based on what information you want the reader to draw from the graph. An Advanced Display of Data Hans Rosling **Probably** one of the most informative **and** modern displays of data can be seen from the work of Hans Rosling. The link above shows a video of/any of the data values When best to use The mean is best used when you data is continuous **and** symmetrical. Often necessary for use in other **statistical** measures. **Lessons** on Arithmetic Mean How to Find the Mean Visit the web site above to learn more about the /

**Statistical** Testing: Thoughts Toward an Architecture We have a population of tests, which may have been sandboxed **and** which may carry self-check info. A test series involves a sample of these tests. We have a population of diagnostics, **probably** too/, Model-Based Testing, Proceedings of Software Quality Week 1997 (not included in the course notes) Michael Deck **and** James Whittaker, **Lessons** learned from fifteen years of cleanroom testing. STAR 97 Proceedings (not included in the course notes). Doug Hoffman/

students. Korean mathematics education seems to have many serious weak points, despite of students very proud achievement. Affective Characteristics: **Lesson** from TIMSS Report Korean students affective characteristics was not friendly to mathematics compared with other countries. In the case of/Time Type of problems Type A (130,000) (100,000) MathⅠ 40% MathⅡ 40% Select 1 among Calculus, **Statistics** **and** **probability**, Discrete math 20% 30 items 100 Minutes Choice:70%, Short Answer:30% Type B (270,000) (300,000) /

dealing with fractions, percentages, **and** **probability** Students will create word problems dealing with real basketball scenarios **and** their particular players Activities: Create their own study guides Split into partners **and** test each other with their/**statistics** **and** give logical reasons to support their players Students will listen **and** ask questions about guest Speaker Wendy Davis’s speech Activities: Students will listen to guest speaker Wendy Davis Students will present their final projects Activities: **Lesson**/

means for you: **Lesson** 6.2.3 Counting Outcomes California Standards: **Statistics**, Data Analysis **and** **Probability** 3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) **and** express the theoretical **probability** of each outcome. **Statistics**, Data Analysis **and** **Probability** 3.3 Represent **probabilities** as ratios, proportions, decimals between 0 **and** 1, **and** percentages between 0 **and** 100 **and** verify that the **probabilities** computed are reasonable; know/

of New Drugs: **Lessons** from Clinical Trials / malignancy Retrieval therapies for solid tumors Surgery, radiation, chemo Phase 3: **Statistical** Considerations post hoc analyses – Post relapse survival **and** MTP in osteosarcoma Surgical resection of metastatic sites necessary for survival No impact/toxicity profile Phase III studies in non-sarcoma indications in combination with chemothearpy: low toxicity **Probable** favorable benefit:risk ratio in phase III trials in sarcoma Regulatory Issues Requirement for placebo /

Session Objectives Explore the distinction between mathematical thinking **and** **statistical** thinking. Examine the development of the **statistics** **and** **probability** content over grades 6 – 11. Introduce overarching themes that provide coherence in the **statistics** **and** **probability** content across the grades. Illustrate development of **statistical** thinking across the grades with a trajectory of **lesson** activities. Explore other dimensions in the development of **statistical** thinking across the grades. 2 © 2012 Common Core/

housekeeping (with Meghan Steinmeyer) Progressions document: Grades 7 **and** 8 & the middle grades spectrum Break Model **lesson**, Part 1: (inspired by) engage ny Grade 8, **Lessons** 13 & 14 Model **lesson**, Part 2: associating Grade 8 **and** high school Closing remarks & For Next Time 8.3 LEARNING INTENTIONS **AND** SUCCESS CRITERIA We are learning to… Describe the progression of **statistics** **and** **probability** concepts in Grades 6-8 of CCSSM Create/

**Statistics** **and** Modelling Course 2011 Topic: Sample **statistics** & expectation Part of Achievement Standard 90643 Solve straightforward problems involving **probability** 4 Credits Externally Assessed NuLake Pages 147 163 Sigma: Old version – Ch 2. New version – Ch 7. **LESSON** 1 – **Probability** distribution Points of today: Learn the meaning of discrete **and** continuous random variables. Use a **probability** distribution table to display outcomes. What is Expected Value **and** how do you calculate it/

Integrating **Probability**, **Statistics** **and** Genetics in Grade 7 Steven Blumsack Emeritus Professor, Mathematics (FSU) Assistant in Research: FCR-STEM (FSU) We will work in terms of 3 (2 if necessary) Each team packet: 3 BLUE, 3 WHITE, 1 YELLOW, 1 PURPLE, 1 penny RATIONALE Integration of mathematics & science – Provides context in mathematics classroom – Opens door for deeper discussions in science – Reduces “Silos” Why **Probability**, **Statistics**, Genetics/

**Statistical** Sampling & Analysis of Sample Data (**Lesson** - 04/A) Understanding the Whole from Pieces Dr. C. Ertuna2 Sampling Sampling is : Collecting sample data from a population **and** Estimating population parameters Sampling is an important tool in business decisions since it is an effective **and**/to observe a particular (cumulative) **probability**. There is a relationship between z-score **and** **probability** over p(x) = (1-Normsdist(z))*tails **and** There is a relationship between z-score **and** the value of the random /

are not physical, they are a tool to measure representations of things. Include a quick **lesson** on a previous culture who used some method of **statistics**. Objective: To recognize trends **and** predict behavior **Probability** is another aspect of **statistics** that uses collecting **and** organizing data in order to see trends **and** predict behavior. It is used to make better judgments. The idea is to bridge the gap/

Diagram P(A C ∩ B C ) P(A) P(B) P(A ∩ B) = 1 Core **Lesson** Find the **probability** using a Venn Diagram. A **statistics** professor gave her class two tests, one on Thursday **and** one on Friday. 31% of students passed both tests, while 62% of students passed the Thursday test. What percent of students passing the Thursday test also passed the Friday/

**Lesson** 15 - 1 Nonparametric **Statistics** Overview Objectives Understand Difference between Parametric **and** Nonparametric **Statistical** Procedures Nonparametric methods use techniques to test claims that are distribution free Vocabulary Parametric **statistical** procedures – inferential procedures that rely on testing claims/results of the test are typically less powerful. Recall that the power of a test refers to the **probability** of making a Type II error. A Type II error occurs when a researcher does not reject the /

**and** observed **probabilities** at transitions Sum the deviation between expected **and** observed **probabilities** /**Statistical** analysis + systems Simplify, improve admin, reliability Simplify, improve admin, reliability Automatic analysis → handles complex systems Automatic analysis → handles complex systems Fast training → scales to frequent system changes Fast training → scales to frequent system changes First round of work promising, learned important **lessons** First round of work promising, learned important **lessons**/

“Stretch” in Data Miao (2015) Kernel Embedding Aizerman, Braverman **and** Rozoner (1964) Motivating idea: Extend scope of linear discrimination,/ (everybody currently does the latter) Kernel Embedding Standard Normal **Probability** Density Kernel Embedding Na ï ve Embedd ’ g, Toy/Note: Embedded data are very non-Gaussian Classical **Statistics**: “Use Prob. Dist’n” Looks Hopeless / Poor generalizability Too big miss important regions Classical **lessons** from kernel smoothing Surprisingly large “reasonable region” I.e/

AP **STATISTICS** **LESSON** 6 - 2 AP **STATISTICS** **LESSON** 6 - 2 **PROBABILITY** MODELS ESSENTIAL QUESTION: What is a **probability** model **and** how can it be used to solve **statistics** problems? Objectives: To define **and** use the vocabulary of **probability**. To design **probability** models that fit real–life problems. Basic Descriptions of **Probability** Models A list of all possible outcomes. A **probability** for each outcome. For example, the **probability** model for a coin toss is one out/

1 Opinionated in **Statistics** by Bill Press **Lessons** #15.5 Poisson Processes **and** Order **Statistics** Professor William H. Press, Department of Computer Science, the University of Texas at Austin In a “constant rate Poisson process”, independent events occur with a constant **probability** per unit time In any small interval t, the **probability** of an event is t In any finite interval , the mean (expected) number of events/

**Statistics** & **Probability** Level E (9 – 12)Algebra & Number Sense, Algebra & Geometry, **Statistics** & **Probability** Shift 1: FOCUS Mile Deep, Inch Wide Where SHOULD we focus? Are we missing the mark? Source: National Council on Education **and** the Economy. What Does It Really Mean to Be College **and**/? Turn this into an advantage Facilitate deep understanding by slowing down Make the **Lesson** Easier/Make the **Lesson** Harder Use Technology! Provide Additional Practice College & Career Readiness Practice Workbooks EMPower /

information! 6. Teacher Support Materials Common Core State Standards Grade 7 & 8: **Statistics** **and** **Probability** High School **Statistics** **and** **Probability**: Interpreting Categorical **and** Quantitative Data High School **Statistics** **and** **Probability**: Making Inferences **and** Justifying Conclusions High School **Statistics** **and** **Probability**: Conditional **Probability** **and** the Rules of **Probability** High School **Statistics** **and** **Probability**: Using **Probability** to Make Decisions Standards for the 21 st Century Learner Standards for the 21/

Hawkes **lesson** 5.1 Original content by D.R.S. Examples of **Probability** Distributions/4, 5, 6 rolled on a die Continuous All real numbers in some interval An age between 10 **and** 80 (10.000000 **and** 80.000000) A dollar amount A height or weight Discrete is our focus for now Discrete A countable number/4952/1000 Win fourth prize $953/1000 Loser$ -5993/1000 Total1000/1000 Expected Value Problems **Statistics** The mean of this **probability** is $ - 0.70, a negative value. This is also called “Expected Value”. Interpretation/

to History Home Page Next page So what do students actually do in history **lessons**? You’ll find yourself doing role plays… constructing a reasoned argument both in writing **and** spoken aloud… playing a variety of fun simulations designed to make ideas easier to grasp/information on each area of study please click below: 1 Number 2 Algebra 3 Ratio, proportion **and** rates of change 4 Geometry **and** measures 5 **Probability** 6 **Statistics** Useful websites: www.mymaths.co.uk www.emaths.co.uk www.bbcbitsize.co.uk www.gcse./

on each area of study please click below: 1 Number 2 Algebra 3 Ratio, proportion **and** rates of change 4 Geometry **and** measures 5 **Probability** 6 **Statistics** Useful websites: www.mymaths.co.uk www.emaths.co.uk www.bbcbitsize.co.uk www./a science context Unit 4: Controlled Assessment Investigative Skills Assignment – this consists of two written assessments plus two **lessons** for practical work **and** data processing Previous Page “Striving for Excellence” Exit Back to Core Subjects Page Back to Core Subjects Page The/

n The Hewlett Packard problem allows the expected value to be computed exactly, but not other **statistics**, such as the **probability** of a loss. Risk Analysis BA 452 **Lesson** C.1 Risk Simulation 32 n Hewlett Packard believes possible values of c 1 (direct labor / possible values of c 2 (parts cost for each unit) depend on the general economy, the overall demand for parts, **and** the pricing policy of Hewlett Packard’s parts suppliers. Specifically, they believe c 2 has a continuous uniform distribution that ranges/

1 **Lesson** 6.2.2 Expressing **Probability** 2 **Lesson** 6.2.2 Expressing **Probability** California Standard: **Statistics**, Data Analysis **and** **Probability** 3.3 Represent **probabilities** as ratios, proportions, decimals between 0 **and** 1, **and** percentages between 0 **and** 100 **and** verify that the **probabilities** computed are reasonable; know that if P is the **probability** of an event, 1– P is the **probability** of an event not occurring. What it means for you: You’ll meet **and** use/

, based on sample evidence **and** **probability** theory, used to determine whether the hypothesis is a reasonable statement **and** should not be rejected, or is unreasonable **and** should be rejected. Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson8-8 Hypothesis Testing Step 1: state null **and** alternative hypothesis Step 2: select a level of significance Step 3: identify the test **statistic** Step 4: formulate a/

If such a confidence interval does not enclose zero then it is unlikely that the two means are equal. There is **probably** a difference between the two means. Who Drives Faster? Our Conclusion: Since _______ lies within the confidence interval, there / parameter π with the sample **statistic** p. Starter **lesson** 7: Two independent populations have means of 85.4 **and** 64.3 respectively **and** standard deviations are 8.7 **and** 6.4. A random sample of 64 is drawn from the first population **and** 36 from the second. /

%) All purple columns **statistically** significantly different at p<0.05 Overall Model Goodness Full data set: School explains 1.1% of variance in gaming Hours 3-8: School explains 1.7% of variance in gaming Student, tutor **lesson**, **and** problem all found to predict significantly larger proportion of variance (Baker, 2007; Baker et al, 2009; Muldner et al, 2010) Slip **Probability** Urban school Suburban/

returns from the past That is, we have some observations drawn from the **probability** distribution –We can estimate the variance **and** expected return using the arithmetic mean of past returns **and** the sample variance Risk **Statistics** Calculating sample **statistics** –Mean, or Average, Return –Sample Variance –Sample Standard Deviation Risk **Statistics** Example: Return, Variance, **and** Standard Deviation YearActual Return Average Return Deviation from the Mean Squared Deviation 1/

: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 5-1 2nd **Lesson** **Probability** **and** Sampling Distributions Business **Statistics**: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 5-2 **Probability** Distributions Continuous **Probability** Distributions Binomial Hypergeometric Poisson **Probability** Distributions Discrete **Probability** Distributions Normal Chi Square Fisher MultinomialStudent-t Business **Statistics**: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 5-3 A discrete/

dependent variable (e.g., run time) is the sum of causal factors **and** random noise. **Statistical** methods assign parts of this variability to the factors **and** the noise. 21 **Lesson**: Keep the big picture in mind Why are you studying this? Load / zLike proof by contradiction: Assert the opposite (the coin is fair) show that the sample result (≥ 8 heads) has low **probability** p, reject the assertion, with residual uncertainty related to p. zEstimate p with a sampling distribution. 44 The logic of hypothesis testing/

EXERCISES 2 CHAPTER ONE THE NATURE **AND** **PROBABILITY** OF **STATISTICS** 3 **LESSON** ESSENTIAL QUESTION Why is it important to study **statistics**? 4 Key Term **Statistics**: the science of conducting studies to collect, organize, summarize, analyze, **and** draw conclusions. 5 Why Study **Statistics**? 1. Students **and** professionals must be able to read **and** understand **statistical** studies performed in their field. Requires knowledge of vocabulary, symbols, concepts, **and** **statistical** procedures used in these studies. 6/

small samples from populations that are not approximately normal. Chi-Square Distribution The distribution of the chi-square **statistic** is called the chi- square distribution. In this **lesson**, we learn to compute the chi-square **statistic** **and** find the **probability** associated with the **statistic**. Suppose we conduct the following **statistical** experiment. We select a random sample of size n from a normal population, having a standard deviation/

CRITERIA We are learning to… Identify productive struggle in our learning **and** teaching Create models for non-linear data Describe the progression of **statistics** **and** **probability** concepts in Grades 6-8 of CCSSM Plan, teach, **and** reflect on a **probability** **and** **statistics**-focused **lesson** that embodies the Mathematics Teaching Practices 7.4 LEARNING INTENTIONS **AND** SUCCESS CRITERIA We will be successful when we can: Connect productive struggle to student outcomes/

grades of my life in college. I never believed I would do that well **and** **probably** wouldn’t have if it had not been for Professor Fine’s encouragement. For two years, I looked forward to taking **statistics**. When the time finally arrived, I did something that I had never done /days Gonna tell him I dream of him every night One of these days Gonna show him I care, Gonna teach him a **lesson** alright I was in a trance when I kissed the teacher Suddenly I took the chance when I kissed the teacher Unit 3 Extraordinary/

of an event is fixed but not known **and** cannot be known The tools of frequentist **statistics** tell us what to expect, under the assumption of certain **probabilities**, about hypothetical repeated observations Frequentist confidence levels (CLs/includes shape information 13 A. Hoecker: **Statistical** IssuesCAT Physics meeting, Feb 9, 2007 Example: **Lessons** from TEVATRON Tom Junk gave an interesting talk about **lessons** from Tevatron. Many concrete examples of **statistics** use cases **and** pitfalls (some touched in this ré/

, we teach the following discrete English **lessons** each week: One **lesson** focusing on Reading Comprehension **and** love of literature One **lesson** focusing on Grammar **and** Punctuation Two **lessons** focussing on Writing, linked to the class/Negative **and** positive numbers Place value Estimation Rounding Long multiplication Fractions, Decimals **and** Percentages 2D **and** 3D shape Regular / irregular polygons Perimeter **and** Area Co-ordinates Translation **and** Rotation Reflection Ratio **and** Proportion **Probability** **Statistics** Digital /

**and** intervals of increasing/decreasing of graphs. HOME LEARNING: ALGEBRA 2; AGENDA; DAY 63: MON. NOV. 30, 2015 (2 nd 9-Week)[ODD-DAY] DISTRICT TESTING [PERIODS 1 & 5] OBJECTIVE: SWBAT: MAFS.912.F-IF.2.4;2.5;3.9: Domain & Range, intercepts, maximum, minimum, increasing/decreasing intervals, end behavior, composition of functions, inverse functions. **Statistics**, **probability**/ CORE ALGEBRA II; THEN UNIT 5 SEQUENCES **AND** SERIES.., Click **LESSON** 1: “SEQUENCES”, WATCH VIDEO **and** complete pages 1 – 4; Submit pages /

provide opportunities for children to simulate many trials with dice **and** spinners, **and** to integrate them into **lessons**: Go to the Math Forum Web site at http://mathforum.org/mathtools **and** then go to Math Topics. Under **Probability** **and** **Statistics** you will ﬁnd **lessons** focusing on various models, including randomness **and** **probability** models. A number of applets (Bar Graph Sorter **and** Circle Graph) for different grade levels are available. National Library/

approaches, the planner uses **lessons** learned to estimate an optimistic, most likely, **and** pessimistic size value for each/**probability** that a software application is operating according to requirements at a given point in time –Availability = [MTTF/ (MTTF + MTTR)] * 100% –Example: Avail. = [68 days / (68 days + 3 days)] * 100 % = 96% 623 Software Safety Focuses on identification **and** assessment of potential hazards to software operation It differs from software reliability –Software reliability uses **statistical**/

**Lesson** 1 **and** **Lesson** 2: Section 10.1 objectives **Lesson** 1: Describe the characteristics of the sampling distribution of Calculate the **probabilities** using the sampling distribution of Determine whether the conditions for performing inference are met. Construct **and** interpret a confidence interval to compare two proportions. **Lesson**/the two studies, Apple introduced the iPod. If the results of the test are **statistically** significant, can we blame iPods for the increased hearing loss in teenagers? example 4:/

Plot your data Dotplot, Stemplot, Histogram Interpret what you see: Shape, Outliers, Center, Spread ©2013 All rights reserved. CCSS 6 th Grade **Statistics** **and** **Probability** 2.0 Describe the distribution of a data set. **Lesson** to be used by EDI-trained teachers only. 1. Shape: Center: Spread: 2. Shape: Center: Spread: The distribution of a data set shows the arrangement of values in the/

Plot your data Dotplot, Stemplot, Histogram Interpret what you see: Shape, Outliers, Center, Spread ©2013 All rights reserved. CCSS 6 th Grade **Statistics** **and** **Probability** 2.0 Describe the distribution of a data set. **Lesson** to be used by EDI-trained teachers only. 1. Shape: Center: Spread: 2. Shape: Center: Spread: The distribution of a data set shows the arrangement of values in the/

today’s **lesson** 1.Frequentist **probabilities** of Poisson-distributed data -with **and** without nuisances 2.Weighted average in presence of correlations -Peeles pertinent puzzle 3.Finding the right model: Fishers F-test 4.Confidence intervals: the Neyman construction -bounded parameter, Gaussian measurement -flip-flopping **and** undercoverage 5.Hypothesis testing **and** the Higgs Search – Bump hunting – Look-elsewhere effect – The LHC Higgs search test **statistic** 1 – **Probabilities** of/

Milagrosa Sánchez Martín School of Psychology Dpt. Experimental Psychology 1 **Lesson** 5 Sampling **and** sampling distribution 2 The **statistical** inference presents two categories: Estimation theory (**lesson** 6): Given an index in the sample, the aim is /1. Sampling distribution of the mean. Standardization Sample Sampling distribution Population Standardization allows to calculate **probabilities** (if you know the **probability** model that has the distribution). We can consider normal distribution when n≥30. 26 4.1./

AP **STATISTICS** **LESSON** 6 - 1 THE IDEA OF **PROBABILITY** ESSENTIAL QUESTION: How is **probability** used in **Statistics**? Objectives: To develop a working understanding of **Probability**. To understand what is meant by “Random,” **and** what it’s characteristics are in the long run. Introduction **Probability** is a branch of mathematics that describes the pattern of chance outcomes. **Probability** is a branch of mathematics that describes the pattern of chance outcomes. The/

the **probability** of getting a cold reduced, increased, or not affected by the vitamins? In this **lesson**, we will learn how to answer this **and** other similar questions. Theory – Intro flipping a coin **and** getting heads rolling a die **and** getting 2 Event A **and** /in PreCalc 40S, **and** 30% failed Math 101. **Statistics** show that 10% of the students had an A in PreCalc 40S **and** still failed Math 101. Are getting an A in PreCalc **and** failing Math 101 independent events? Solution: Let A **and** B represent the /

Sampling Methods Classified as either **Probability** or Non-**Probability**. **Probability** samples, each member of the population has a known non-zero **probability** of being selected. The advantage of **probability** sampling is that sampling error / of lies: Lies, Damned Lies, **and** **Statistics** Descriptive **Statistics** The majority of our data collection will be done through sampling Populations versus Samples Population parameters: μ **and** σ Sample **statistics**: Х **and** s Descriptive **Statistics** Measures of Central Tendency: Mean – /

At project start Over **and** over, repeatedly, again **and** again, until project end Risk Management **Probability** of risk occurrence (P) How likely is the risk event? Can be classified by judgment Can be classified by **statistical** tools Risk Management Impact /does organization structure affect how this is handled? Project Closure – Post Mortem Gather **lessons** learned Sometimes called “post mortem” Analyze what went right **and** what went wrong on project Analyze what would have been done differently in hindsight/

/Dolp hins/Dolphins.html http://www.rossmanchance.com/applets/Dolp hins/Dolphins.html 14 Conclusion Experimental result is **statistically** significant **And** what is the logic behind that? Observed result very unlikely to occur by chance (random assignment) alone/in the details” Conclusions/**Lessons** Learned Don’t overlook null model in the simulation Simulation vs. Real study Plausible vs. Possible How much worry about being a tail **probability** How much worry about p-value = **probability** that null hypothesis is /

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