Description:

This is the online, interactive version of OpenIntro's Advanced High School Statistics (https://www.openintro.org/book/ahss/). It was developed by Emiliano Vega and Ralf Youtz of Portland Community College using PreTeXt.

Advanced High School Statistics covers a first course in statistics, providing an introduction to applied statistics that is clear, concise, and accessible. This book was written to align with the AP© Statistics Course Description, but it's also popular in non-AP courses and community colleges.

We hope readers will take away three ideas from this book in addition to forming a foundation of statistical thinking and methods:

1. Statistics is an applied field with a wide range of practical applications.

2. You don't have to be a math guru to learn from real, interesting data.

3. Data are messy, and statistical tools are imperfect. But, when you understand the strengths and weaknesses of these tools, you can use them to learn about the real world.

This resource can be used in providing real-life activity for students by conducting survey. Results of their survey will be organized and presented through text, graphs and tables with research ethics observed.

Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability.  The idea of using a smooth curve to model a data distribution is introduced along with using tables and techonolgy to find areas under a normal curve.  Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.  Data is used from random samples to estimate a population mean or proportion.  Students calculate margin of error and interpret it in context.  Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.

Developed for fifth grade and above. Primary biological content area covered:; Plant growth; Seedling morphology; Hypothesis testing; Experimental design; Line graphing; Introductory statistics.Biology In Elementary Schools is a Saint Michael's College student project. The teaching ideas on this page have been found, refined, and developed by students in a college-level course on the teaching of biology at the elementary level. Unless otherwise noted, the lesson plans have been tried at least once by students from our partner schools. This wiki has been established to share ideas about teaching biology in elementary schools. The motivation behind the creation of this page is twofold: 1. to provide an outlet for the teaching ideas of a group of college educators participating in a workshop-style course; 2. to provide a space where anyone else interested in this topic can place their ideas.

This activity encourages students to analyze center and spread of the number of chocolate chips in 5 different brands of chocolate chip cookies.

Students compare real-time Earth and Mars measurements for temperature, wind speed, humidity and atmospheric pressure by accessing Internet-data resources from NASA.

A statistics lesson on describing and making claims from data representations, specifically linearly increasing data. Applies ideas of rate-of-change to develop writing a linear equation to fit the data, using the equation to interpolate and extrapolate additional information, and integrating the mathematical interpretation appropriately into a social sciences argument.

This is a free textbook teaching introductory statistics for undergraduates in Psychology. This textbook is part of a larger OER course package for teaching undergraduate statistics in Psychology, including this textbook, a lab manual, and a course website. All of the materials are free and copiable, with source code maintained in Github repositories.

Application of Mathematical Models and Techniques in the field of Statistics.

Pawan Kumar Ray
Assistant Professor
Harkamaya College of Education
6thMile Tadong Gangtok
Email-ccc4job@gmail.com
9832359082/7908401075

Abstract

Mathematics is the science of measurement, quantity and magnitude. Developing children's abilities for mathematics is the main goal of mathematics education. Its knowledge is exact, systematic, logical and clear. Mathematics involves the process for intellectual development of mental faculties. Besides the mental ability, mathematics develops some quality like concentration, truthfulness, seriousness and reasoning. Thus, in the words of Locke it is rightly said that, “Mathematics is a way to settle in the mind the habit of reasoning”. Statistics plays a vital role in every fields of human activity. It has important role in determining the existing position of per capita income, unemployment, population growth rate, housing, schooling medical facilities etc in a country. Modeling and Statistics are two branches of applied mathematics. Modeling involves fitting equations to data, usually just approximately. Statistics is the science of uncertainty. Mathematics is the most closely related subject “Statistics” in our daily life. This paper deals with the concept of the Mathematical techniques, Modeling .The Importance & Uses of Mathematical techniques and Modeling in the field of Statistics. It discusses the different Mathematical techniques and Modeling in respect to statistics. The paper also discusses “How to make statistics easy for learner by using Mathematical techniques and Modeling?”
Key words: Mathematical Modeling, Mathematical Techniques, Statistics, Population.

This applied mathematics textbook covers Matrices and Pathways, Statistics and Probability, Finance, Cyclic, Recursive and Fractal Patterns, Vectors, and Design. The approach used is primarily data driven, using numerical and geometrical problem-solving techniques.

This is a "first course" in the sense that it presumes no previous course in probability. The units are modules taken from the unpublished text: Paul E. Pfeiffer, ELEMENTS OF APPLIED PROBABILITY, USING MATLAB. The units are numbered as they appear in the text, although of course they may be used in any desired order. For those who wish to use the order of the text, an outline is provided, with indication of which modules contain the material.

Measuring the dimensions of nano-circuits requires an expensive, high-resolution microscope with integrated video camera and a computer with sophisticated imaging software, but in this activity, students measure nano-circuits using a typical classroom computer and (the free-to-download) GeoGebra geometry software. Inserting (provided) circuit pictures from a high-resolution microscope as backgrounds in GeoGebra's graphing window, students use the application's tools to measure lengths and widths of circuit elements. To simplify the conversion from the on-screen units to the real circuits' units and the manipulation of the pictures, a GeoGebra measuring interface is provided. Students export their data from GeoGebra to Microsoft® Excel® for graphing and analysis. They test the statistical significance of the difference in circuit dimensions, as well as obtain a correlation between average changes in original vs. printed circuits' widths. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note below for details.

This course is an arithmetic course intended for college students, covering whole numbers, fractions, decimals, percents, ratios and proportions, geometry, measurement, statistics, and integers using an integrated geometry and statistics approach. The course uses the late integers model—integers are only introduced at the end of the course.

In this video segment from TV411, figure skaters compute their average daily practice time.

This resource consists of a Java applet and expository text. The applet is a simulation of the ballot experiment: The votes in an election are randomly counted. The event of interest is that the winning candidate is always ahead in the vote count.

Beginning econometrics students often have an uneven preparation in statistics. The simulation gives students a clearer understanding of the behavior of OLS estimators.

Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP (http://www.jasp-stats.org), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder’s BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

David McCandless turns complex data sets (like worldwide military spending, media buzz, Facebook status updates) into beautiful, simple diagrams that tease out unseen patterns and connections. Good design, he suggests, is the best way to navigate information glut -- and it may just change the way we see the world. A quiz, thought provoking question, and links for further study are provided to create a lesson around the 18-minute video. Educators may use the platform to easily "Flip" or create their own lesson for use with their students of any age or level.

This resource consists of a Java applet and expository text. The applet is a simulation of Bertrand's experiment: a random chord on a circle The event of interest is whether the length of the chord is larger than the length of the inscribed equilateral triangle. Three models for generating the random chord can be used.

Outliers may not be the result of actual observations, but rather the result of errors in data collection, data recording, or other parts of the data life cycle. This can be used to identify outliers for closer examination.

Students act as R&D entrepreneurs, learning ways to research variables affecting the market of their proposed (hypothetical) products. They learn how to obtain numeric data using a variety of Internet tools and resources, sort and analyze the data using Excel and other software, and discover patterns and relationships that influence and guide decisions related to launching their products. First, student pairs research and collect pertinent consumer data, importing the data into spreadsheets. Then they clean, organize, chart and analyze the data to inform their product production and marketing plans. They calculate related statistics and gain proficiency in obtaining and finding relationships between variables, which is important in the work of engineers as well as for general technical literacy and decision-making. They summarize their work by suggesting product launch strategies and reporting their findings and conclusions in class presentations. A finding data tips handout, project/presentation grading rubric and alternative self-guided activity worksheet are provided. This activity is ideal for a high school statistics class.

This resource consists of a Java applet and expository text. The applet is a simulation of the birthday experiment: a sample of size n is chose at random and with replacement from the first m positive integers. The random variable of interest is the number of distinct sample values. The event of interest is that all sample values are distinct.

This resource consists of a Java applet and expository text. The applet simulates Buffon's coin experiment. The radius of the coin can be varied. The applet illustrates a random experiment, the sample space, random variables, events, probability, and relative frequency.

This resource consists of a Java applet and expository text. The applet simulates Buffon's needle experiment and the corresponding approximation of pi. The event of interest is that the needle crosses a crack. The length of the needle can be varied. The applet illustrates a random experiment, the sample space, random variables, probability, and relative frequency.

There is growing body of evidence to support that students who directly experience authentic scientific research are more likely to continue onto advanced degrees and careers in Science, Technology, Engineering and Mathematics (STEM). In an effort to introduce more students to the benefits of scientific research we have drawn on an ongoing research project aimed at understanding how Corals Respond to the Environment (CRE) to develop an interdisciplinary laboratory course based on Authentic Research Experiences (ARE). A small cohort of undergraduate students enrolled in a semester-long course, entitled CREARE, perform biochemical experiments in the laboratory, analyze environmental data by R statistical software and prepared a report modeled after a research manuscript to present their work. The impact of CREARE on student learning gains and attitudes towards science is being measured, as is the impact of CREARE on participants' career choices and retention in STEM. This multidisciplinary research program addresses the impact of climate change on the health of a critically endangered coral species, ultimately leading to a better stewardship of this invaluable resource. Furthermore, CREARE offers a unique experience for students, one that may serve as a model for the development of more research-based courses, leading to improved retention in our STEM departments.

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By the end of this session, you will be able to: Define standard deviationCalculuate starndard deviationInterpret standard deviation scores

This resource consists of a Java applet and expository text. The applet is a simulation of drawing n cards from a standard deck. The parameter n can be varied.

This resource consists of a Java applet and expository text. The applet simulates the chuck-a-luck experiment of rolling 3 fair dice. The random variable of interest is the net profit of the player.

This resource consists of a Java applet and expository text. The applet is a simulation of the experiment that consists of tossing a coin and then rolling either a red die or a green die, depending on the outcome of the coin toss. The probability of heads and the distributions of the two dice can be specified. The applet illustrates a two-stage experiment.

The Coke vs. Pepsi Taste Test Challenge has students design and carry out an experiment to determine whether or not students are able to correctly identify two brands of cola in a blind taste test.In the first stage of the activity students design and conduct the experiment. In the second part of the activity students use Sampling SIM software (freely downloadable from http://www.tc.umn.edu/~delma001/stat_tools/) to simulate and gather information on what would be expected under chance conditions (i.e., if students obtained correct answers only by guessing). The students then compare the observed results to the chance results and make an inference about whether a given student can in fact correctly identify Coke and Pepsi in a blind taste test. Finally, the experiment is critiqued in terms of how well it met the standards for a good experiment.

This activity allows students to gain a better understanding of the experimental process and causality through considering control, random assignment, and possible confounding variables. The activity also allows students to begin to understand the process of hypothesis testing by comparing their observed results of the taste test to the results obtained through Sampling SIM (which model would be obtained by chance). Students make an inference about whether particular students in their class can truly tell the difference between Coke and Pepsi by reasoning about how surprising the observed results are compared to the simulated distribution of correct identifications by guessing. The activity also provides an opportunity for discussing generalizability to a population.

Published by OpenStax College, Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it.

CODAP (Common Online Data Analysis Platform) is an easy to use data analysis environment that can be used in a wide variety of educational settings. CODAP is designed for grades 5 through 14, and aimed at teachers and curriculum developers. CODAP can be used across the curriculum to help students summarize, visualize, and interpret data, Conadvancing their skills to use data as evidence to support a claim.

In this model eliciting activity (MEA), students are hired by a travel magazine to determine if two airlines that fly into Chicago are equally reliable. They examine data of flight arrival delay times for both airlines flying out of the same city. They first identify measures that can be used to compare the two airlines. Working in small groups, the students decide the size of a meaningful difference between the airlines for each measure and use that information to determine a rule that for deciding if one airline is more reliable than another. The students apply their rule to flight arrival delay data for the two airlines from four additional departure cities, and use the results to write a report to the magazine editor on whether or not one airline is more reliable than the other. This activity can serve as an introduction to ideas of central tendency and variability, and prepares students for formal approaches to comparing groups.

An in-class statistics activity for computing and interpreting the standard deviation from a sample.

The applets in this section of Statistical Java allow you to see how levels of confidence are achieved through repeated sampling. The confidence intervals are related to the probability of successes in a Binomial experiment.

The applets in this section allow you to see how the common Xbar control chart is constructed with known variance. The Xbar chart is constructed by collecting a sample of size n at different times t.

Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise).