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Stanford Online

Statistical learning with r.

SOHS-YSTATSLEARNING

Stanford School of Humanities and Sciences

This is an introductory-level course in supervised learning, with a focus on regression and classification methods. The syllabus includes: linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; tree-based methods, random forests and boosting; support-vector machines. Some unsupervised learning methods are discussed: principal components and clustering (k-means and hierarchical).

This is not a math-heavy class, so we try and describe the methods without heavy reliance on formulas and complex mathematics. We focus on what we consider to be the important elements of modern data analysis. Computing is done in R. There are lectures devoted to R, giving tutorials from the ground up, and progressing with more detailed sessions that implement the techniques in each chapter. We also offer a separate version of the course called Statistical Learning with Python - the chapter lectures are the same, but the lab lectures and computing are done using Python. 

The lectures cover all the material in An Introduction to Statistical Learning, with Applications in R by James, Witten, Hastie and Tibshirani, with Applications in R (second addition) by James, Witten, Hastie and Tibshirani (Springer, 2021). The pdf for this book is available for free on the book website .

Prerequisites

Introductory level understanding of core concepts in statistics, linear algebra, and computing.

Core Competencies

Overview of statistical learning

• Linear regression
• Classification
• Resampling methods
• Linear model selection and regularization
• Moving beyond linearity
• Tree-based methods
• Support vector machines
• Deep learning
• Survival modeling
• Unsupervised learning
• Multiple testing
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• Lectures: Mon/Wed 3-4:20pm in Pigott Hall 113
• Sections: Fri 1:30-2:30pm in 200-030
• Osbert Bastani (office hours: Tue 10am-12pm, Thu 10am-12pm in Gates 438)
• Peng Xu (office hours: Mon 10am-12pm, Wed 10am-12pm in Huang Basement)
• Homeworks (40%) : there will be three homeworks (plus a warmup which does not count towards your grade), centered around proving properties of statistical procedures. Each homework must be submitted through Gradescope . Sign up for the course using entry code M4V34N . You are encouraged to use LaTeX to writeup your homeworks (here's a template ), but this is not a requirement. You will receive one (1) bonus point for submitting a typed written assignment (e.g. LaTeX, Microsoft Word). We will accept scanned handwritten assignments but they will not receive the bonus point.
• Exam (25%) : open-book, open-notes. Problems will be like the homeworks, but simpler. You can use laptops as long as you turn off the wireless. Date: Wed Nov 14, 6-10 PM, Bishop Auditorium, Lathrop296
• Paper review (30%) : you will write a 2-4 page review of papers. The goal is to learn to read technically demanding papers critically, and hopefully in the process, generate novel research ideas. Your review should not only summarize the main result of the paper, but critique it, instantiate it on examples, discuss its overall significance, and suggest possible future directions. See this Google doc for detailed guidelines and a list of papers. The paper reviews can be done in pairs. Paper reviews that are done in pairs will be evaluated with a slightly higher bar, and they ideally should contain reviews for two closely-related papers and are allowed two additional pages. Appendix or references beyond the page limit are allowed, but you will not be graded based on them.   Instead of doing the paper review, with approval from the course staff on the project topic, you can do a final project. Please come to the Tengyu Ma or Yu Bai's office hours to request the approval by briefly describing the project plan. We don't encourage you to do the project unless you own research area is closely related to machine learning theory. The project can be done in pairs. The page limit for project report is 8 pages, not including reference or appendix.   The review and the project should be submitted electronically by 11pm .
• Scribe notes (5%) : Because there is no textbook or set of readings that perfectly fits this course, you will be asked to scribe a note for a lecture in LaTeX. The course staff will select one note for each lecture and share it with other students. 1% bonus credit will be given if your note is selected for posting. See this Google doc for the detailed guidelines. The scribe notes are due 2 days after the lecture (11pm Wed for Mon lecture, and Fri 11pm for Wed lecture). Please sign up here before Sept 29th and plan the time ahead. Extra credits will be given to the notes that are selected for posting. The scribe notes can be done in pairs.

There is no required text for the course. A number of useful references:

Percy Liang's course notes from previous offerings of this course

Peter Bartlett's statistical learning theory course

Boyd and Vandenberghe's Convex Optimization

Sham Kakade's statistical learning theory course

Martin Wainwright's statistical learning theory course

• Lectures: Mon/Wed 3-4:20pm in Thornt110
• Sections: Fri 1:30-2:30pm in 200-030
• Osbert Bastani (office hours: Tue 10am-12pm, Thu 10am-12pm in Gates 438)
• Peng Xu (office hours: Mon 10am-12pm, Wed 10am-12pm in Huang Basement)
• Homeworks (30%) : there will be three homeworks (plus a warmup which does not count towards your grade), centered around proving properties of statistical procedures. You will also implement and run some of the algorithms as a reality check. Each homework must be turned in at the beginning of class (hard copy), as well as electronically by 11pm . Only the hard copy version will be graded; the electronic copy is just for our records. You are encouraged to use LaTeX to typeset your homeworks; we've provided a template for your convenience.
• Exam (40%) : open-book, open-notes. Problems will be like the homeworks, but simpler. You can use laptops as long as you turn off the wireless. Date: Feb. 25 6-9pm.
• Paper reviews (30%) : you will write two 2-4 page reviews of papers. The goal is to learn to read technically demanding papers critically, and hopefully in the process, generate novel research ideas. Your review should not only summarize the main result of the paper, but critique it, instantiate it on examples, discuss its overall significance, and suggest possible future directions. See this Google doc for detailed guidelines and a list of papers. Each review should be submitted electronically by 11pm . Instead of doing the last paper review, with approval from the course staff on the project topic, you can do a final project, perhaps extending one of the earlier reviews to produce novel results. The project can be done in pairs.

To submit electronically, open up a terminal, (i) copy your submission file(s) (e.g., hw0.pdf ) to cardinal.stanford.edu : scp <your submission file(s)> <your SUNetID>@cardinal.stanford.edu: and (ii) run the submit script: ssh <your SUNetID>cardinal.stanford.edu python /usr/class/cs229t/WWW/submit.py <hw0|hw1|hw2|hw3|p1|p2|p3> . You can submit multiple times; each submission will just replace the previous one.

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STAT 430: Basics of Statistical Learning

University of illinois at urbana-champaign, fall 2017, dalpiaz, schedule - homework - quizzes - projects, syllabus - compass - r4sl.

• First day of class! Course overview and syllabus discussion.
• Materials : Syllabus Slides , Full Syllabus
• ISL Videos : Opening Remarks and Examples , Supervised and Unsupervised Learning
• Quick probability review. Recapping some R basics.
• Reading : R4SL Chapter 2 , R4SL Chapter 3
• Slides : Probability Recap , R Introduction
• Lab : R Basics , R Basics Solutions
• Introduction to rmarkdown .
• Slides : rmarkdown Introduction
• No class! Labor Day
• More rmarkdown details and practice. What is a model?
• Reading : R4SL Chapter 3
• Lab : rmarkdown , rmarkdown Solutions
• Begin recap of regression basics.
• Reading : ISL 3.1 - 3.4, R4SL Chapter 4
• ISL Slides : Linear Regression
• ISL Videos : Simple Linear Regression , Hypothesis Testing , Interpreting Regression Coefficients , Model Selection and Qualitative Predictors , Interactions and Nonlinearity
• Deadline : Homework 00 Due
• Review using lm() for regression models in R .
• Reading : R4SL Chapter 4
• Introduce the supervised learning, regression, task. Discuss the test-train split and models that generalize to unseen data.
• Reading : ISL 2.1 - 2.2
• ISL Slides : Statistical Learning
• ISL Videos : Statistical Learning and Regression , Assessing Model Accuracy and Bias-Variance Trade-off
• Lab : Test-Train Split , Test-Train Split Solutions
• Continue discussion of regression in the context of statistical learning.
• Slides : Linear Models for Statistical Learning, Regression
• Deadline : Homework 01 Due
• Introduce KNN. Compare non-parametric methods to parametric methods. Discuss tuning parameters versus model parameters.
• Reading : R4SL Chapter 7 (Currently very sparse notes.)
• Continue discussion of KNN. Compare KNN to linear models. Some live coding examples.
• Finish discussion of KNN
• Deadline : Homework 02 Due
• Bias-Variance Tradeoff
• Reading : R4SL Chapter 8
• Slides : Bias-Variance Tradeoff
• Begin classification.
• Reading : ISL 4.1, R4SL Chapter 9
• Slides : Classification Introduction
• More classification. Introduction to logistic regression
• Reading : ISL 4.2 - 4.3, R4SL Chapter 10
• ISL Slides : Classification
• ISL Videos : Introduction to Classification
• Deadline : Homework 03 Due
• Continued discussion of logistic regression.
• Reading : ISL 4.3, R4SL Chapter 10
• ISL Videos : Logistic Regression , Multiple Logistic Regression
• KNN for classification.
• Reading : R4SL Chapter 12
• Generative methods in R .
• Reading : ISL 4.4, R4SL Chapter 11
• Deadline : Homework 04 Due
• Continued discussion of generative methods. Details of univariate LDA.
• ISL Videos : Linear Discriminant Analysis and Bayes Theorem , Univariate Linear Discriminant Analysis
• Continued discussion of generative methods. Multivariate LDA, QDA, Naive Bayes.
• ISL Videos: Multivariate Linear Discriminant Analysis , Quadratic Discriminant Analysis and Naive Bayes
• Some final thoughts on generative methods. Some recap of classification methods. Some R details.
• Deadline : Homework 05 Due
• Begin discussing Statistical Learning in practice.
• Deadline : None. No homework during quiz week.
• Cross-validation and caret .
• Reading: ISL 5.1, R4SL Chapter 20 , R4SL Chapter 21
• ISL Slides: Resampling
• ISL Videos: Validation Set Approach , k-fold Cross-Validation , Cross-Validation: The Right and Wrong Ways
• More cross-validation and caret .
• Deadline : Homework 06 Due
• Some comments on variable selection.
• Reading: ISL 6.1, R4SL Chapter 22
• ISL Slides: Model Selection
• ISL Videos: Best Subset Selection , Forward Stepwise Selection , Backward Stepwise Selection , Estimating Test Error I , Estimating Test Error II
• Entering the modern age. Introducing regularization.
• Reading: ISL 6.2, R4SL Chapter 24 - Regularization
• ISL Videos: Shrinkage Methods and Ridge Regression , The Lasso , Tuning Parameter Selection
• More on ridge and lasso. Using ridge and lasso in R .
• Reading: ISL 6.2, R4SL Chapter 24 - Regularization , R4SL Chapter 25 - Elastic Net
• Deadline : Homework 07 Due
• Elastic net.
• R4SL: Elastic Net
• Overview: Introduction to trees.
• Reading: ISL 8.1
• ISL Slides: Trees
• Additonal Slides: Part II: Tree-based Methods
• ISL Videos: Decision Trees , Pruning a Decision Tree , Classification Trees and Comparison with Linear Models
• Discussed some finer details of R .
• Deadline : Homework 08 Due
• Deadline : Final Project Group Choice
• Continuation of tree discussion. Introduction to ensemble methods, mostly random forests.
• Reading: ISL 8.2
• R4SL: Ensemble Methods
• Additonal Slides: Part I: Pruning, Bagging, Boosting
• ISL Videos: Bootstrap Aggregation (Bagging) and Random Forests , Boosting and Variable Importance
• Continuation of tree discussion. Introduction to ensemble methods, mostly boosting.
• Extensions of random forests and boosting, in R . Some summary of supervised learning.
• Additional Slides: Supervised Learning Review
• Reading: Extremely Randomized Trees, Ranger, XGBoost [ rmarkdown ]
• Reading: Statistical Modeling: The Two Cultures
• Reading: Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?
• No class. Fall break.
• Deadline : Homework 09 Due
• No class . Consider a group meeting.
• Unsupervised learning. Clustering.
• Reading: ISL 10.1 - 10.3
• R4SL: Unsupervised Learning
• ISL Slides: Unsupervised Learning
• Additional Slides: Unsupervised Learning, Part I, Clustering
• ISL Videos: Unsupervised Learning and Principal Components Analysis , Exploring Principal Components Analysis and Proportion of Variance Explained , K-means Clustering , Hierarchical Clustering
• Unsupervised learning. Clustering in R .
• Deadline : Project proposals. No homework is due.
• Unsupervised learning. PCA. Clustering again.
• Additional Slides: Unsupervised Learning, Part II, PCA
• No class. Office hours 8 - 10 at David’s office. Work on projects!
• Discussion of graduate student project results. Thoughts on keeping up to date with data science and machine learning.
• Reading: Some Machine Learning and Data Science Resources
• Deadline : Homework 10 Due
• No class. Finals!
• Deadline : Final Project Report
• Deadline : Final Project Peer Review

Homework 00

• Due: Friday, September 8
• Assignment: [ html ] [ pdf ] [ zip ]
• Solution: [ zip ]

Homework 01

• Due: Friday, September 15

Homework 02

• Due: Friday, September 22

Homework 03

Homework 04.

• Due: Friday, October 6

Homework 05

• Due: Friday, October 13

Homework 06

• Due: Friday, October 27

Homework 07

• Due: Friday, November 3

Homework 08

• Due: Friday, November 10

Homework 09

• Due: Monday, November 20

Homework 10

• Due: Wednesday, December 13
• Date: Wednesday, October 18
• Review: [ In-Class Practice Probelms ]
• Date: Wednesday, December 6

Group Final Project

• Group Choice - Friday, November 10, 11:59 PM
• Analysis Proposal - Friday, December 1, 11:59 PM
• Report Template
• Peer Evaluation - Thursday, December 21, 10:00 PM

Graduate Student Project

• Autograder - Saturday, December 9, 11:59 PM
• Report - Saturday, December 9, 11:59 PM

Synopsis (摘要)

This course is open to graduates and senior undergraduates in applied mathematics, statistics, and engineering who are interested in learning from data. It covers hot topics in statistical learning, also known as machine learning, featured with various in-class projects in computer vision, pattern recognition, computational advertisement, bioinformatics, and social networks, etc. An emphasis this year is on deep learning with convolutional neural networks. Prerequisite: linear algebra, basic probability and multivariate statistics, convex optimization; familiarity with R, Matlab, and/or Python, Torch for deep learning, etc.

Reference (参考教材)

An Introduction to Statistical Learning, with applications in R. By James, Witten, Hastie, and Tibshirani

ISLR-python, By Jordi Warmenhoven .

ISLR-Python: Labs and Applied, by Matt Caudill .

The Elements of Statistical Learning. 2nd Ed. By Hastie, Tibshirani, and Friedman

statlearning-notebooks , by Sujit Pal, Python implementations of the R labs for the StatLearning: Statistical Learning online course from Stanford taught by Profs Trevor Hastie and Rob Tibshirani.

Instructors:

Time and venue:.

TuTh 4:30-5:50pm Rm4504 (Lift 25/26), Academic Bldg Piazza discussion forum: sign-up link

Homework and Projects:

Weekly homeworks, monthly mini-projects, and a final major project. No final exam. For 3-project plan, homework and projects will be counted in grading by 20-20-20-40 in percentage.

Grading scheme: [ description ]

Teaching Assistant (助教):

Mr. ZHU, Weizhi, Email: statml.hw (add "AT gmail DOT com" afterwards)

Tutorial Material

Schedule (时间表)

• [ slides in pdf ]
• Homework 1 [pdf] . Deadline: 09/28/2015, Monday. Mark on the head of your homework: Name - Student ID .
• Homework 2 [pdf] . Deadline: 10/12/2015, Monday. Mark on the head of your homework: Name - Student ID .
• Project 1 [pdf] . Deadline: 10/12/2015, Monday. Team work with no more than FIVE (5) collaborators.
• Jiechao XIONG, A Dynamic Approach to Variable Selection
• Homework 3 [pdf] . Deadline: 10/19/2015, Monday. Mark on the head of your homework: Name - Student ID .
• Homework 4 [pdf] . Deadline: 10/26/2015, Monday. Mark on the head of your homework: Name - Student ID .
• Homework 5 [pdf] . Deadline: 11/02/2015, Monday. Mark on the head of your homework: Name - Student ID .
• Xuening ZHU, Network Vector Regression
• Homework 6 [pdf] . Deadline: 11/09/2015, Monday. Mark on the head of your homework: Name - Student ID .

Datasets (to-be-updated)

• [Animal Sleep Data] Animal species sleeping hours vs. other features
• [Anzhen Heart Data] Heart Operation Effect Prediction , provided by Dr. Jinwen Wang, Anzhen Hospital
• [Beer Data] 877 beers dataset , provided by Mr. Richard Sun, Shanghai
• [Crime Data] Crime rates in 59 US cities during 1970-1992
• [Real-Time-Bidding Algorithm Competition Data] Contest Website
• [红楼梦人物事件矩阵] a 376-by-475 matrix (374-by-475 updated by WAN, Mengting) for character-event appearance in A Dream of Red Mansion (Xueqin Cao) [374 Characters.txt (for R/read.table)] [HongLouMeng374.csv] [HongLouMeng376.xls] [.mat] [readme.m]

• [Keywords Pricing] Keywords and profit index in paid search advertising, by Hansheng Wang (Guanghua, PKU). [readme.txt] [data in csv]
• [Radon Data] Radon measurements of 12,687 houses in US
• [Wells Data] Switch unsafe wells for arsenic pollution in Bangladesh
• to-be-done...

Statistical Learning

Course material for bst 263, general information.

• An Introduction to Statistical Learning , by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani.
• The Elements of Statistical Learning , by Trevor Hastie, Robert Tibshirani, and Jerome Friedman.

Lecture notes

• 1. Introduction (Course overview, Choosing among methods)
• 2. Probability and linear algebra basics
• 3. Measuring performance (K-nearest neighbors, MSE, Bias-variance, Classification error rate, Bayes optimal)
• knn.r (R code for KNN regression, MSE, Bias-variance tradeoff)
• knn-classifier.r (R code for KNN classifier, Error rate, Bayes optimal classifier)
• 4. Lab on KNN and measuring performance
• 5. Linear regression (Probabilistic model, Basis functions, Estimation, Uncertainty quantification)
• 6. Lab on Linear regression
• 7. Classification (Loss functions, Confusion matrix, ROC curve, Logistic regression, LDA/QDA)
• classification.r (R code for classification topics)
• 8. Lab on Classification
• 9. Cross-validation (k-fold CV, Choosing model settings with CV, Choosing # of folds)
• cv.r (R code for cross-validation topics)
• 10. Lab on Cross-validation
• 11. Penalized regression (Subset selection, Model selection, Ridge, Lasso, Elastic net)
• 12. Lab on Penalized regression
• 13. Principal components analysis (Intuition, Covariance method, SVD method, Principal components regression)
• 14. Lab on PCA
• (In progress)

Homework assignments

• Homework 1 (Probability and linear algebra basics)
• Homework 2 (Measuring performance, Bias-variance)
• Homework 3 (Linear regression)
• Homework 4 (Classification)
• Homework 5 (Cross-validation)
• Homework 6 (Penalized regression)
• Midterm solutions

An Introduction to Statistical Learning

Exercise solutions in r, 1 introduction.

This bookdown document provides solutions for exercises in the book “An Introduction to Statistical Learning” by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani.

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Introduction to Statistics

Table of Contents

Course contents.

• About This Course
• Course Contents at a Glance
• Learning Outcomes

Faculty Resources

• OHM Assessments
• I Need Help

Module 1: Sampling and Data

• Introduction to Sampling and Data
• Definitions of Statistics, Probability, and Key Terms
• Sampling and Data
• Frequency, Frequency Tables, and Levels of Measurement
• Experimental Design and Ethics
• Section Exercises
• Answers to Selected Exercises

Module 2: Descriptive Statistics

• Introduction to Descriptive Statistics
• Stem-and-Leaf Graphs (Stemplots)
• Histograms, Frequency Polygons, and Time Series Graphs
• Measures of the Location of the Data
• Measures of the Center of the Data
• Skewness and the Mean, Median, and Mode
• Measures of the Spread of Data
• When to use each measure of Central Tendency

Module 3: Probability

• Introduction to Probability Topics
• The Terminology of Probability
• Independent and Mutually Exclusive Events
• Two Basic Rules of Probability
• Contingency Tables
• Tree and Venn Diagrams

Module 4: Discrete Random Variables

• Introduction to Discrete Random Variables
• Probability Distribution Function (PDF) for a Discrete Random Variable
• Mean or Expected Value and Standard Deviation
• Binomial Distribution
• Geometric Distribution
• Poisson Distribution

Module 5: Continuous Random Variables

• Introduction to Continuous Random Variables
• Continuous Probability Functions
• The Uniform Distribution
• The Exponential Distribution

Module 6: Normal Distribution

• Introduction to the Normal Distribution
• The Standard Normal Distribution
• Using the Normal Distribution

Module 7: The Central Limit Theorem

• Introduction to the Central Limit Theorem
• The Central Limit Theorem for Sample Means (Averages)
• The Central Limit Theorem for Sums
• Using the Central Limit Theorem

Module 8: Confidence Intervals

• Introduction to Confidence Intervals
• A Single Population Mean using the Normal Distribution
• A Single Population Mean using Student's t Distribution
• A Population Proportion

Module 9: Hypothesis Testing With One Sample

• Introduction to Hypothesis Testing with One Sample
• Null and Alternative Hypotheses
• Outcomes and the Type I and Type II Errors
• Distribution Needed for Hypothesis Testing
• Rare Events, the Sample, Decision and Conclusion
• Additional Information and Full Hypothesis Test Examples

Module 10: Hypothesis Testing With Two Samples

• Introduction to Hypothesis Testing with Two Samples
• Two Population Means with Unknown Standard Deviations
• Two Population Means with Known Standard Deviations
• Comparing Two Independent Population Proportions
• Matched or Paired Samples

Module 11: The Chi Square Distribution

• Introduction to The Chi-Square Distribution
• Facts About the Chi-Square Distribution
• Goodness-of-Fit Test
• Test of Independence
• Test for Homogeneity
• Comparison of the Chi-Square Tests
• Test of a Single Variance

Module 12: Linear Regression and Correlation

• Introduction to Linear Regression and Correlation
• Linear Equations
• Scatter Plots
• The Regression Equation
• Testing the Significance of the Correlation Coefficient

Module 13: F-Distribution and One-Way ANOVA

• Introduction to F Distribution and One-Way ANOVA
• One-Way ANOVA
• The F Distribution and the F-Ratio
• Facts about the F Distribution
• Test of Two Variances
• Relationships in an ANOVA Table

Module 14: Multiple and Logistic Regression

• Introduction to Multiple and Logistic Regression
• Model Selection
• Checking Model Assumptions Using Graphs
• Introduction to Logistic Regression
• Appendix A: Review Exercises (Ch 3-13)
• Appendix A-1: Solutions to Review Exercises (Ch 3-13)
• Appendix B: Practice Tests (1-4) and Final Exams
• Appendix C: Data Sets
• Appendix D: Group and Partner Projects
• Appendix E: Solution Sheets
• Appendix F: Mathematical Phrases, Symbols, and Formulas
• Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators
• Appendix H: Tables

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Statistics and Probability Worksheets

Welcome to the statistics and probability page at Math-Drills.com where there is a 100% chance of learning something! This page includes Statistics worksheets including collecting and organizing data, measures of central tendency (mean, median, mode and range) and probability.

Students spend their lives collecting, organizing, and analyzing data, so why not teach them a few skills to help them on their way. Data management is probably best done on authentic tasks that will engage students in their own learning. They can collect their own data on topics that interest them. For example, have you ever wondered if everyone shares the same taste in music as you? Perhaps a survey, a couple of graphs and a few analysis sentences will give you an idea.

Statistics has applications in many different fields of study. Budding scientists, stock market brokers, marketing geniuses, and many other pursuits will involve managing data on a daily basis. Teaching students critical thinking skills related to analyzing data they are presented will enable them to make crucial and informed decisions throughout their lives.

Probability is a topic in math that crosses over to several other skills such as decimals, percents, multiplication, division, fractions, etc. Probability worksheets will help students to practice all of these skills with a chance of success!

Most Popular Statistics and Probability Worksheets this Week

Mean, Median, Mode and Range Worksheets

Calculating the mean, median, mode and range are staples of the upper elementary math curriculum. Here you will find worksheets for practicing the calculation of mean, median, mode and range. In case you're not familiar with these concepts, here is how to calculate each one. To calculate the mean, add all of the numbers in the set together and divide that sum by the number of numbers in the set. To calculate the median, first arrange the numbers in order, then locate the middle number. In sets where there are an even number of numbers, calculate the mean of the two middle numbers. To calculate the mode, look for numbers that repeat. If there is only one of each number, the set has no mode. If there are doubles of two different numbers and there are more numbers in the set, the set has two modes. If there are triples of three different numbers and there are more numbers in the set, the set has three modes, and so on. The range is calculated by subtracting the least number from the greatest number.

Note that all of the measures of central tendency are included on each page, but you don't need to assign them all if you aren't working on them all. If you're only working on mean, only assign students to calculate the mean.

In order to determine the median, it is necessary to have your numbers sorted. It is also helpful in determining the mode and range. To expedite the process, these first worksheets include the lists of numbers already sorted.

• Calculating Mean, Median, Mode and Range from Sorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Normally, data does not come in a sorted list, so these worksheets are a little more realistic. To find some of the statistics, it will be easier for students to put the numbers in order first.

• Calculating Mean, Median, Mode and Range from Unsorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Collecting and Organizing Data

Teaching students how to collect and organize data enables them to develop skills that will enable them to study topics in statistics with more confidence and deeper understanding.

• Constructing Line Plots from Small Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Smaller Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Smaller Numbers (Small Data Set) Construct Line Plots with Larger Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Larger Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Larger Numbers (Small Data Set)
• Constructing Line Plots from Larger Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided Construct Line Plots with Smaller Numbers and Lines Only Provided Construct Line Plots with Smaller Numbers Construct Line Plots with Larger Numbers and Lines with Ticks Provided Construct Line Plots with Larger Numbers and Lines Only Provided Construct Line Plots with Larger Numbers

Interpreting and Analyzing Data

Answering questions about graphs and other data helps students build critical thinking skills. Standard questions include determining the minimum, maximum, range, count, median, mode, and mean.

• Answering Questions About Stem-and-Leaf Plots Stem-and-Leaf Plots with about 25 data points Stem-and-Leaf Plots with about 50 data points Stem-and-Leaf Plots with about 100 data points
• Answering Questions About Line Plots Line Plots with Smaller Data Sets and Smaller Numbers Line Plots with Smaller Data Sets and Larger Numbers Line Plots with Larger Data Sets and Smaller Numbers Line Plots with Larger Data Sets and Larger Numbers
• Answering Questions About Broken-Line Graphs Answer Questions About Broken-Line Graphs
• Answering Questions About Circle Graphs Circle Graph Questions (Color Version) Circle Graph Questions (Black and White Version) Circle Graphs No Questions (Color Version) Circle Graphs No Questions (Black and White Version)
• Answering Questions About Pictographs Answer Questions About Pictographs

Probability Worksheets

• Calculating Probabilities with Dice Sum of Two Dice Probabilities Sum of Two Dice Probabilities (with table)

Spinners can be used for probability experiments or for theoretical probability. Students should intuitively know that a number that is more common on a spinner will come up more often. Spinning 100 or more times and tallying the results should get them close to the theoretical probability. The more sections there are, the more spins will be needed.

• Calculating Probabilities with Number Spinners Number Spinner Probability (4 Sections) Number Spinner Probability (5 Sections) Number Spinner Probability (6 Sections) Number Spinner Probability (7 Sections) Number Spinner Probability (8 Sections) Number Spinner Probability (9 Sections) Number Spinner Probability (10 Sections) Number Spinner Probability (11 Sections) Number Spinner Probability (12 Sections)

Non-numerical spinners can be used for experimental or theoretical probability. There are basic questions on every version with a couple extra questions on the A and B versions. Teachers and students can make up other questions to ask and conduct experiments or calculate the theoretical probability. Print copies for everyone or display on an interactive white board.

• Probability with Single-Event Spinners Animal Spinner Probability ( 4 Sections) Animal Spinner Probability ( 5 Sections) Animal Spinner Probability ( 10 Sections) Letter Spinner Probability ( 4 Sections) Letter Spinner Probability ( 5 Sections) Letter Spinner Probability ( 10 Sections) Color Spinner Probability ( 4 Sections) Color Spinner Probability ( 5 Sections) Color Spinner Probability ( 10 Sections)
• Probability with Multi-Event Spinners Animal/Letter Combined Spinner Probability ( 4 Sections) Animal/Letter Combined Spinner Probability ( 5 Sections) Animal/Letter Combined Spinner Probability ( 10 Sections) Animal/Letter/Color Combined Spinner Probability ( 4 Sections) Animal/Letter/Color Combined Spinner Probability ( 5 Sections) Animal/Letter/Color Combined Spinner Probability ( 10 Sections)

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