepts are that theoretical equations must be dimensionally homogeneous and empirical equations have limited applications. Dimensional analysis methods include Rayleigh's method of exponential relationships and Buckingham's Π-method of grouping variables into dimensionless terms.
Episode 39 : Hopper Design
Episode 39 : Hopper Design
Problem:
1 -experiments with shear box jenike on a particulate catalyst to give the family
yield locus as in 1. given that the bulk density is 1000 kg/m3 particulates and wall friction angle is 15
a-from design chart silo cone, do design a mass flow hopper for the material.
b-if the average size is 100 um, calculate the discharge flow rate passing through the discharge opening
2 - For the above materials using stainless steel is required to store 1000 tons of particulate in it. Coefficient of friction at the wall is given as 0.45 for each value and the formula that you use the appropriate justify the design.
a - draw the dimensions of the silo you and draw a vertical stress profile and the wall of the silo whole time say powerful particle
b- specify the maximum vertical stress and the wall of the silo you
c - if you use several different approaches in the design you provide appropriate recommendations to your employer for work before the end of the casting device fabrication started.
d - if problems such as the formation of the entrance are available after a certain time interval suggest measures - flow improvement measures to be taken to your employer
SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
Line integral,Strokes and Green Theorem
The document defines key concepts related to line integrals of vector fields. It defines a vector as having both magnitude and direction. It then defines a line integral as integrating a function along a line, and defines a vector field as a region where a vector quantity (like magnetic field) assigns a unique vector value to each point. Finally, it discusses the definition of a line integral of a vector field, and three fundamental theorems relating line integrals to other integrals: the gradient theorem relating it to differences of a potential function at endpoints, Green's theorem relating it to a double integral, and Stokes' theorem relating it to a surface integral.
MUMS: Transition & SPUQ Workshop - Gradient-Free Construction of Active Subsp...
MUMS: Transition & SPUQ Workshop - Gradient-Free Construction of Active Subsp...The Statistical and Applied Mathematical Sciences Institute
Recent developments in the field of reduced order modeling - and in particular, active subspace construction - have made it possible to efficiently approximate complex models by constructing low-order response surfaces based upon a small subspace of the original high dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In this talk, we discuss a gradient free active subspace algorithm that is feasible for high dimensional parameter spaces where finite-difference techniques are impractical. We illustrate an initialized gradient-free active subspace algorithm for a neutronics example implemented with SCALE6.1.7th math c2 -l39
1) The document is notes from a math lesson that includes an assignment due the next day, a warm-up with conversion and fraction problems, an introduction to proportions, and examples of solving proportions.
2) The lesson introduces proportions as statements where two ratios are equal and provides the "McDonald's Arches" method for solving for missing values.
3) Practice problems include solving proportions with variables representing the missing values.
Dimesional Analysis
This document discusses dimensional analysis and its applications. It begins with an introduction to dimensions, units, fundamental and derived dimensions. It then discusses dimensional homogeneity, methods of dimensional analysis including Rayleigh's method and Buckingham's π-theorem. The document also covers model analysis, similitude, model laws, model and prototype relations. It provides examples of applying Rayleigh's method and Buckingham's π-theorem to define relationships between variables. Finally, it discusses different types of forces acting on fluids and dimensionless numbers, and provides model laws for Reynolds, Froude, Euler and Weber numbers.
Dimensional analysis
Dimensional analysis is a technique for simplifying physical problems by reducing the number of variables. It is useful for presenting experimental data, solving problems without exact theories, checking equations, and establishing relative importance of phenomena. Dimensional analysis refers to the physical nature and units of quantities. It can be used to develop equations for fluid phenomena, convert between unit systems, and reduce variables in experiments. Two common methods are Rayleigh's method, which determines expressions involving a maximum of four variables, and Buckingham's π-method, which arranges variables into dimensionless groups. Dimensional analysis provides a partial solution and requires understanding the relevant phenomena.
C1h2
The document discusses dimensional analysis, which is a technique used to express physical quantities in terms of base quantities. It defines basic and derived quantities, and lists common base quantities like length, mass, and time. The document also shows how to use dimensional analysis to determine the units and dimensional consistency of equations. Examples are provided to illustrate determining units, checking if equations are dimensionally correct, and deriving relationships between physical quantities.
10. fm dimensional analysis adam
The document discusses dimensional analysis and modeling. It covers:
1) The seven primary dimensions used in physics - mass, length, time, temperature, current, amount of light, and amount of matter. All other dimensions can be formed from combinations of these.
2) Dimensional homogeneity, which requires that every term in an equation must have the same dimensions.
3) Nondimensionalization, which involves dividing terms by variables and constants to render the equation dimensionless. This produces dimensionless parameters like the Reynolds and Froude numbers.
4) Similarity between models and prototypes in experiments, which requires geometric, kinematic, and dynamic similarity achieved by matching dimensionless groups.
Gradient Steepest method application on Griewank Function
The document discusses applying the gradient method to minimize the Griewank test function. It outlines the gradient method algorithm, shows simulation results for different starting points that converge in few iterations, and improvements made to ensure the algorithm finds the global minimum regardless of starting point by continuing to search after reaching local minima. The conclusions state the gradient method performs well locally but extensions were needed to locate the true global minimum for the Griewank function.
Fluids Lab
This document outlines an experiment to analyze converging-diverging (CD) nozzles. The experiment has two parts: 1) analyzing the outlet conditions of a single nozzle by comparing experimental and theoretical data, and 2) studying relationships between nozzle design parameters (area ratio, divergence angle) and flow characteristics (outlet speed, efficiency) for several nozzles. The document provides relevant theory, equipment descriptions, procedures, and methods to determine the success of each part. The goal is to better understand subsonic flow through CD nozzles and relationships between nozzle geometry and performance.
Statistics formula
This document provides formulas for various statistical concepts:
1. It outlines formulas for calculating the mean, median, mode, quartiles, standard deviation, and other measures of central tendency and dispersion for both individual and combined data sets.
2. It also includes formulas for calculating weighted aggregative indexes, correlation, regression, and time series analysis using the least squares method.
3. Various tests for index numbers and formulas using coefficients and assumed means are presented.
Akash[1]
This document provides formulas for various statistical concepts including measures of central tendency, dispersion, correlation, regression, and time series analysis. It defines formulas for calculating the mean, median, mode, standard deviation, quartiles, correlation coefficients, regression coefficients, and time series forecasting using least squares. Various methods for weighted aggregative indexes and dealing with time series data are also summarized.
Statistics formula
This document provides formulas for various statistical concepts:
1) It outlines formulas for calculating the mean, median, mode, and standard deviation for both individual and combined data sets. Weighted means and aggregate price indices are also covered.
2) Correlation coefficients are defined using formulas involving the sum of products of deviations or sums of actual values. Regression equations are presented using the method of least squares.
3) Additional topics covered include quartiles, skewness, index numbers, and time series analysis using least squares regression.
Raj
This document provides formulas and definitions for various statistical concepts including:
- Mean, median, mode, standard deviation, and correlation for individual, discrete, continuous, and combined data sets.
- Formulas for price indices like Laspeyre's, Paasche's, and Fisher's index.
- Formulas for regression analysis using the least squares method to find the regression coefficients for the line of best fit.
More Related Content
What's hot
Hydraulic similitude and model analysis
The document discusses dimensional analysis, similitude, and model analysis. It provides background on how dimensional analysis and model testing are used to study fluid mechanics problems. Dimensional analysis uses the dimensions of physical quantities to determine which parameters influence a phenomenon. Model testing in a laboratory allows measurements to be applied to larger scale systems using similitude. Buckingham's π-theorem is introduced as a way to non-dimensionalize variables when there are more variables than fundamental dimensions. Rayleigh's and Buckingham's methods are demonstrated on an example of determining the resisting force on an aircraft.
Application of vector integration
This document discusses the application of vector integration in various domains. It begins by defining vector calculus concepts like del, gradient, curl, and divergence. It then presents several theorems of vector integration. Next, it explains how vector integration can be used to find the rate of change of fluid mass and analyze fluid circulation, vorticity, and the Bjerknes Circulation Theorem regarding sea breezes. It also discusses using vector calculus concepts in electricity and magnetism.
Dimensional analysis - Part 1
1. Dimensional Analysis definition necessity
2. Fundamental quantities- Primary Dimensions
3. Non Primary Dimensions
4. Secondary derived Dimensions
5. Dimensionless quantities
6. Necessity and objectives of Dimensional Analysis
7. Dimensional Homogeneity
8.Methods of Dimensional Analysis
9. Rayleigh's Method of dimensional analysis
10. Numerical Problem on Rayleigh's Method of dimensional analysis
REYLEIGH’S METHOD,BUCKINGHAM π-THEOREM
This document discusses two methods of dimensional analysis: Rayleigh's method and Buckingham π-theorem. Rayleigh's method expresses dependent variables as an exponential function of independent variables. It is useful for problems with 3-4 variables but difficult above that. Buckingham π-theorem states that variables can be grouped into dimensionless π terms, with the number of terms equal to the total variables minus the number of fundamental dimensions. This allows problems with many variables to be solved through grouping and repeating variables. Both methods involve setting up equations using dimensional homogeneity to solve for exponent values.
Sdarticle 2
This document summarizes a numerical simulation of flow between two rotating coaxial frustum cones. The simulation found that the fluid does not flow directly out of the outlet, but flows upward to a certain height, generating a vortex area with large velocity and pressure. This reflux area moves upward as the Reynolds number increases. For small frustum inclinations, the flow becomes unstable with very large velocity and pressure, even at small rotation rates. The study compares the flow properties to Taylor-Couette flow between rotating cylinders.
Shelf life calculation of drugs
This document discusses the calculation of shelf life for drug products. Shelf life is defined as the time when one can be 95% confident that a product contains not less than 90% of the active drug ingredient. Data from stability studies of three batches over 18 months was analyzed. A linear regression analysis found the degradation rate constant to be 0.267 mg/month. Using this, the time for the drug concentration to reach 90% of the initial concentration was calculated to be 25.5 months. The lower 95% confidence interval for this time was determined to be 19.8 months.
Free Ebooks Download
1. Dimensional analysis and the concept of similitude allow experiments using scale models to be used to study full-scale systems. Dimensional analysis uses Buckingham pi theorem to determine the minimum number of dimensionless groups needed to describe a phenomenon in terms of the variables involved.
2. For a model to accurately simulate a prototype system, the dimensionless pi groups that describe the phenomenon must be equal between the model and prototype. This establishes the modeling laws or similarity requirements that a model must satisfy.
3. Common dimensionless groups in fluid mechanics include the Reynolds number, Froude number, Strouhal number, and Weber number. These groups arise frequently in analyzing experimental data from fluid mechanics problems.
Dimensional analysis
Dimensional analysis is a mathematical technique used to establish relationships between physical quantities in fluid phenomena. It involves considering the dimensions of quantities and grouping dimensionless parameters to better understand flows. Dimensional analysis provides guidance for experimental work by indicating important influencing factors. It is applied to develop equations, convert between units, reduce experimental variables, and enable model studies through similitude. The key concepts are that theoretical equations must be dimensionally homogeneous and empirical equations have limited applications. Dimensional analysis methods include Rayleigh's method of exponential relationships and Buckingham's Π-method of grouping variables into dimensionless terms.
Episode 39 : Hopper Design
Episode 39 : Hopper Design
Problem:
1 -experiments with shear box jenike on a particulate catalyst to give the family
yield locus as in 1. given that the bulk density is 1000 kg/m3 particulates and wall friction angle is 15
a-from design chart silo cone, do design a mass flow hopper for the material.
b-if the average size is 100 um, calculate the discharge flow rate passing through the discharge opening
2 - For the above materials using stainless steel is required to store 1000 tons of particulate in it. Coefficient of friction at the wall is given as 0.45 for each value and the formula that you use the appropriate justify the design.
a - draw the dimensions of the silo you and draw a vertical stress profile and the wall of the silo whole time say powerful particle
b- specify the maximum vertical stress and the wall of the silo you
c - if you use several different approaches in the design you provide appropriate recommendations to your employer for work before the end of the casting device fabrication started.
d - if problems such as the formation of the entrance are available after a certain time interval suggest measures - flow improvement measures to be taken to your employer
SAJJAD KHUDHUR ABBAS
Ceo , Founder & Head of SHacademy
Chemical Engineering , Al-Muthanna University, Iraq
Oil & Gas Safety and Health Professional – OSHACADEMY
Trainer of Trainers (TOT) - Canadian Center of Human
Development
Line integral,Strokes and Green Theorem
The document defines key concepts related to line integrals of vector fields. It defines a vector as having both magnitude and direction. It then defines a line integral as integrating a function along a line, and defines a vector field as a region where a vector quantity (like magnetic field) assigns a unique vector value to each point. Finally, it discusses the definition of a line integral of a vector field, and three fundamental theorems relating line integrals to other integrals: the gradient theorem relating it to differences of a potential function at endpoints, Green's theorem relating it to a double integral, and Stokes' theorem relating it to a surface integral.
MUMS: Transition & SPUQ Workshop - Gradient-Free Construction of Active Subsp...
MUMS: Transition & SPUQ Workshop - Gradient-Free Construction of Active Subsp...The Statistical and Applied Mathematical Sciences Institute
Recent developments in the field of reduced order modeling - and in particular, active subspace construction - have made it possible to efficiently approximate complex models by constructing low-order response surfaces based upon a small subspace of the original high dimensional parameter space. These methods rely upon the fact that the response tends to vary more prominently in a few dominant directions defined by linear combinations of the original inputs, allowing for a rotation of the coordinate axis and a consequent transformation of the parameters. In this talk, we discuss a gradient free active subspace algorithm that is feasible for high dimensional parameter spaces where finite-difference techniques are impractical. We illustrate an initialized gradient-free active subspace algorithm for a neutronics example implemented with SCALE6.1.7th math c2 -l39
1) The document is notes from a math lesson that includes an assignment due the next day, a warm-up with conversion and fraction problems, an introduction to proportions, and examples of solving proportions.
2) The lesson introduces proportions as statements where two ratios are equal and provides the "McDonald's Arches" method for solving for missing values.
3) Practice problems include solving proportions with variables representing the missing values.
Dimesional Analysis
This document discusses dimensional analysis and its applications. It begins with an introduction to dimensions, units, fundamental and derived dimensions. It then discusses dimensional homogeneity, methods of dimensional analysis including Rayleigh's method and Buckingham's π-theorem. The document also covers model analysis, similitude, model laws, model and prototype relations. It provides examples of applying Rayleigh's method and Buckingham's π-theorem to define relationships between variables. Finally, it discusses different types of forces acting on fluids and dimensionless numbers, and provides model laws for Reynolds, Froude, Euler and Weber numbers.
Dimensional analysis
Dimensional analysis is a technique for simplifying physical problems by reducing the number of variables. It is useful for presenting experimental data, solving problems without exact theories, checking equations, and establishing relative importance of phenomena. Dimensional analysis refers to the physical nature and units of quantities. It can be used to develop equations for fluid phenomena, convert between unit systems, and reduce variables in experiments. Two common methods are Rayleigh's method, which determines expressions involving a maximum of four variables, and Buckingham's π-method, which arranges variables into dimensionless groups. Dimensional analysis provides a partial solution and requires understanding the relevant phenomena.
C1h2
The document discusses dimensional analysis, which is a technique used to express physical quantities in terms of base quantities. It defines basic and derived quantities, and lists common base quantities like length, mass, and time. The document also shows how to use dimensional analysis to determine the units and dimensional consistency of equations. Examples are provided to illustrate determining units, checking if equations are dimensionally correct, and deriving relationships between physical quantities.
10. fm dimensional analysis adam
The document discusses dimensional analysis and modeling. It covers:
1) The seven primary dimensions used in physics - mass, length, time, temperature, current, amount of light, and amount of matter. All other dimensions can be formed from combinations of these.
2) Dimensional homogeneity, which requires that every term in an equation must have the same dimensions.
3) Nondimensionalization, which involves dividing terms by variables and constants to render the equation dimensionless. This produces dimensionless parameters like the Reynolds and Froude numbers.
4) Similarity between models and prototypes in experiments, which requires geometric, kinematic, and dynamic similarity achieved by matching dimensionless groups.
Gradient Steepest method application on Griewank Function
The document discusses applying the gradient method to minimize the Griewank test function. It outlines the gradient method algorithm, shows simulation results for different starting points that converge in few iterations, and improvements made to ensure the algorithm finds the global minimum regardless of starting point by continuing to search after reaching local minima. The conclusions state the gradient method performs well locally but extensions were needed to locate the true global minimum for the Griewank function.
Fluids Lab
This document outlines an experiment to analyze converging-diverging (CD) nozzles. The experiment has two parts: 1) analyzing the outlet conditions of a single nozzle by comparing experimental and theoretical data, and 2) studying relationships between nozzle design parameters (area ratio, divergence angle) and flow characteristics (outlet speed, efficiency) for several nozzles. The document provides relevant theory, equipment descriptions, procedures, and methods to determine the success of each part. The goal is to better understand subsonic flow through CD nozzles and relationships between nozzle geometry and performance.
What's hot (18)
MUMS: Transition & SPUQ Workshop - Gradient-Free Construction of Active Subsp...
MUMS: Transition & SPUQ Workshop - Gradient-Free Construction of Active Subsp...
Gradient Steepest method application on Griewank Function
Gradient Steepest method application on Griewank Function
Similar to Business statestics formullas
Statistics formula
This document provides formulas for various statistical concepts:
1. It outlines formulas for calculating the mean, median, mode, quartiles, standard deviation, and other measures of central tendency and dispersion for both individual and combined data sets.
2. It also includes formulas for calculating weighted aggregative indexes, correlation, regression, and time series analysis using the least squares method.
3. Various tests for index numbers and formulas using coefficients and assumed means are presented.
Akash[1]
This document provides formulas for various statistical concepts including measures of central tendency, dispersion, correlation, regression, and time series analysis. It defines formulas for calculating the mean, median, mode, standard deviation, quartiles, correlation coefficients, regression coefficients, and time series forecasting using least squares. Various methods for weighted aggregative indexes and dealing with time series data are also summarized.
Statistics formula
This document provides formulas for various statistical concepts:
1) It outlines formulas for calculating the mean, median, mode, and standard deviation for both individual and combined data sets. Weighted means and aggregate price indices are also covered.
2) Correlation coefficients are defined using formulas involving the sum of products of deviations or sums of actual values. Regression equations are presented using the method of least squares.
3) Additional topics covered include quartiles, skewness, index numbers, and time series analysis using least squares regression.
Raj
This document provides formulas and definitions for various statistical concepts including:
- Mean, median, mode, standard deviation, and correlation for individual, discrete, continuous, and combined data sets.
- Formulas for price indices like Laspeyre's, Paasche's, and Fisher's index.
- Formulas for regression analysis using the least squares method to find the regression coefficients for the line of best fit.
Statistics formula43[1]
This document contains formulas and definitions for various statistical concepts including measures of central tendency, dispersion, correlation, regression, and time series analysis. It defines formulas for calculating the mean, median, mode, standard deviation, quartiles, correlation coefficients, and regression coefficients. It also outlines methods for time series analysis using least squares regression and calculating index numbers over time.
Max flows via electrical flows (long talk)
1) The document describes algorithms for solving the maximum flow and electrical flow problems on graphs.
2) It introduces the multiplicative weight update method, which can be used to find an approximate maximum flow in Oε(m3/2) time by reducing the problem to approximating electrical flows.
3) The algorithm works by having the "follower" maintain a distribution over edges using MWU based on "money" or congestion values revealed by approximate electrical flow computations.
Mathematics of nyquist plot [autosaved] [autosaved]
This document provides a summary of a lecture on the mathematics of Nyquist plots. Some key topics covered include:
- Complex calculus concepts like Cauchy's theorem and the principle of argument.
- Derivation of the Cauchy-Riemann equations.
- Analytic functions and Cauchy's integral formula.
- Residue theorem and its application to determining stability using encirclements in the Nyquist plot.
- Construction of the Nyquist path and an example application to determine stability of a closed-loop system.
07-Convolution.pptx signal spectra and signal processing
The document discusses convolution, which is a mathematical operation used to describe the output of a linear time-invariant system when its input is another function. Convolution combines two sequences to produce a third sequence. It has properties like commutativity and associativity. To perform a convolution, the sequences can be directly evaluated as a summation, plotted graphically and multiplied/summed, or calculated using a slide rule method by shifting and multiplying corresponding terms.
14.pdf
This document discusses evaluating regression models and regularization techniques. It introduces adjusted R-squared (Adj R2) as a metric to evaluate regression models in addition to R-squared and p-values from ANOVA. Adj R2 accounts for the number of predictors in the model. The document also discusses regularization techniques like ridge and lasso regression that perform variable shrinkage. Ridge regression minimizes residuals subject to a constraint on the sum of squared coefficients. Lasso regression similarly minimizes residuals but constrains the sum of the absolute values of coefficients.
Abhishek[1]
This document contains formulas and definitions for various statistical concepts including measures of central tendency, dispersion, correlation, regression, and time series analysis. It defines formulas for calculating the mean, median, mode, standard deviation, quartiles, correlation coefficients, and linear regression coefficients using both direct and short-cut methods. It also outlines tests for index numbers and methods for weighted aggregation.
Lecture # 20.pptx
Here are the steps to solve these problems:
1) Let a = 4 (first term), r = 1/2 (common ratio)
Then the nth term is an = a(r)n-1
Setting an = 1/8, we get:
1/8 = 4(1/2)n-1
1/8 = 2(1/2)n-1
n-1 = 3
n = 4
Therefore, the 4th term is 1/8.
2) Let a = first term, r = common ratio
Given: a2 = 9, a4 = 1
a2 = a(r)
9 = a(r)
Generalised 2nd Order Active Filter Prototype_B
This document summarizes a student project on generalized 2nd order active filter prototypes. It includes:
- Deriving voltage transfer functions for bandpass, lowpass, highpass, and bandstop filters using generalized circuit topologies.
- Key equations relating the voltage transfer function to component values.
- MATLAB simulation to prove the equations and find cutoff frequencies and gain.
- Deriving the phase response equation and simulating the bandpass filter's phase shift and frequency response.
- Discussing issues encountered like op-amp stability and varying SPICE models.
simple linear regression - brief introduction
Goal of regression analysis: quantitative description and
prediction of the interdependence between two or more variables.
• Definition of the correlation
• The specification of a simple linear regression model
• Least squares estimators: construction and properties
• Verification of statistical significance of regression model
Core 2 revision notes
1. Indices involve rules for exponents like xa+b = xaxb and (xa)b = xab. Solving exponential equations uses these rules.
2. Graph transformations include translations, stretches, reflections, and asymptotes. Translations replace x with (x-a) and y with (y-b).
3. Sequences are functions with successive terms defined by a rule. Geometric sequences multiply successive terms by a constant ratio while arithmetic sequences add a constant.
correlation (3).pdf
This document discusses different methods of calculating correlation coefficients and regression equations between two variables X and Y, including:
- Direct and short cut methods to calculate the Pearson correlation coefficient r
- Spearman's rank correlation coefficient rs
- Regression equations to predict X from Y and Y from X using the least squares method
- The relationship between the correlation coefficient r and the regression coefficients
Física Integrales_Katherine Jaya
This document discusses triple integrals in 3 dimensions. It defines a triple integral as the limit of Riemann sums as the norm of the partition approaches 0. It states that a triple integral of a continuous function over a rectangular parallelepiped region is equal to the iterated integral of the function with respect to dzdydx. Examples are provided to demonstrate how to set up and evaluate triple integrals over various regions in 3D space, including in rectangular, cylindrical and other coordinate systems.
Form 1 Chapter 3 - CIKGU HARNISH SKOR IMPIAN
This document provides information about squares, square roots, cubes, and cube roots. It includes examples of evaluating expressions with exponents, determining whether numbers are perfect squares or cubes, and solving problems involving exponents. Key concepts covered are the definitions of exponents, properties like a^2 = a x a and a^3 = a x a x a, and evaluating expressions both with and without a calculator. Examples are provided to illustrate each concept.
Statistics formula
The document contains formulas and explanations for various statistical concepts including:
1) Mean, median, mode, and weighted mean formulas for individual discrete, continuous, and combined data.
2) Standard deviation formulas including direct, short cut, and step deviation methods for individual and combined discrete and continuous data.
3) Formulas for other concepts like correlation, regression, time series analysis, index numbers, and skewness.
4) Explanations of techniques like least squares method, time reversal test, and factor reversal test as they apply to various statistical analyses.
Vectors in mechanics
Newtonian mechanics in vector form:
Elements of vectors, operations on vectors, kinematics, Laws of Newton, Momentum & Impulse
Group No 05, calculus.pptx
1) The document introduces concepts of differential calculus including derivatives, limits, continuity, and fundamental rules of taking derivatives.
2) It provides examples of calculating derivatives using notations like delta f, limits, and various derivative rules including the power rule, product rule, and quotient rule.
3) Methods for finding local maxima and minima are discussed, including using the first derivative test and analyzing stationary points where the first derivative is zero based on whether the derivative is increasing or decreasing on both sides.
Similar to Business statestics formullas (20)
Mathematics of nyquist plot [autosaved] [autosaved]
Mathematics of nyquist plot [autosaved] [autosaved]
07-Convolution.pptx signal spectra and signal processing
07-Convolution.pptx signal spectra and signal processing
More from ABHISHEK SHARMA
WHAT IS COMMERCE ? @! 108
THIS PPT IS BASICALLY ABOUT TERM COMMERCE. WHAT IT IS. WHAT IS E- COMMERCE. WHAT ARE THE VARIOUS FEATURES OF COMMERCE.
Marketing & sales @!108
This document discusses marketing and sales management. It defines marketing as managing exchange relationships and customer satisfaction. There are three types of marketing: marketplace, marketspace, and meta market. Sales management aims to achieve sales targets through developing sales forces and techniques. It is an important continuous function that generates revenue, jobs, and customer feedback.
Intellectual property right abhishek shrama@! 108
this PPT comprises an introduction, definition, and various types of intellectual property rights & advantages of intellectual property rights surely will help learner to understand the subject effectively.
Go air vision and mission @!108
It is about go air vision and mission and a consist strategies adopted by the go air to achieve success and SWOT analysis of the concern
Worker’s Participation in Management Decision making – with special reference...
In recent years research and discussions on workers' participation in decision-making have dominated much of management literature. In its broadest possible sense, workers' participation means wider involvement and participation by a company's employee in the decision making process of that organization. With the outbreak of the First World War, an acute industrial unrest was experienced in those countries where its impact was intense. In countries like England, West Germany, France and the USA.
IMC ( INTEGRATED MARKETING COMMUNICATION )
This presentation provide a complete overview about the integrated marketing communication consist various avenue of marketing communication & also contain marketing and Branding.
Statr-up India
It is about start- up campaign launched by PM Modi for encouraging the new creative entrepreneur. It consist introduction, and description about various aspect about this scheme.
INDIAN FINANCIAL SYSTEM ( meaning , definition, structure )
It is about Indian Financial system. It defines IFS and structure. Surly will help you more to know about the Topic.
Event marketing @!108
Event marketing involves designing live events like concerts, fairs, or exhibitions to promote products, organizations, or causes. It provides an interactive experience for a targeted audience to influence them and meet marketing objectives. Some key types of events include trade shows, field marketing events, and user conferences. Event marketing is important for brand building, highlighting new features, rejuvenating brands, and creating brand identity. While it can be large and expensive with short term benefits, event marketing also helps communicate messages and obtain feedback when done effectively.
Out of box thinking
The document discusses out of the box thinking. It begins by defining out of the box thinking as thinking differently, unconventionally, or from a new perspective. It then lists 11 ways to think out of the box, including studying another industry, learning about another religion, taking a class, reading unfamiliar genres, writing a poem, drawing a picture, turning problems upside down, working backwards, asking a child for advice, embracing randomness, and taking a shower to spark new ideas.
Saa@108(3)
This document contains student exam results including their roll numbers, names, scores on different subjects and components, total marks, percentage, and grade. It lists the results of 8 students initially, then provides additional details for 3 of those students. It also contains a bar graph comparing the total marks of the 8 students and a table with their roll numbers and total marks.
Managment by objective
Management by Objectives (MBO) is a performance management approach where employees and organizations jointly set goals and objectives. It is based on the principle that goal alignment between employees and the organization will lead to more successful work performance. MBO involves managers and subordinates together defining common goals, individual responsibilities, expected results, and using these measures to guide work and assess contributions. Key aspects of MBO include cascading goals through the organization, setting specific objectives for each member, participative decision making, explicit time periods, and providing performance feedback.
B p r ( @! 108 )
This document discusses business process re-engineering and is presented by Sapna Devi, an MBA student with a specialization in Total Quality Management. The presentation provides an overview of business process re-engineering and concludes by thanking the audience and wishing them a nice day.
Growing importance of hrm ( @! 108 )
Human resources management (HRM) involves managing an organization's workforce and is becoming increasingly important. HRM deals with policies and systems related to recruiting, performance evaluation, compensation, and employee discipline. It also helps organizations comply with employment laws and maintain consistency in areas like compensation and promotions. As the workforce becomes more complex due to factors like new technologies and foreign competition, HRM plays a central role in strategic business decisions and matching employee skills to organizational goals. Maintaining engaged employees also gives organizations a competitive advantage in today's market.
TOTAL QUALITY MANAGEMENT ( Integration of juran, deming & crosby tqm prog...
The document discusses the integration of quality programs as presented by Deming, Juran, and Crosby. Some of the key points emphasized across all three approaches include: requiring top management support and commitment; providing continuous education and training; ensuring measurement is critical; giving workers the means to do a good job; viewing improvements not just in terms of the final product; attributing most quality problems to management policies or actions; applying the approaches in every organization; minimizing post-production inspection; requiring effective communication and teamwork at all levels; having no shortcuts to quality; involving suppliers in quality practices; pursuing quality as a continuous effort; and achieving quality through reducing variance.
Business statestics formullas
This document provides an overview of various statistical concepts including measures of central tendency (mean, median, mode), measures of dispersion (range, quartile deviation, standard deviation), correlation, regression, and time series analysis. It defines formulas and methods for calculating common statistical metrics like the arithmetic mean, weighted mean, median, mode, range, quartile deviation, standard deviation, correlation coefficients, regression coefficients, and time series forecasting using least squares. Examples of calculating these statistics are given for individual, discrete, and continuous data series.
More from ABHISHEK SHARMA (16)
Worker’s Participation in Management Decision making – with special reference...
Worker’s Participation in Management Decision making – with special reference...
INDIAN FINANCIAL SYSTEM ( meaning , definition, structure )
INDIAN FINANCIAL SYSTEM ( meaning , definition, structure )
TOTAL QUALITY MANAGEMENT ( Integration of juran, deming & crosby tqm prog...
TOTAL QUALITY MANAGEMENT ( Integration of juran, deming & crosby tqm prog...
Recently uploaded
一比一原版(UMN文凭证书)明尼苏达大学毕业证如何办理
毕业原版【微信:176555708】【(UMN毕业证书)明尼苏达大学毕业证】【微信:176555708】成绩单、外壳、offer、留信学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路），我们拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信176555708】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信176555708】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
→ 【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
STATATHON: Unleashing the Power of Statistics in a 48-Hour Knowledge Extravag...
"Join us for STATATHON, a dynamic 2-day event dedicated to exploring statistical knowledge and its real-world applications. From theory to practice, participants engage in intensive learning sessions, workshops, and challenges, fostering a deeper understanding of statistical methodologies and their significance in various fields."
Learn SQL from basic queries to Advance queries
Dive into the world of data analysis with our comprehensive guide on mastering SQL! This presentation offers a practical approach to learning SQL, focusing on real-world applications and hands-on practice. Whether you're a beginner or looking to sharpen your skills, this guide provides the tools you need to extract, analyze, and interpret data effectively.
Key Highlights:
Foundations of SQL: Understand the basics of SQL, including data retrieval, filtering, and aggregation.
Advanced Queries: Learn to craft complex queries to uncover deep insights from your data.
Data Trends and Patterns: Discover how to identify and interpret trends and patterns in your datasets.
Practical Examples: Follow step-by-step examples to apply SQL techniques in real-world scenarios.
Actionable Insights: Gain the skills to derive actionable insights that drive informed decision-making.
Join us on this journey to enhance your data analysis capabilities and unlock the full potential of SQL. Perfect for data enthusiasts, analysts, and anyone eager to harness the power of data!
#DataAnalysis #SQL #LearningSQL #DataInsights #DataScience #Analytics
一比一原版(UCSB文凭证书)圣芭芭拉分校毕业证如何办理
毕业原版【微信:176555708】【(UCSB毕业证书)圣芭芭拉分校毕业证】【微信:176555708】成绩单、外壳、offer、留信学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路），我们拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信176555708】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信176555708】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
→ 【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
一比一原版(UO毕业证)渥太华大学毕业证如何办理
UO毕业证录取书【微信95270640】购买（渥太华大学毕业证成绩单硕士学历）Q微信95270640代办UO学历认证留信网伪造渥太华大学学位证书精仿渥太华大学本科/硕士文凭证书补办渥太华大学 diplomaoffer,Transcript购买渥太华大学毕业证成绩单购买UO假毕业证学位证书购买伪造渥太华大学文凭证书学位证书,专业办理雅思、托福成绩单，学生ID卡，在读证明，海外各大学offer录取通知书，毕业证书，成绩单，文凭等材料:1:1完美还原毕业证、offer录取通知书、学生卡等各种在读或毕业材料的防伪工艺（包括 烫金、烫银、钢印、底纹、凹凸版、水印、防伪光标、热敏防伪、文字图案浮雕，激光镭射，紫外荧光，温感光标）学校原版上有的工艺我们一样不会少，不论是老版本还是最新版本，都能保证最高程度还原，力争完美以求让所有同学都能享受到完美的品质服务。
文凭办理流程：
1客户提供办理信息：姓名生日专业学位毕业时间等（如信息不确定可以咨询顾问：微信95270640我们有专业老师帮你查询）；
2开始安排制作毕业证成绩单电子图；
3毕业证成绩单电子版做好以后发送给您确认；
4毕业证成绩单电子版您确认信息无误之后安排制作成品；
5成品做好拍照或者视频给您确认；
6快递给客户（国内顺丰国外DHLUPS等快读邮寄）。
7完成交易删除客户资料
高精端提供以下服务：
一：渥太华大学渥太华大学毕业证文凭证书全套材料从防伪到印刷水印底纹到钢印烫金
二：真实使馆认证（留学人员回国证明）使馆存档
三：真实教育部认证教育部存档教育部留服网站可查
四：留信认证留学生信息网站可查
五：与学校颁发的相关证件1:1纸质尺寸制定（定期向各大院校毕业生购买最新版本毕,业证成绩单保证您拿到的是鲁昂大学内部最新版本毕业证成绩单微信95270640）
A.为什么留学生需要操作留信认证?
留信认证全称全国留学生信息服务网认证,隶属于北京中科院。①留信认证门槛条件更低,费用更美丽,并且包过,完单周期短,效率高②留信认证虽然不能去国企,但是一般的公司都没有问题,因为国内很多公司连基本的留学生学历认证都不了解。这对于留学生来说,这就比自己光拿一个证书更有说服力,因为留学学历可以在留信网站上进行查询!
B.为什么我们提供的毕业证成绩单具有使用价值？
查询留服认证是国内鉴别留学生海外学历的唯一途径但认证只是个体行为不是所有留学生都操作所以没有办理认证的留学生的学历在国内也是查询不到的他们也仅仅只有一张文凭。所以这时候我们提供的和学校颁发的一模一样的毕业证成绩单就有了使用价值。只硕大的蛇皮袋手里拎着长铁钩正站在门口朝黑色的屋内张望不好坏人小偷山娃一怔却也灵机一动立马仰起头双手拢在嘴边朝楼上大喊：“爸爸爸——有人找——那人一听朝山娃尴尬地笑笑悻悻地走了山娃立马“嘭的一声将铁门锁死心却咚咚地乱跳当山娃跟父亲说起这事时父亲很吃惊抚摸着山娃的头说还好醒得及时要不家早被人掏空了到时连电视也没得看啰不过父亲还是夸山娃能临危不乱随机应变有胆有谋山娃笑笑说那都是书上学的看童话和小说时多
一比一原版(harvard毕业证书）哈佛大学毕业证如何办理
一模一样【微信：A575476】【(harvard毕业证书）哈佛大学毕业证成绩单Offer】【微信：A575476】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信：A575476】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信：A575476】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
Experts live - Improving user adoption with AI
Bekijk de slides van onze sessie Enhancing Modern Workplace Efficiency op Experts Live 2024.
原版制作(unimelb毕业证书)墨尔本大学毕业证Offer一模一样
学校原件一模一样【微信：741003700 】《(unimelb毕业证书)墨尔本大学毕业证》【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
Analysis insight about a Flyball dog competition team's performance
Insight of my analysis about a Flyball dog competition team's last year performance. Find more: https://github.com/rolandnagy-ds/flyball_race_analysis/tree/main
Population Growth in Bataan: The effects of population growth around rural pl...
A population analysis specific to Bataan.
一比一原版(Unimelb毕业证书)墨尔本大学毕业证如何办理
原版制作【微信:41543339】【(Unimelb毕业证书)墨尔本大学毕业证】【微信:41543339】《成绩单、外壳、雅思、offer、留信学历认证（永久存档/真实可查）》采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路），我们拥有全套进口原装设备，特殊工艺都是采用不同进口机器一比一制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信41543339】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信41543339】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理
毕业原版【微信:176555708】【(GWU,GW毕业证书)乔治·华盛顿大学毕业证】【微信:176555708】成绩单、外壳、offer、留信学历认证（永久存档真实可查）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路），我们拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信176555708】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信176555708】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
→ 【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
University of New South Wales degree offer diploma Transcript
澳洲UNSW毕业证书制作新南威尔士大学假文凭定制Q微168899991做UNSW留信网教留服认证海牙认证改UNSW成绩单GPA做UNSW假学位证假文凭高仿毕业证申请新南威尔士大学University of New South Wales degree offer diploma Transcript
Open Source Contributions to Postgres: The Basics POSETTE 2024
Postgres is the most advanced open-source database in the world and it's supported by a community, not a single company. So how does this work? How does code actually get into Postgres? I recently had a patch submitted and committed and I want to share what I learned in that process. I’ll give you an overview of Postgres versions and how the underlying project codebase functions. I’ll also show you the process for submitting a patch and getting that tested and committed.
原版一比一利兹贝克特大学毕业证(LeedsBeckett毕业证书)如何办理
原版制作【微信:41543339】【利兹贝克特大学毕业证(LeedsBeckett毕业证书)】【微信:41543339】《成绩单、外壳、雅思、offer、真实留信官方学历认证（永久存档/真实可查）》采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【我们承诺采用的是学校原版纸张（纸质、底色、纹路）我们拥有全套进口原装设备，特殊工艺都是采用不同机器制作，仿真度基本可以达到100%，所有工艺效果都可提前给客户展示，不满意可以根据客户要求进行调整，直到满意为止！】
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信41543339】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信41543339】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：客户在留信官方认证查询网站查询到认证通过结果后付款，不成功不收费！
在线办理(英国UCA毕业证书)创意艺术大学毕业证在读证明一模一样
学校原件一模一样【微信：741003700 】《(英国UCA毕业证书)创意艺术大学毕业证》【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
End-to-end pipeline agility - Berlin Buzzwords 2024
We describe how we achieve high change agility in data engineering by eliminating the fear of breaking downstream data pipelines through end-to-end pipeline testing, and by using schema metaprogramming to safely eliminate boilerplate involved in changes that affect whole pipelines.
A quick poll on agility in changing pipelines from end to end indicated a huge span in capabilities. For the question "How long time does it take for all downstream pipelines to be adapted to an upstream change," the median response was 6 months, but some respondents could do it in less than a day. When quantitative data engineering differences between the best and worst are measured, the span is often 100x-1000x, sometimes even more.
A long time ago, we suffered at Spotify from fear of changing pipelines due to not knowing what the impact might be downstream. We made plans for a technical solution to test pipelines end-to-end to mitigate that fear, but the effort failed for cultural reasons. We eventually solved this challenge, but in a different context. In this presentation we will describe how we test full pipelines effectively by manipulating workflow orchestration, which enables us to make changes in pipelines without fear of breaking downstream.
Making schema changes that affect many jobs also involves a lot of toil and boilerplate. Using schema-on-read mitigates some of it, but has drawbacks since it makes it more difficult to detect errors early. We will describe how we have rejected this tradeoff by applying schema metaprogramming, eliminating boilerplate but keeping the protection of static typing, thereby further improving agility to quickly modify data pipelines without fear.
Recently uploaded (20)
STATATHON: Unleashing the Power of Statistics in a 48-Hour Knowledge Extravag...
STATATHON: Unleashing the Power of Statistics in a 48-Hour Knowledge Extravag...
Udemy_2024_Global_Learning_Skills_Trends_Report (1).pdf
Udemy_2024_Global_Learning_Skills_Trends_Report (1).pdf
Challenges of Nation Building-1.pptx with more important
Challenges of Nation Building-1.pptx with more important
Analysis insight about a Flyball dog competition team's performance
Analysis insight about a Flyball dog competition team's performance
Population Growth in Bataan: The effects of population growth around rural pl...
Population Growth in Bataan: The effects of population growth around rural pl...
DATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docx
DATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docx
University of New South Wales degree offer diploma Transcript
University of New South Wales degree offer diploma Transcript
Open Source Contributions to Postgres: The Basics POSETTE 2024
Open Source Contributions to Postgres: The Basics POSETTE 2024
End-to-end pipeline agility - Berlin Buzzwords 2024
End-to-end pipeline agility - Berlin Buzzwords 2024
Business statestics formullas
- 1. BUSINESS STATISTICS PRESENTED BY :- ABHISHEK SHARMA MBA 1ST 17PBA003
- 2. CENTRAL TENDANCY MEAN MEDIAN ( M ) MODE ( Z)
- 3. AIRTHMATIC MEAN Formula Individual Discrete Continuous DIRECT 𝜮𝑿 𝑵 𝜮𝒇𝑿 𝑵 𝜮𝒇𝒎 𝑵 SHORT CUT A+ 𝜮𝒅 𝑵 A+ 𝜮𝒇𝒅 𝑵 A+ 𝜮𝒇𝒅 𝑵 STEP DEVIATION A+ 𝚺𝐟𝐝′ 𝑵 ∗ 𝐢 A+ 𝜮𝒇𝒅 𝑵 ∗ 𝐢 (d=X-X͞ )
- 4. WEIGHTED MEAN • * WEIGHTED MEAN - ∑𝑾𝑿 ∑𝑾 • HERE, ∑𝑾 IS SUM OF WEIGHT • ∑𝑾𝑿 IS SUM OF WX = W *X
- 5. COMBINED MEAN • X123 = HERE, N1 IS NO. OF VALUE of 1ST SERIES , N2 IS NO. OF VALUE OF 2ND SERIES
- 6. MEDIAN ( M ) Individual & Discrete M= Size of N+1 th item 2 (when in points add = L+U 2 N = NO. OF SERIES OR SUM OR FREFUANCY Continuous M = Size of N th item 2 N/2 lies in particular C.I. M= l1 𝑁 2 −𝑐𝑓 𝑓 ∗ 𝑖
- 7. MODE ( Z ) • (1. INDIVIDUAL SERIES = MOST RECCURING NO. • (2. DISCRETE SERIES = BIGGEST NO. IN F , IT STRAIGHT VALUE IN ‘X’ (3. CONTINUE SERIES = f1 =biggest no. in ‘F’ , f0 = previous no. from f1 and f2 = next no. from f1. Z=𝐿1 + 𝑓1−𝑓0 2𝑓1−𝑓0−𝑓2 *I OR Z=3M-2X͞ ( AIRHTMATIC MEAN )
- 8. DISPERSION RANGE QUARTILE DEVIATION MEAN DEVIATION STANDERED DEVIATION
- 9. RANGE (R) =Largest value-Smallest value (L-S), Coefficient CR= 𝐿−𝑆 𝐿+𝑆
- 10. QUARTILE DEVIATION • Individual & Discrete Continuous Q1= Size of 𝑵+𝟏 𝟒 th item Q3= Size of 𝟑 𝑵+𝟏 𝟒 th item QD= 𝑸𝟑−𝑸𝟏 𝟐 , Q1= Size of 𝑵 𝟒 th item Q3= Size of 3 𝑵 𝟒 th item QD=𝑳 + 𝑵 𝟒 −𝒄𝒇 𝒇 ∗ 𝒊 Coefficient of Q.D. = 𝑸𝟑−𝑸𝟏 𝑸𝟑+𝑸𝟏
- 11. MEAN DEVIATION • Individual Discrete & CONTINOUS COFFICENT MD= 𝜮│𝒅/ 𝑵 MD= 𝜮𝒇│𝒅│ 𝑵 𝑴𝑫 𝑴𝑬𝑫𝑰𝑨𝐍 𝑶𝑹 𝑴𝑬𝑨𝑵
- 12. Coefficient of SD = ϭ 𝑋 And Coefficient of variation = ϭ 𝑋 ∗ 100 Combined SD = 𝑵 𝟏ϭ 𝟏+𝑵 𝟐ϭ 𝟐+𝑵 𝟏 𝒅 𝟏+𝑵₂𝒅₂ 𝑵 𝟏+𝑵₂ STANDERED DEVIATION ( ) DIRECT SHORT CUT STEP DEVIATION Individual =SD= 𝜮𝐱 𝟐 𝑵 OR 𝜮(𝑿−𝑿 𝑵 𝜮𝒅𝒙 𝟐 𝑵 − ( 𝜮𝒅𝒙 𝑵 )² = 𝜮𝒅𝒙 𝟐 𝑵 − ( 𝜮𝒅𝒙 𝑵 )² ∗ 𝑪 Discrete & continuous S.D. = 𝜮𝒇𝐱 𝟐 𝑵 𝜮𝒇𝒅𝒙² 𝑵 − ( 𝜮𝒇𝒅𝒙 𝑵 )² 𝜮𝒅𝒙′ 𝟐 𝑵 − ( 𝜮𝒅𝒙′ 𝑵 )² ∗ 𝑪 dx’= 𝒅𝒙 𝑪
- 13. SKEWNESS Karl pearson Bowley Kelly SKP = 𝐌𝐞𝐚𝐧−𝐌𝐨𝐝𝐞 𝑺𝑫 SKB = 𝐐𝟑+𝐐𝟏−𝟐 𝑴𝑬𝑫𝑰𝑨𝑵 𝐐𝟑−𝐐𝟏 SKk = 𝐝𝟗+𝐝𝟏−𝟐𝐌𝐞𝐝𝐢𝐚𝐧 𝐝𝟗−𝐝𝟏
- 14. INDEX NUMBER • Simple Methods Formula Price Quantity Simple aggregative 𝜮𝒑𝟏 𝜮𝒑𝟎 ∗ 𝟏𝟎𝟎 𝜮𝒒𝟏 𝜮𝒒𝟎 ∗ 𝟏𝟎𝟎 SimpleAverage Price Relative 𝚺 𝒑𝟏 𝒑𝟎 ∗ 𝟏𝟎𝟎 𝑵 𝚺 𝒒𝟏 𝒒𝟎 ∗ 𝟏𝟎𝟎 𝑵
- 15. INDEX NUMBER • Weighted aggregative Methods • Time Reversal Test : Po1 X P1 = 1 • Factor Reversal Test P01 X Q01 = ΣP1q1/ΣP0q0 Formula Price Quantity Laspeyre’s 𝚺𝐩𝟏𝐪𝟎 𝚺𝐩𝟎𝐪𝟎 ∗ 𝟏𝟎𝟎 𝚺𝐪𝟏𝐩𝟎 𝚺𝐪𝟎𝐩𝟎 ∗ 𝟏𝟎𝟎 Paaschee’s 𝚺𝐩𝟏𝐪𝟏 𝚺𝐩𝟎𝐪𝟏 ∗ 𝟏𝟎𝟎 𝚺𝐪𝟏𝐩𝟏 𝚺𝐪𝟎𝐩𝟏 ∗ 𝟏𝟎𝟎 Fisher’s 𝚺𝐩𝟏𝐪𝟎 𝚺𝐩𝟎𝐪𝟎 ∗ 𝚺𝐩𝟏𝐪𝟏 𝚺𝐩𝟎𝐪𝟏 ∗ 𝟏𝟎𝟎 𝚺𝐪𝟏𝐩𝟎 𝚺𝐪𝟎𝐩𝟎 ∗ 𝚺𝐪𝟏𝐩𝟏 𝚺𝐪𝟎𝐩𝟏 ∗ 𝟏𝟎𝟎 Dorbish & Bowley’s 𝚺𝐩𝟏𝐪𝟎 𝚺𝐩𝟎𝐪𝟎 + 𝚺𝐩𝟏𝐪𝟏 𝚺𝐩𝟎𝐪𝟏 ∗ 𝟏𝟎𝟎 𝟐 𝚺𝐪𝟏𝐩𝟎 𝚺𝐪𝟎𝐩𝟎 + 𝚺𝐪𝟏𝐩𝟏 𝚺𝐪𝟎𝐩𝟏 ∗ 𝟏𝟎𝟎 𝟐 Marshall edgeworth’s 𝚺𝐩𝟏𝐪𝟎 + 𝚺𝐩𝟏𝐪𝟏 𝐩𝟎𝐪𝟎 + 𝐩𝟎𝐪𝟏 ∗ 𝟏𝟎𝟎 𝚺𝐪𝟏𝐪𝟎 + 𝚺𝐪𝟏𝐩𝟏 𝚺𝐪𝟎𝐩𝟎 + 𝚺𝐪𝟎𝐩𝟏 ∗ 𝟏𝟎𝟎
- 16. CO-RELATION • KARL PEARSON METHODS :- 2. SPEARMEN METHODS :- (3. CON CURRENT DEVIATION :- rc = + + 𝟐𝒄 −𝒏 𝒏 (Actual mean) Assumed mean) Actual data r= 𝚺𝐱𝐲 𝚺𝐱 𝟐.𝚺𝐲 𝟐 r= 𝐍.𝚺𝐝𝐱𝐝𝐲−𝚺𝐝𝐱.𝚺𝐝𝐲 𝐍𝚺𝐝𝐱²− 𝚺𝐝𝐱 𝟐. 𝐍.𝚺𝐝𝐲²−(𝚺𝐝𝐲)² r= 𝐍.𝚺𝐗𝐘−𝚺𝐗.𝚺𝐘 𝐍.𝚺𝐗²− 𝚺𝐗 𝟐. 𝚺𝐘²−(𝚺𝐘)² WHEN RANK ARE GIEVAN WHEN RANK ARE NOT GIVEN WHENRANK ARE EQUAL R= 1 - 𝟔𝜮𝐃𝟐 𝐍𝟑 −𝐍 R= 1 - 𝟔𝜮𝐃𝟐 𝐍𝟑 −𝐍 R= 1 - 𝟔(𝜮𝐃𝟐+ 𝟏 𝟏𝟐 𝒎𝟑−𝒎+ 𝟏 𝟏𝟐 𝒎𝟑−𝒎+ 𝟏 𝟏𝟐 𝒎𝟑−𝟑) 𝐍𝟑 −𝐍
- 17. REGRESSION • (1. ALGEBRIC METHOD :- ( 2. NON – ALGEBRIC METHOD – ( I. ACTUAL METHOD :- co- efficient = bxy x byx (3. ASSUMED METHOD :- co- efficient = bxy x byx 1.Y on X Y=a+ bX ΣY=Na+bΣx ΣXY=aΣX+bΣX² 2.X on Y X=a+ bY ΣX=Na+bΣY ΣXY=aΣY+bΣY² 1.Y on X Y-Y̅=byx(X-X̅) byx= 𝚺𝐱𝐲 𝚺𝐱² 2.X on Y X-X̅=bxy(Y-Y̅ ) bxy= 𝚺𝐱𝐲 𝚺𝐲² 1.Y on X Y-Y̅=byx(X-X̅) , byx= 𝐍.𝚺𝐝𝐱𝐝𝐲−𝚺𝐝𝐱.𝚺𝐝𝐲 𝐍.𝚺𝐝𝐱²−(𝚺𝐝𝐱)² 2. X on Y X-X̅=bxy(Y-Y̅) , bxy= 𝐍.𝚺𝐝𝐱𝐝𝐲−𝚺𝐝𝐲.𝚺𝐝𝐱 𝐍.𝚺𝐝𝐲²−(𝚺𝐝𝐲)²
- 18. TIME SERIES • Least square method - Yс = a +bX • if x =0 then a = ∑𝒚 𝑵 b = ∑𝒙𝒚 ∑𝐱²
- 19. THANK YOU