Chebyshev theorem
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Chebyshev's theorem establishes that at least three-quarters of observations in a data set will lie within 2 standard deviations of the mean, and at least eight-ninths will lie within 3 standard deviations. The empirical rule states that approximately 68% of observations are within 1 standard deviation of the mean, 95% are within 2 standard deviations, and almost all are within 3 standard deviations, assuming a normal distribution. The document suggests applying these rules to analyze graduation percentages of classmates.
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This document provides an overview of key concepts in statistics. It discusses how statistics is used to collect, organize, summarize, present, and analyze numerical data to derive valid conclusions. It defines common statistical terminology like data, quantitative vs. qualitative data, measures of central tendency (mean, median, mode), measures of variability (range, standard deviation), the normal distribution curve, and coefficient of variation. The document also explains common statistical tests like the z-test, t-test, ANOVA, chi-square test and concepts like sensitivity and specificity. Overall, the document serves as a high-level introduction to foundational statistical methods and analyses.
3 measures of central dendency
This document discusses measures of central tendency, which are summary measures that describe the middle or center of a data set with a single value. The three main measures are the mode, median, and mean. The mode is the most frequently occurring value, the median is the middle value when data are arranged in order, and the mean is the average calculated by summing all values and dividing by the total number of data points. The appropriate measure depends on the shape and type of data. Symmetrical distributions have equal mode, median and mean, while skewed distributions cause the mean to be "pulled" away from the middle.
Epidemological methods
Study of the distribution and determinants of
health-related states or events in specified populations and the application of this study to control health problems.
John M. Last, Dictionary of Epidemiology
statisticsintroductionofbusinessstats.ppt
This document provides an introduction to descriptive statistics including measures of central tendency (mean, median, mode) and measures of dispersion (range, standard deviation, variance). It explains how to calculate and interpret these statistics. Examples are provided using data on professors' weights to demonstrate calculating mean, median, mode, standard deviation, and using percentiles. Different types of graphs are introduced for organizing data such as histograms, bar graphs, pie charts, line graphs and scatter plots.
Epidemiology Lectures for UG
This document discusses sampling distributions and their use in making statistical inferences from data. It begins by defining key aspects of sampling distributions, including the statistic of interest (e.g. mean, proportion), random selection of samples, sample size, and population. It then generates a sampling distribution using an example of calculating the mean number of months since patients' last medical examination across different samples. The document outlines important characteristics of sampling distributions and how the central limit theorem applies. It also discusses how to construct confidence intervals and conduct hypothesis testing using sampling distributions.
Is ignorance bliss
It is argued that when it comes to nuisance parameters an assumption of ignorance is harmful. On the other hand this raises problems as to how far one should go in searching for further data when combining evidence.
Similar to Chebyshev theorem (20)
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Vam
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Project networks
A publisher has contracted an author to produce a textbook. The production process involves the author submitting a manuscript and files, editing, sample page and cover design, artwork, formatting, and printing. The critical path through the network is the author submitting the manuscript, editing, formatting, artwork approval, plate production, and binding, taking 17 weeks total to complete the project.
Or flowchart
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Maximisation problem
The document presents a linear programming problem to determine the optimal production mix for two products (P1 and P2) that maximizes profit. The products have different processing times and resource requirements on milling and drilling machines, which have limited weekly hours. The problem is formulated as a linear program to maximize total profit subject to the machine hour constraints. Slack variables are introduced and the problem is solved using the simplex method to find the optimal production levels of 50 units of P1 and 20 units of P2, yielding maximum profit of Rs. 20,500.
Lpp numerical
an LPP problem asked in aktu mba exam in 2008 (operations research) formulated, and solved using simplex method
Lpp numerical solved
a linear programming problem asked in aktu mba exam of operations research in 2008, formulated, and solved using graphical method
Lpp formulation
This document presents a linear programming problem involving assigning quality inspectors to minimize total inspection costs. There are two types of inspectors (Grade I and Grade II) with different inspection rates and accuracy. The objective is to minimize total costs based on wages, inspection pieces, and error costs with constraints on minimum inspection pieces and available inspectors.
Lp formulation
This document formulates a linear programming problem to determine the optimal production quantities of Products P1 and P2 given machine time and contribution margin constraints. Product P1 takes 4 hours on machine M1 and 2 hours on M2, while Product P2 takes 2 hours on M1 and 4 hours on M2. The objective is to maximize total contribution by choosing the quantities x1 and x2 subject to the 60 hours available on M1, 48 hours on M2, and non-negativity constraints.
Graphical method
The document describes a production problem involving two products (P1 and P2) that are manufactured using two machines (M1 and M2). P1 requires 4 hours on M1 and 2 hours on M2, while P2 requires 2 hours on M1 and 4 hours on M2. The goal is to determine the optimal quantities of P1 and P2 to maximize total contribution, given 60 hours available on M1 and 48 hours on M2. This problem is modeled as a linear programming problem and graphically solved by plotting the constraint lines and finding their intersection point.
Games
The document contains information about game theory including pure strategies, mixed strategies, and solving games. It provides examples of games represented as payoff matrices and discusses applying the principles of dominance, algebraic methods for 2x2 games, graphical methods for 2xn and mx2 games, and linear programming for mxn games. It also includes an example analyzing a 6x6 game modeling the Allied invasion of Normandy in WWII.
Game theory
Four teams will participate in a game involving selecting strategies of A or B. The aim is to score the maximum dividends. Scoring is based on the number of As and Bs selected. The document then explains the Prisoner's Dilemma game theory concept where two prisoners can either cooperate or betray each other, and discusses why rational individuals may not cooperate even if it is in their best interest to do so.
Dual formulation example
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Decision tree solved
A finance manager is considering drilling a well on their property. Based on past data, there is a 70% chance of finding water at 20 meters depth, and a 20% chance of finding water between 20-25 meters if no water is found at 20 meters. The costs to drill are Rs.500 per meter plus Rs.15,000 to buy water externally if the well is not drilled. The optimal decision tree strategy is to first drill to 20 meters, and if no water, then drill further to 25 meters, resulting in an expected cost of Rs. 11,350.
Decision theory numerical
The grocer must decide how many cases of milk to stock for tomorrow's demand. Each case sold yields a profit of Rs.3, but unsold cases at the end of the day lose Rs.5. Historical demand data shows the number of cases demanded and the probability of each quantity. The optimal decision can be determined by calculating the expected monetary value (EMV) of stocking different quantities of milk based on the probabilities and outcomes. The expected profit for the grocer if they stock the quantity with the highest EMV is Rs.47.7.
Crashing
project management. crashing a network. finding optimum duration and optimum cost of project. operations research (OR)
Assignment model problems
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Minimisation problem
a minimisation linear programming problem (LPP), solved using simplex method (operations research: OR)
Operations research
Operations research (OR) is a tool used to increase the effectiveness of managerial decisions. It can help with profit maximization, production management like determining optimal product mix and scheduling, financial management, marketing management, and personnel management. Some common OR models include linear programming, transportation, assignment, and sequencing problems. OR uses mathematical techniques like linear programming, decision theory, game theory, queuing theory, simulation, network analysis, and inventory models.
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QU本科学位证成绩单【微信95270640】《皇后大学毕业证书原版制作QU成绩单》【Q微信95270640】《仿制QU毕业证成绩单皇后大学学位证书pdf电子图》，A.为什么留学生需要操作留信认证?
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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。
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A.为什么留学生需要操作留信认证?
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Healthy economic development requires properly managing the banking industry of any
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Chebyshev theorem
- 2. Relations between the Mean and the Standard Deviation • The mean is a measure of the centrality of a set of observations. • The standard deviation is a measure of their spread. • There are two general rules that establish a relation between these measures and the set of observations. • The first is called Chebyshev’s theorem. • The second is the empirical rule.
- 3. Chebyshev’s Theorem • At least three-quarters of the observations in a set will lie within 2 standard deviations of the mean. • At least eight-ninths of the observations in a set will lie within 3 standard deviations of the mean.
- 4. Chebyshev’s Theorem • In other words,
- 5. The Empirical Rule If the distribution of the data is more or less symmetrical (normal distribution), then: • Approximately 68% of the observations will be within 1 standard deviation of the mean. • Approximately 95% of the observations will be within 2 standard deviations of the mean. • A vast majority of the observations (all, or almost all) will be within 3 standard deviations of the mean.
- 6. Problem • Check the applicability of Chebyshev’s theorem and the empirical rule for the graduation percentages of your batch-mates.