MATH 214 (NOTES) Math 214 Al Nosedal. Department of Mathematics Indiana University of Pennsylvania. MATH 214 (NOTES) p. 1/3
|
|
- Edith Reynolds
- 6 years ago
- Views:
Transcription
1 MATH 214 (NOTES) Math 214 Al Nosedal Department of Mathematics Indiana University of Pennsylvania MATH 214 (NOTES) p. 1/3
2 CHAPTER 1 DATA AND STATISTICS MATH 214 (NOTES) p. 2/3
3 Definitions. Statistics is defined as the science of collecting, analyzing, presenting, and interpreting data. Data are the facts and figures collected, analyzed, and summarized for presentation and interpretation. Elements are the entities on which data are collected. A variable is a characteristic of interest for the elements. Data can also be classified as either qualitative or quantitative. Qualitative data include labels or names used to identify an attribute of each element. Quantitative data require numeric values that indicate how much or how many. MATH 214 (NOTES) p. 3/3
4 Descriptive Statistics Most of the statistical information in newspapers, magazines, company reports, and other publications consists of data that are summarized and presented in a form that is easy for the reader to understand. Such summaries of data, which may be tabular, graphical, or numerical, are referred to as descriptive statistics. MATH 214 (NOTES) p. 4/3
5 Statistical Inference Many situations require information about a large group of elements. But, because of time, cost, and other considerations, data can be collected from only a small portion of the group. The larger group of elements in a particular study is called the population, and the smaller group is called the sample. As one of its major contributions, statistics uses data from a sample to make estimates and test hypotheses about the characteristics of a population through a process referred to as statistical inference. MATH 214 (NOTES) p. 5/3
6 CHAPTER 2 DESCRIPTIVE STATISTICS: TABULAR AND GRAPHICAL PRESENTATIONS MATH 214 (NOTES) p. 6/3
7 Summarizing Qualitative Data Frequency distribution. A frequency distribution is a tabular summary of data showing the number (frequency) of items in each of several nonoverlapping classes. Relative frequency of a class = Frequency of the class n where n represents the total number of observations. MATH 214 (NOTES) p. 7/3
8 Bar graphs and pie charts A bar graph, is a graphical device for depicting qualitative data summarized in a frequency, relative frequency, or percent frequency distribution. On one axis of the graph, we specify the labels that are used for the classes (categories). A frequency, relative frequency, or percent frequency scale can be used for the other axis of the graph. The pie chart provides another graphical device for presenting relative frequency and percent frequency distributions for qualitative data. MATH 214 (NOTES) p. 8/3
9 Summarizing Quantitative Data A common graphical presentation of quantitative data is a histogram. This graphical summary can be prepared for data previously summarized in either a frequency, relative frequency, or percent frequency distribution. A histogram is constructed by placing the variables of interest on the horizontal axis and the frequency, relative frequency, or percent frequency on the vertical axis. MATH 214 (NOTES) p. 9/3
10 Exercise (page 40) 11. Consider the following data a. Develop a frequency distribution using classes of 12-14, 15-17, 18-20, 21-23, and b. Develop a relative frequency distribution and a percent frequency distribution using the classes in part (a). c. Make a histogram. MATH 214 (NOTES) p. 10/3
11 Solution class freq. relative freq. percent freq / / / / / MATH 214 (NOTES) p. 11/3
12 Describing distributions with numbers How much do people with a bachelor s degree (but no higher degree) earn? Here are the incomes of 15 such people, chosen at random by the Census Bureau in March 2002 and asked how much they earned in Most people reported their incomes to the nearest thousand dollars, so we have rounded their responses to thousands of dollars How could we find the "typical" income for people with a bachelor s degree (but no higher degree)? MATH 214 (NOTES) p. 12/3
13 Describing distributions with numbers How much do people with a bachelor s degree (but no higher degree) earn? Here are the incomes of 15 such people, chosen at random by the Census Bureau in March 2002 and asked how much they earned in Most people reported their incomes to the nearest thousand dollars, so we have rounded their responses to thousands of dollars How could we find the "typical" income for people with a bachelor s degree (but no higher degree)? MATH 214 (NOTES) p. 12/3
14 CHAPTER 3 DESCRIPTIVE STATISTICS: NUMERICAL MEASURES MATH 214 (NOTES) p. 13/3
15 Measuring center: the mean The most common measure of center is the ordinary arithmetic average, or mean. To find the mean of a set of observations, add their values and divide by the number of observations. If the n observations are x 1,x 2,...,x n, their mean is (1) or in more compact notation, x = x 1 + x x n n (2) x = 1 n n x i i=1 MATH 214 (NOTES) p. 14/3
16 Measuring center: the median The median M is the midpoint of a distribution, the number such that half the observations are smaller and the other half are larger. To find the median of the distribution: Arrange all observations in order of size, from smallest to largest. If the number of observations n is odd, the median M is the center observation in the ordered list. Find the location of the median by counting n+1 2 observations up from the bottom of the list. MATH 214 (NOTES) p. 15/3
17 Measuring center: the median (cont.) If the number of observations n is even, the median M is the mean of the two center observations in the ordered list. Find the location of the median by counting n+1 2 observations up from the bottom of the list. MATH 214 (NOTES) p. 16/3
18 The quartiles Q 1 and Q 3 To calculate the quartiles: Arrange the observations in increasing order and locate the median M in the ordered list of observations. The first quartile Q 1 is the median of the observations whose position in the ordered list is to the left of the location of the overall median The third quartile Q 3 is the median of the observations whose position in the ordered list is to the right of the location of the overall median MATH 214 (NOTES) p. 17/3
19 Side-by-side Boxplots Example. Here are the numbers of home runs that Babe Ruth hit in his 15 years with the New York Yankees, 1920 to 1934: Another home run hitter is Mark McGwire, who retired after the 2001 season. Here are McGwire s home run counts for 1987 to 2001: Find the five-number summaries and make side-by-side boxplots to compare these two home run hitters. What do your plots show? MATH 214 (NOTES) p. 18/3
20 Measures of association between 2 variables Covariance (sample covariance) You can compute the covariance, S XY using the following formula: (3) S XY = n i=1 x iy i n 1 n xȳ n 1 MATH 214 (NOTES) p. 19/3
21 Probability: Colors of M & M s If you draw an M & M candy at random from a bag of the candies, the candy you draw will have one of the seven colors. The probability of drawing each color depends on the proportion of each color among all candies made. Here is the distribution for milk chocolate M & M s: Color Purple Yellow Red Probability Color Orange Brown Green Blue Probability ? MATH 214 (NOTES) p. 20/3
22 Colors of M & M s (cont.) a) What must be the probability of drawing a blue candy? b) What is the probability that you do not draw a brown candy? c) What is the probability that the candy you draw is either yellow, orange, or red? MATH 214 (NOTES) p. 21/3
23 Conditional probability Problem. Josh and Al are avid tennis players and they enjoy playing matches against each other. They do, however, have one difference of opinion on the court. Al likes to have a nice long warm-up session at the start where they hit the ball back and forth and back and forth. Josh s ideal warm-up is to bend at the waist to tie his sneakers and to adjust his shorts. Al thinks that when they rush through the warm-up, he doesn t play as well. MATH 214 (NOTES) p. 22/3
24 Conditional probability (cont.) The following table shows the outcomes of their last 20 matches, along with the type of warm-up before they started keeping score. Does the type of warm-up have an influence on the outcome of a match? Warm-up time Al wins Josh wins Total Less than 10 min min. or more Total MATH 214 (NOTES) p. 23/3
25 CHAPTER 7 SAMPLING DISTRIBUTIONS MATH 214 (NOTES) p. 24/3
26 Example A couple plans to have three children. There are 8 possible arrangements of girls and boys. For example, GGB means the first two children are girls and the third child is a boy. All 8 arrangements are (approximately) equally likely. a) Write down all 8 arrangements of the sexes of three children. What is the probability of any one of these arrangements? MATH 214 (NOTES) p. 25/3
27 Example (cont.) b) Let X be the number of girls the couple has. What is the probability that X = 2? c) Starting from your work in a), find the distribution of X. That is, what values can X take, and what are the probabilities for each value? MATH 214 (NOTES) p. 26/3
28 Problem We are interested in estimating the average number of cars per household in a little town call Statstown. Let X represent the number of cars in a house picked at random. God knows that X has a Binomial distribution with n = 4 and p = 0.5. Suppose that we can only afford a sample of size 4 and that we are going to use this sample to estimate that population average. MATH 214 (NOTES) p. 27/3
29 Problem (cont.) What we are going to do next is called a simulation. First, we will draw a lot of random samples coming from a Binomial Distribution with n = 4 and p = 0.5. Then we will make a histogram for all the x s corresponding to our samples. We are going to do this do see what the histogram of x looks like. This will give us an idea of what to expect in a similar situation. MATH 214 (NOTES) p. 28/3
30 Central Limit Theorem Draw a random sample of size n from any population with mean µ and finite standard deviation σ. When n is large, the sampling distribution of the sample mean x is approximately Normal: (4) x is approximately N(µ, σ n ) MATH 214 (NOTES) p. 29/3
31 Example The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not Normal. a) Let x be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution of x according to the central limit theorem? MATH 214 (NOTES) p. 30/3
32 Example (cont.) b) What is the approximate probability that x is less than 2? c) What is the approximate probability that there are fewer than 100 accidents at the intersection in a year? (Hint: Restate this event in terms of x) MATH 214 (NOTES) p. 31/3
33 CHAPTER 9 HYPOTHESIS TESTS MATH 214 (NOTES) p. 32/3
34 Do you want to become a millionaire? Let s say that one of you is invited to this popular show. As you probably know, you have to answer a series of multiple choice questions and there are four possible answers to each question. Perhaps you also have seen that if you don t know the answer to a question you could either "jump the question" or you could "ask the audience". Suppose that you run into a question for which you don t know the answer with certainty and you decide to "ask the audience". Let s say that you initially believe that the right answer is A. Then you ask the audience and only 2% of the audience shares your opinion. What would you do? Change your initial belief or reject it? MATH 214 (NOTES) p. 33/3
35 TO BE CONTINUED... MATH 214 (NOTES) p. 34/3
MATH 214 (NOTES) Math 214 Al Nosedal. Department of Mathematics Indiana University of Pennsylvania. MATH 214 (NOTES) p. 1/11
MATH 214 (NOTES) Math 214 Al Nosedal Department of Mathematics Indiana University of Pennsylvania MATH 214 (NOTES) p. 1/11 CHAPTER 6 CONTINUOUS PROBABILITY DISTRIBUTIONS MATH 214 (NOTES) p. 2/11 Simple
More informationWhat is Statistics? 13.1 What is Statistics? Statistics
13.1 What is Statistics? What is Statistics? The collection of all outcomes, responses, measurements, or counts that are of interest. A portion or subset of the population. Statistics Is the science of
More informationFrequencies. Chapter 2. Descriptive statistics and charts
An analyst usually does not concentrate on each individual data values but would like to have a whole picture of how the variables distributed. In this chapter, we will introduce some tools to tabulate
More informationChapter 5. Describing Distributions Numerically. Finding the Center: The Median. Spread: Home on the Range. Finding the Center: The Median (cont.
Chapter 5 Describing Distributions Numerically Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide
More informationDistribution of Data and the Empirical Rule
302360_File_B.qxd 7/7/03 7:18 AM Page 1 Distribution of Data and the Empirical Rule 1 Distribution of Data and the Empirical Rule Stem-and-Leaf Diagrams Frequency Distributions and Histograms Normal Distributions
More informationChapter 1 Midterm Review
Name: Class: Date: Chapter 1 Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A survey typically records many variables of interest to the
More informationAlgebra I Module 2 Lessons 1 19
Eureka Math 2015 2016 Algebra I Module 2 Lessons 1 19 Eureka Math, Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced, distributed, modified, sold,
More informationChapter 6. Normal Distributions
Chapter 6 Normal Distributions Understandable Statistics Ninth Edition By Brase and Brase Prepared by Yixun Shi Bloomsburg University of Pennsylvania Edited by José Neville Díaz Caraballo University of
More informationLesson 7: Measuring Variability for Skewed Distributions (Interquartile Range)
: Measuring Variability for Skewed Distributions (Interquartile Range) Exploratory Challenge 1: Skewed Data and its Measure of Center Consider the following scenario. A television game show, Fact or Fiction,
More informationMeasuring Variability for Skewed Distributions
Measuring Variability for Skewed Distributions Skewed Data and its Measure of Center Consider the following scenario. A television game show, Fact or Fiction, was canceled after nine shows. Many people
More informationMath 81 Graphing. Cartesian Coordinate System Plotting Ordered Pairs (x, y) (x is horizontal, y is vertical) center is (0,0) Quadrants:
Math 81 Graphing Cartesian Coordinate System Plotting Ordered Pairs (x, y) (x is horizontal, y is vertical) center is (0,0) Ex 1. Plot and indicate which quadrant they re in. A (0,2) B (3, 5) C (-2, -4)
More informationSTAT 113: Statistics and Society Ellen Gundlach, Purdue University. (Chapters refer to Moore and Notz, Statistics: Concepts and Controversies, 8e)
STAT 113: Statistics and Society Ellen Gundlach, Purdue University (Chapters refer to Moore and Notz, Statistics: Concepts and Controversies, 8e) Learning Objectives for Exam 1: Unit 1, Part 1: Population
More informationChapter 27. Inferences for Regression. Remembering Regression. An Example: Body Fat and Waist Size. Remembering Regression (cont.)
Chapter 27 Inferences for Regression Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 27-1 Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley An
More informationdownload instant at
13 Introductory Statistics (IS) / Elementary Statistics (ES): Chapter 2 Form A Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Classify the
More informationHistograms and Frequency Polygons are statistical graphs used to illustrate frequency distributions.
Number of Families II. Statistical Graphs section 3.2 Histograms and Frequency Polygons are statistical graphs used to illustrate frequency distributions. Example: Construct a histogram for the frequency
More informationChapter 3. Averages and Variation
Chapter 3 Averages and Variation Understandable Statistics Ninth Edition By Brase and Brase Prepared by Yixun Shi Bloomsburg University of Pennsylvania Measures of Central Tendency We use the term average
More informationBox Plots. So that I can: look at large amount of data in condensed form.
LESSON 5 Box Plots LEARNING OBJECTIVES Today I am: creating box plots. So that I can: look at large amount of data in condensed form. I ll know I have it when I can: make observations about the data based
More informationAP Statistics Sampling. Sampling Exercise (adapted from a document from the NCSSM Leadership Institute, July 2000).
AP Statistics Sampling Name Sampling Exercise (adapted from a document from the NCSSM Leadership Institute, July 2000). Problem: A farmer has just cleared a field for corn that can be divided into 100
More informationMATH& 146 Lesson 11. Section 1.6 Categorical Data
MATH& 146 Lesson 11 Section 1.6 Categorical Data 1 Frequency The first step to organizing categorical data is to count the number of data values there are in each category of interest. We can organize
More informationNAA ENHANCING THE QUALITY OF MARKING PROJECT: THE EFFECT OF SAMPLE SIZE ON INCREASED PRECISION IN DETECTING ERRANT MARKING
NAA ENHANCING THE QUALITY OF MARKING PROJECT: THE EFFECT OF SAMPLE SIZE ON INCREASED PRECISION IN DETECTING ERRANT MARKING Mudhaffar Al-Bayatti and Ben Jones February 00 This report was commissioned by
More informationThe One Penny Whiteboard
The One Penny Whiteboard Ongoing, in the moment assessments may be the most powerful tool teachers have for improving student performance. For students to get better at anything, they need lots of quick
More informationWhen do two squares make a new square
45 # THREE SQUARES When do two squares make a new square? Figure This! Can you make a new square from two squares? Hint: Cut two squares from a sheet of paper and tape them together as in the diagram.
More informationEstimating. Proportions with Confidence. Chapter 10. Copyright 2006 Brooks/Cole, a division of Thomson Learning, Inc.
Estimating Chapter 10 Proportions with Confidence Copyright 2006 Brooks/Cole, a division of Thomson Learning, Inc. Principal Idea: Survey 150 randomly selected students and 41% think marijuana should be
More informationCOMP Test on Psychology 320 Check on Mastery of Prerequisites
COMP Test on Psychology 320 Check on Mastery of Prerequisites This test is designed to provide you and your instructor with information on your mastery of the basic content of Psychology 320. The results
More informationLesson 7: Measuring Variability for Skewed Distributions (Interquartile Range)
: Measuring Variability for Skewed Distributions (Interquartile Range) Student Outcomes Students explain why a median is a better description of a typical value for a skewed distribution. Students calculate
More informationDot Plots and Distributions
EXTENSION Dot Plots and Distributions A dot plot is a data representation that uses a number line and x s, dots, or other symbols to show frequency. Dot plots are sometimes called line plots. E X A M P
More informationWhy t? TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson
Math Objectives Students will recognize that when the population standard deviation is unknown, it must be estimated from the sample in order to calculate a standardized test statistic. Students will recognize
More informationObjective: Write on the goal/objective sheet and give a before class rating. Determine the types of graphs appropriate for specific data.
Objective: Write on the goal/objective sheet and give a before class rating. Determine the types of graphs appropriate for specific data. Khan Academy test Tuesday Sept th. NO CALCULATORS allowed. Not
More information9.2 Data Distributions and Outliers
Name Class Date 9.2 Data Distributions and Outliers Essential Question: What statistics are most affected by outliers, and what shapes can data distributions have? Eplore Using Dot Plots to Display Data
More informationChapter 2 Describing Data: Frequency Tables, Frequency Distributions, and
Frequency Chapter 2 - Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation Chapter 2 Describing Data: Frequency Tables, Frequency Distributions, and 1. Pepsi-Cola has a
More informationFull file at
Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) A parcel delivery service lowered its prices and finds that
More informationUNIVERSITY OF MASSACHUSETTS Department of Biostatistics and Epidemiology BioEpi 540W - Introduction to Biostatistics Fall 2002
1 UNIVERSITY OF MASSACHUSETTS Department of Biostatistics and Epidemiology BioEpi 540W - Introduction to Biostatistics Fall 2002 Exercises Unit 2 Descriptive Statistics Tables and Graphs Due: Monday September
More informationT HE M AGIC OF G RAPHS AND S TATISTICS
p01.qxd 10/29/03 9:25 AM Page 1 I T HE M AGIC OF G RAPHS AND S TATISTICS It s hard to get through a day without seeing a graph or chart somewhere, whether you re reading a newspaper or a magazine, watching
More informationSampler Overview. Statistical Demonstration Software Copyright 2007 by Clifford H. Wagner
Sampler Overview Statistical Demonstration Software Copyright 2007 by Clifford H. Wagner (w44@psu.edu) Introduction The philosophy behind Sampler is that students learn mathematics and statistics more
More informationHomework Packet Week #5 All problems with answers or work are examples.
Lesson 8.1 Construct the graphical display for each given data set. Describe the distribution of the data. 1. Construct a box-and-whisker plot to display the number of miles from school that a number of
More informationAP Statistics Sec 5.1: An Exercise in Sampling: The Corn Field
AP Statistics Sec.: An Exercise in Sampling: The Corn Field Name: A farmer has planted a new field for corn. It is a rectangular plot of land with a river that runs along the right side of the field. The
More informationStatistics for Engineers
Statistics for Engineers ChE 4C3 and 6C3 Kevin Dunn, 2013 kevin.dunn@mcmaster.ca http://learnche.mcmaster.ca/4c3 Overall revision number: 19 (January 2013) 1 Copyright, sharing, and attribution notice
More informationd. Could you represent the profit for n copies in other different ways?
Special Topics: U3. L3. Inv 1 Name: Homework: Math XL Unit 3 HW 9/28-10/2 (Due Friday, 10/2, by 11:59 pm) Lesson Target: Write multiple expressions to represent a variable quantity from a real world situation.
More informationTHE USE OF RESAMPLING FOR ESTIMATING CONTROL CHART LIMITS
THE USE OF RESAMPLING FOR ESTIMATING CONTROL CHART LIMITS Draft of paper published in Journal of the Operational Research Society, 50, 651-659, 1999. Michael Wood, Michael Kaye and Nick Capon Management
More informationChapter 2 Notes.notebook. June 21, : Random Samples
2.1: Random Samples Random Sample sample that is representative of the entire population. Each member of the population has an equal chance of being included in the sample. Each sample of the same size
More informationLecture 10: Release the Kraken!
Lecture 10: Release the Kraken! Last time We considered some simple classical probability computations, deriving the socalled binomial distribution -- We used it immediately to derive the mathematical
More informationNETFLIX MOVIE RATING ANALYSIS
NETFLIX MOVIE RATING ANALYSIS Danny Dean EXECUTIVE SUMMARY Perhaps only a few us have wondered whether or not the number words in a movie s title could be linked to its success. You may question the relevance
More informationEXPLORING DISTRIBUTIONS
CHAPTER 2 EXPLORING DISTRIBUTIONS 18 16 14 12 Frequency 1 8 6 4 2 54 56 58 6 62 64 66 68 7 72 74 Female Heights What does the distribution of female heights look like? Statistics gives you the tools to
More informationChapter 4. Displaying Quantitative Data. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Chapter 4 Displaying Quantitative Data Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Dealing With a Lot of Numbers Summarizing the data will help us when we look at large
More informationTutorial 0: Uncertainty in Power and Sample Size Estimation. Acknowledgements:
Tutorial 0: Uncertainty in Power and Sample Size Estimation Anna E. Barón, Keith E. Muller, Sarah M. Kreidler, and Deborah H. Glueck Acknowledgements: The project was supported in large part by the National
More information1/ 19 2/17 3/23 4/23 5/18 Total/100. Please do not write in the spaces above.
1/ 19 2/17 3/23 4/23 5/18 Total/100 Please do not write in the spaces above. Directions: You have 50 minutes in which to complete this exam. Please make sure that you read through this entire exam before
More informationCalculated Percentage = Number of color specific M&M s x 100% Total Number of M&M s (from the same row)
Name: Date: Period: The M&M (not the rapper) Lab Who would have guessed that the idea for M&M s Plain Chocolate Candies was hatched against the backdrop of the Spanish Civil War? Legend has it that, while
More informationMath 7 /Unit 07 Practice Test: Collecting, Displaying and Analyzing Data
Math 7 /Unit 07 Practice Test: Collecting, Displaying and Analyzing Data Name: Date: Define the terms below and give an example. 1. mode 2. range 3. median 4. mean 5. Which data display would be used to
More informationUser Guide. S-Curve Tool
User Guide for S-Curve Tool Version 1.0 (as of 09/12/12) Sponsored by: Naval Center for Cost Analysis (NCCA) Developed by: Technomics, Inc. 201 12 th Street South, Suite 612 Arlington, VA 22202 Points
More informationE X P E R I M E N T 1
E X P E R I M E N T 1 Getting to Know Data Studio Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics, Exp 1: Getting to
More informationReviews of earlier editions
Reviews of earlier editions Statistics in medicine ( 1997 by John Wiley & Sons, Ltd. Statist. Med., 16, 2627Ð2631 (1997) STATISTICS AT SQUARE ONE. Ninth Edition, revised by M. J. Campbell, T. D. V. Swinscow,
More informationHow Large a Sample? CHAPTER 24. Issues in determining sample size
388 Resampling: The New Statistics CHAPTER 24 How Large a Sample? Issues in Determining Sample Size Some Practical Examples Step-Wise Sample-Size Determination Summary Issues in determining sample size
More informationSampling Plans. Sampling Plan - Variable Physical Unit Sample. Sampling Application. Sampling Approach. Universe and Frame Information
Sampling Plan - Variable Physical Unit Sample Sampling Application AUDIT TYPE: REVIEW AREA: SAMPLING OBJECTIVE: Sampling Approach Type of Sampling: Why Used? Check All That Apply: Confidence Level: Desired
More informationJumpstarters for Math
Jumpstarters for Math Short Daily Warm-ups for the Classroom By CINDY BARDEN COPYRIGHT 2005 Mark Twain Media, Inc. ISBN 10-digit: 1-58037-297-X 13-digit: 978-1-58037-297-8 Printing No. CD-404023 Mark Twain
More informationWestern Statistics Teachers Conference 2000
Teaching Using Ratios 13 Mar, 2000 Teaching Using Ratios 1 Western Statistics Teachers Conference 2000 March 13, 2000 MILO SCHIELD Augsburg College www.augsburg.edu/ppages/schield schield@augsburg.edu
More informationGraphical Displays of Univariate Data
. Chapter 1 Graphical Displays of Univariate Data Topic 2 covers sorting data and constructing Stemplots and Dotplots, Topic 3 Histograms, and Topic 4 Frequency Plots. (Note: Boxplots are a graphical display
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level *0192736882* STATISTICS 4040/12 Paper 1 October/November 2013 Candidates answer on the question paper.
More informationCongratulations to the Bureau of Labor Statistics for Creating an Excellent Graph By Jeffrey A. Shaffer 12/16/2011
Congratulations to the Bureau of Labor Statistics for Creating an Excellent Graph By Jeffrey A. Shaffer 12/16/2011 The Bureau of Labor Statistics (BLS) has published some really bad graphs and maps over
More informationN12/5/MATSD/SP2/ENG/TZ0/XX. mathematical STUDIES. Wednesday 7 November 2012 (morning) 1 hour 30 minutes. instructions to candidates
88127402 mathematical STUDIES STANDARD level Paper 2 Wednesday 7 November 2012 (morning) 1 hour 30 minutes instructions to candidates Do not open this examination paper until instructed to do so. A graphic
More informationUse black ink or black ball-point pen. Pencil should only be used for drawing. *
General Certificate of Education June 2009 Advanced Subsidiary Examination MATHEMATICS Unit Statistics 1B MS/SS1B STATISTICS Unit Statistics 1B Wednesday 20 May 2009 1.30 pm to 3.00 pm For this paper you
More informationBlueline, Linefree, Accuracy Ratio, & Moving Absolute Mean Ratio Charts
INTRODUCTION This instruction manual describes for users of the Excel Standard Celeration Template(s) the features of each page or worksheet in the template, allowing the user to set up and generate charts
More information11, 6, 8, 7, 7, 6, 9, 11, 9
1. The Jackson Middle School cross country team is making a box plot of the time it takes each person on the team to run a mile, rounded to the nearest minute. The times are shown below. 11, 6, 8, 7, 7,
More informationVisual Encoding Design
CSE 442 - Data Visualization Visual Encoding Design Jeffrey Heer University of Washington A Design Space of Visual Encodings Mapping Data to Visual Variables Assign data fields (e.g., with N, O, Q types)
More informationForce & Motion 4-5: ArithMachines
Force & Motion 4-5: ArithMachines Physical Science Comes Alive: Exploring Things that Go G. Benenson & J. Neujahr City Technology CCNY 212 650 8389 Overview Introduction In ArithMachines students develop
More informationRelationships Between Quantitative Variables
Chapter 5 Relationships Between Quantitative Variables Three Tools we will use Scatterplot, a two-dimensional graph of data values Correlation, a statistic that measures the strength and direction of a
More informationEstimation of inter-rater reliability
Estimation of inter-rater reliability January 2013 Note: This report is best printed in colour so that the graphs are clear. Vikas Dhawan & Tom Bramley ARD Research Division Cambridge Assessment Ofqual/13/5260
More informationComparing Distributions of Univariate Data
. Chapter 3 Comparing Distributions of Univariate Data Topic 9 covers comparing data and constructing multiple univariate plots. Topic 9 Multiple Univariate Plots Example: Building heights in Philadelphia,
More informationNotes Unit 8: Dot Plots and Histograms
Notes Unit : Dot Plots and Histograms I. Dot Plots A. Definition A data display in which each data item is shown as a dot above a number line In a dot plot a cluster shows where a group of data points
More informationBootstrap Methods in Regression Questions Have you had a chance to try any of this? Any of the review questions?
ICPSR Blalock Lectures, 2003 Bootstrap Resampling Robert Stine Lecture 3 Bootstrap Methods in Regression Questions Have you had a chance to try any of this? Any of the review questions? Getting class notes
More informationMore About Regression
Regression Line for the Sample Chapter 14 More About Regression is spoken as y-hat, and it is also referred to either as predicted y or estimated y. b 0 is the intercept of the straight line. The intercept
More information1. MORTALITY AT ADVANCED AGES IN SPAIN MARIA DELS ÀNGELS FELIPE CHECA 1 COL LEGI D ACTUARIS DE CATALUNYA
1. MORTALITY AT ADVANCED AGES IN SPAIN BY MARIA DELS ÀNGELS FELIPE CHECA 1 COL LEGI D ACTUARIS DE CATALUNYA 2. ABSTRACT We have compiled national data for people over the age of 100 in Spain. We have faced
More information*On-Line appendix for non-tables, by Margo Schlanger
*Anne Morrison Piehl and Margo Schlanger, *Determinants of Civil Rights Filings in Federal District Court by Jail and Pris on Inmates, *1 Journal of Empirical Legal Studies 79 (March 2004) *On-Line appendix
More informationFor the SIA. Applications of Propagation Delay & Skew tool. Introduction. Theory of Operation. Propagation Delay & Skew Tool
For the SIA Applications of Propagation Delay & Skew tool Determine signal propagation delay time Detect skewing between channels on rising or falling edges Create histograms of different edge relationships
More informationAnswers. Chapter 9 A Puzzle Time MUSSELS. 9.1 Practice A. Technology Connection. 9.1 Start Thinking! 9.1 Warm Up. 9.1 Start Thinking!
. Puzzle Time MUSSELS Technolog Connection.. 7.... in. Chapter 9 9. Start Thinking! For use before Activit 9. Number of shoes x Person 9. Warm Up For use before Activit 9.. 9. Start Thinking! For use before
More informationRelationships. Between Quantitative Variables. Chapter 5. Copyright 2006 Brooks/Cole, a division of Thomson Learning, Inc.
Relationships Chapter 5 Between Quantitative Variables Copyright 2006 Brooks/Cole, a division of Thomson Learning, Inc. Three Tools we will use Scatterplot, a two-dimensional graph of data values Correlation,
More informationTHE MONTY HALL PROBLEM
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln MAT Exam Expository Papers Math in the Middle Institute Partnership 7-2009 THE MONTY HALL PROBLEM Brian Johnson University
More informationProblem Points Score USE YOUR TIME WISELY USE CLOSEST DF AVAILABLE IN TABLE SHOW YOUR WORK TO RECEIVE PARTIAL CREDIT
Stat 514 EXAM I Stat 514 Name (6 pts) Problem Points Score 1 32 2 30 3 32 USE YOUR TIME WISELY USE CLOSEST DF AVAILABLE IN TABLE SHOW YOUR WORK TO RECEIVE PARTIAL CREDIT WRITE LEGIBLY. ANYTHING UNREADABLE
More informationMultiple-point simulation of multiple categories Part 1. Testing against multiple truncation of a Gaussian field
Multiple-point simulation of multiple categories Part 1. Testing against multiple truncation of a Gaussian field Tuanfeng Zhang November, 2001 Abstract Multiple-point simulation of multiple categories
More informationChapter 7 Probability
Chapter 7 Probability Copyright 2006 Brooks/Cole, a division of Thomson Learning, Inc. 7.1 Random Circumstances Random circumstance is one in which the outcome is unpredictable. Case Study 1.1 Alicia Has
More informationRelease Year Prediction for Songs
Release Year Prediction for Songs [CSE 258 Assignment 2] Ruyu Tan University of California San Diego PID: A53099216 rut003@ucsd.edu Jiaying Liu University of California San Diego PID: A53107720 jil672@ucsd.edu
More informationAnalysis of data from the pilot exercise to develop bibliometric indicators for the REF
February 2011/03 Issues paper This report is for information This analysis aimed to evaluate what the effect would be of using citation scores in the Research Excellence Framework (REF) for staff with
More informationSTAT 250: Introduction to Biostatistics LAB 6
STAT 250: Introduction to Biostatistics LAB 6 Dr. Kari Lock Morgan Sampling Distributions In this lab, we ll explore sampling distributions using StatKey: www.lock5stat.com/statkey. We ll be using StatKey,
More informationMeasurement User Guide
N4906 91040 Measurement User Guide The Serial BERT offers several different kinds of advanced measurements for various purposes: DUT Output Timing/Jitter This type of measurement is used to measure the
More informationSection 2.1 How Do We Measure Speed?
Section.1 How Do We Measure Speed? 1. (a) Given to the right is the graph of the position of a runner as a function of time. Use the graph to complete each of the following. d (feet) 40 30 0 10 Time Interval
More informationTI-Inspire manual 1. Real old version. This version works well but is not as convenient entering letter
TI-Inspire manual 1 Newest version Older version Real old version This version works well but is not as convenient entering letter Instructions TI-Inspire manual 1 General Introduction Ti-Inspire for statistics
More informationTelephone calls and the Brontosaurus Adam Atkinson
Telephone calls and the Brontosaurus Adam Atkinson (ghira@mistral.co.uk) This article provides more detail than my talk at GG with the same title. I am occasionally asked questions along the lines of When
More informationConfidence Intervals for Radio Ratings Estimators
Social Statistics Section JSM 009 Confidence Intervals for Radio Ratings Estimators Richard Griffiths 1 1 Arbitron, Inc., 9705 Patuxent Woods Drive, Columbia, MD 1046 Abstract Arbitron s current method
More informationCancer in females. Visual Display of (Public Health) Data - Theory and Practice. Michael C. Samuel, Dr. P.H. Senior Epidemiologist / Data Scientist
Visual Display of (Public Health) Data - Theory and Practice Michael C. Samuel, Dr. P.H. Senior Epidemiologist / Data Scientist Cancer in females 200.00 150.00 100.00 50.00 C&R Lu. Breast 60.00 40.00 20.00
More informationKey Maths Facts to Memorise Question and Answer
Key Maths Facts to Memorise Question and Answer Ways of using this booklet: 1) Write the questions on cards with the answers on the back and test yourself. 2) Work with a friend to take turns reading a
More information6 ~ata-ink Maximization and Graphical Design
6 ~ata-ink Maximization and Graphical Design So far the principles of maximizing data-ink and erasing have helped to generate a series of choices in the process of graphical revision. This is an important
More informationChapter 7: RV's & Probability Distributions
Chapter 7: RV's & Probability Distributions Name 1. Professor Mean is planning the big Statistics Department Super Bowl party. Statisticians take pride in their variability, and it is not certain what
More informationSEVENTH GRADE. Revised June Billings Public Schools Correlation and Pacing Guide Math - McDougal Littell Middle School Math 2004
SEVENTH GRADE June 2010 Billings Public Schools Correlation and Guide Math - McDougal Littell Middle School Math 2004 (Chapter Order: 1, 6, 2, 4, 5, 13, 3, 7, 8, 9, 10, 11, 12 Chapter 1 Number Sense, Patterns,
More informationTable of Contents. Introduction...v. About the CD-ROM...vi. Standards Correlations... vii. Ratios and Proportional Relationships...
Table of Contents Introduction...v About the CD-ROM...vi Standards Correlations... vii Ratios and Proportional Relationships... 1 The Number System... 10 Expressions and Equations... 23 Geometry... 27
More informationResampling Statistics. Conventional Statistics. Resampling Statistics
Resampling Statistics Introduction to Resampling Probability Modeling Resample add-in Bootstrapping values, vectors, matrices R boot package Conclusions Conventional Statistics Assumptions of conventional
More informationCentre for Economic Policy Research
The Australian National University Centre for Economic Policy Research DISCUSSION PAPER The Reliability of Matches in the 2002-2004 Vietnam Household Living Standards Survey Panel Brian McCaig DISCUSSION
More informationREACHING THE UN-REACHABLE
UNITED STATES REACHING THE UN-REACHABLE 5 MYTHS ABOUT THOSE WHO WATCH LITTLE TO NO TV SHIFT HAPPENS. IT S WELL DOCUMENTED. U.S. HOMES IN MILLIONS Cable Telco Satellite We Project MVPDs Will Lose About
More informationCommon assumptions in color characterization of projectors
Common assumptions in color characterization of projectors Arne Magnus Bakke 1, Jean-Baptiste Thomas 12, and Jérémie Gerhardt 3 1 Gjøvik university College, The Norwegian color research laboratory, Gjøvik,
More information10.4 Inference as Decision. The 1995 O.J. Simpson trial: the situation
10.4 Inference as Decision The 1995 O.J. Simpson trial: the situation Nicole Brown Simpson and Ronald Goldman were brutally murdered sometime after 10:00 pm on June 12, 1994. Nicole was the wife of O.J.
More informationDIFFERENTIATE SOMETHING AT THE VERY BEGINNING THE COURSE I'LL ADD YOU QUESTIONS USING THEM. BUT PARTICULAR QUESTIONS AS YOU'LL SEE
1 MATH 16A LECTURE. OCTOBER 28, 2008. PROFESSOR: SO LET ME START WITH SOMETHING I'M SURE YOU ALL WANT TO HEAR ABOUT WHICH IS THE MIDTERM. THE NEXT MIDTERM. IT'S COMING UP, NOT THIS WEEK BUT THE NEXT WEEK.
More informationThe Urbana Free Library Patron Survey. Final Report
The Urbana Free Library Patron Survey Final Report CIRSS Center for Informatics Research in Science and Scholarship Graduate School of Library and Information Science University of Illinois at Urbana-Champaign
More information