Save this PDF as:

Size: px
Start display at page:

Transcription

1 Applications 1. a. Median height is 15.7 cm. Order the 1 heights from shortest to tallest. Since 1 is even, average the two middle numbers, 15.6 cm and 15.8 cm. b. Median stride distance is cm. Order the 1 stride distances from shortest to longest. Since 1 is even, average the two middle numbers, cm and cm. c. The median height is about 1.2 (1.7535) times the median stride distance. (Note: For Exercise 2, you might explore with the students what a line drawn at stride distance = height, 1.2 means.) 2. a. The graph indicates that, in general, taller people have longer stride distances. Knowing a person s stride will not definitively tell you that person s height, but 1.2 (stride distance) would be a good estimate. (See Exercise 1.) Stride Distance (cm) Height related to Stride Distance a. b. Identify the shortest height and then look at the corresponding stride distance; shorter people do have shorter strides. c. 1.2(stride distance) = height i. 18 cm; 1.2(15) = 18 ii. 18 cm; 1.2(9) = 18 iii. 132 cm; 1.2(11) = 132 Arm span (cm) Height and Arm Span 19 y Height (cm) b. The line suggests that arm span is always equal to height. (Note: This exercise is used in Exercise 5.) c. The line will have equation a = h. d. i. arm span equals height. ii. arm span is greater than height iii. arm span is less than height x Height (cm) Thinking With Mathematical Models 1

2 4. a. (See Figure 1.) b. The data suggest that for jet planes the body length is consistently longer than the wingspan. For propeller planes the opposite is true. c. If you ignore the differences between jet and propeller planes, the trend line has equation W =.8 L and the prediction would be (4, 41.2). (Note: Student equations are likely to be different than the best fit equations provided in this answer.) If you separate jets from propeller planes and draw two trend lines, the predictions would be: Jet: Trend line: W = L - 6; Prediction: (4, 34) Propeller: Trend line: W =.86 L + 9.1; Prediction: (4, 43.5) d. If you ignore the differences between jet and propeller planes, the trend line has equation W =.8 L and the prediction would be (63.5, 6). (Note: Student equations are likely to be different than the best fit equations provided in this answer.) If you separate jets from propeller planes and draw two trend lines, the predictions would be: Jet: Trend line: W = L - 6; Prediction: (66, 6) Propeller: Trend line: W =.86 L + 9.1; Prediction: (59.2, 6) 5. a. The equation w = / using w for wingspan and / for body length is not a good fit of the data. b. Estimates of a linear model that is a good fit will vary. w = 2 / is a pretty good estimate. This line has y intercept (, ) and slope 2, meaning that wingspan is twice body length. c. Using the linear model from part (b), the predicted wingspan would be 1 inches for a body length of 6 inches. Figure Airplanes: Body Length and Wingspan 8 Wingspan (m) Body Length (m) Thinking With Mathematical Models 2

3 6. a. Science Scores Relationship between Math and Science Scores Math Scores b. The math and science scores are similar for each student. c. See the line drawn on the graph. (Note: The line s = m is a good fit for the data.) d. Student 2 appears to be an outlier, having a higher science score than would be predicted by the math score. e. The correlation coefficient is closest to r = 1. (Note: The actual value is r =.96 but students can t estimate that value.) 7. a. Relationship between Math Score and Distance from School 3.5 Distance from School a. b. There does not seem to be a relationship between math score and distance a student lives from school. The points in the scatter plot do not cluster in a linear pattern. c. The correlation coefficient is closest to r =. (Note: The actual value is r =.2 but students can t estimate that value.) Average Time (min) Relationship between Number of Servers and Average Time to Fill an Order Number of Servers b. If anything, the data show a trend for higher average time when there are more servers. (Note: This is a very small data set.) c. The point (5,.3) is an outlier. This might be because the serving time at the restaurant seems much shorter than what one expects from the trend in the data points. d. The correlation coefficient is closest to r =.5 or 1. (Note: The actual value is r =.76 but students can t estimate that value.) Math Score Thinking With Mathematical Models 3

4 9. a. Math Scores Number of Absences and Math Scores Number of Absences b. There is a clear trend relating absences to math scores, with more absences generally associated with lower math scores. c. Students should graph a line close to the best fit line. The line of best fit has equation m =-7.1 a + 93, meaning that each additional absence is associated with a decrease of about 7 test score points. d. The correlation coefficient is closest to r =-1. (Note: The actual value is r =-.95 but students can t estimate that value. This indicates a strong negative association between the variables.) of 163 cm. The standard deviation of 8.6 suggests that a large fraction of the heights are between 135 and 152 cm. 11. a. (See Figure 2.) b. mean = 139.; median = 139; range = 18; standard deviation = 4.26 c. The graph of heights for students in Class 1 are clustered between 136 and 142 cm, with 17 of the 23 heights in this interval. The mean of 139 cm is the same as the median at the center of the distribution. There are four unusual heights, 13, 132, 147, and 148 cm. The standard deviation of 4.26 suggests that a large fraction of the heights will be between about 135 and 143 cm. d. This sample of student heights in Class 2 has greater variability than the sample in Class 1. e. Neither class data set is good for predicting the height of a typical student. The two samples have quite different mean and median heights and the data from Class 2 is very spread out which makes a typical student hard to identify. 1. The graph of heights for students in Class 2 has two clusters. The larger cluster is found between 136 and 14 cm. The smaller cluster is found between 144 and 148 cm. The mean of and median of 145 are close to each other at the center of the distribution. The graph shows that a student in Class 2 has an unusual height Figure Heights from Class 1 Thinking With Mathematical Models 4

5 12. a. Set A has mean = 1; Set B has mean = 1; Set C has mean = 1. b. Set A has standard deviation = 2.236; Set B has standard deviation = ; Set C has standard deviation = 9. c. Set B has no standard deviation because the values are all equal to the mean. Set C has two values that are the same and smaller than any values in Set A. Set C also has two values that are the same and larger than any values in Set A. This means that Set C has the greatest standard deviation because it has the greatest spread. Connections 14. a. A ratio greater than 1 means arm span is greater than height. On a plot of (h, s) data and the line s = h, these points would be above the model line. b. A ratio equal to 1 means height is equal to arm span. On a plot of (h, s) data and the line s = h, these points would be on the model line. c. A ratio less than 1 means arm span is less than height. On a plot of (h, s) data and the line s = h, these points would be above the model line. 15. C; In comparing shoes and jump height, look at the clusters to describe differences of the two distributions since measures of center lead to the same conclusion. (Note: The case for either choice B or choice C could be made based on the mean or clustering.) Extensions 21. a. F =.25 s + 4 b. See graph. ; None (this part of the graph would not be used in this context) 5 F: about 4 1 F: about F: about 688 Temperature F 13. a. Mean = +3, a. The distribution is skewed to the right when the mean is greater than the median. b. The distribution is skewed to the left when the mean is less than the median. c. When the mean and median are equal, the distribution is symmetrical. 17. H; The mode is 1, which is higher than either the mean or median. 18. B; 5 (6.7) - 4 (7.2) = 4.7 3(9) H; 4 = 89. a. one possible answer: 1, 2, 3, b. Standard deviation = b. one possible answer: 1, 2, 3 c. one possible answer: 2, 2, 2 Temperature versus Chirps y 5 x 4 6 Number of Chirps, s Thinking With Mathematical Models 5

6 c. i. 6 chirps ii. 1 chirps iii. 18 chirps 22. a. (See Figure 3.) b. T c = 5 36 x iv. 24 chirps Figure 3 Temperature versus Chirps Temperature C Frequency Thinking With Mathematical Models 6

7 c. The line is a good fit and a good model because the points cluster close to it and there are no outliers. (See Figure 4.) 23. a. The mean and the median are about the same, suggesting a roughly symmetric distribution of estimated weights. b. The mean is less than the median, suggesting a distribution that is somewhat skewed left. c. The correlation coefficient is closest to r = 1. (Note: The actual value is r =.81 but students can t estimate that value.) 24. a. The actual counts vary from 39 to 67 with a median of (halfway between the 17th and 18th counts). c. Points near the line represent cases where the estimates and actual counts are approximately equal. d. Points above the line represent cases where the estimate is greater than the actual count. e. Points below the line represent cases where the estimate is less than the actual count. f. Answers will vary. Most students made poor estimates since there are few points on or near the estimate = actual count line. The range of estimates is much greater than the range of actual counts. The median of estimates is much greater than the median of actual counts. b. The estimates vary from to 2, with median of (halfway between the 17th and 18th estimates). Figure 4 Temperature versus Chirps Temperature ( C) Frequency Thinking With Mathematical Models 7

8 g. A correlation coefficient for the variables of estimates and the actual counts is approximately zero (r =-.13). h. Answers will vary. Change the x axis. Make the maximum 8 or 1, and change the increment from 1 to 5. This spreads out the points horizontally. If the y axis is lengthened, then increments could be changed from 1 to 5 and this would spread the points out as well. 25. C; As the number of MP3s downloaded increases, the amount of unused space decreases. 26. a. The graph is clearly an upward curve. The rates of change in weight are, for points between 5 and 75, about 3 pounds per inch and, for points between 125 and 15, about 12 pounds per inch. (Note: Using the slope formula m = y 2 - y x 2 - x 1, then 75-5 = pounds per inch = 12 pounds per inch.) b. Students may choose a quadratic or a cubic family of functions. These graphs have roughly the same shape as the graph of the model of the relationship between pumpkin circumference and pumpkin weight. Testing values for k, might lead to a simple quadratic like w =.3c 2. From a geometric perspective, weight is proportional to the cube of circumference making it directly proportional to volume or the cube of three linear dimensions. Considering that the core of a pumpkin is much less dense than the outer shell, the quadratic relationship is supported by the proportional relationship between surface area of the pumpkin (or the square of the circumference) and the pumpkin weight. Thinking With Mathematical Models 8

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression

Exercise 1.12 (Pg. 22-23)

Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

AP Statistics Solutions to Packet 2

AP Statistics Solutions to Packet 2 The Normal Distributions Density Curves and the Normal Distribution Standard Normal Calculations HW #9 1, 2, 4, 6-8 2.1 DENSITY CURVES (a) Sketch a density curve that

Session 7 Bivariate Data and Analysis

Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares

Session 1.6 Measures of Central Tendency

Session 1.6 Measures of Central Tendency Measures of location (Indices of central tendency) These indices locate the center of the frequency distribution curve. The mode, median, and mean are three indices

Utah Core Curriculum for Mathematics

Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions

Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

STAT 155 Introductory Statistics. Lecture 5: Density Curves and Normal Distributions (I)

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Lecture 5: Density Curves and Normal Distributions (I) 9/12/06 Lecture 5 1 A problem about Standard Deviation A variable

5 Week Modular Course in Statistics & Probability Strand 1. Module 2

5 Week Modular Course in Statistics & Probability Strand 1 Module 2 Analysing Data Numerically Measures of Central Tendency Mean Median Mode Measures of Spread Range Standard Deviation Inter-Quartile Range

Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability

DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability RIT Score Range: Below 171 Below 171 Data Analysis and Statistics Solves simple problems based on data from tables* Compares

Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

Research Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement

Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value.

Algebra 1 Course Title

Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept

DesCartes (Combined) Subject: Mathematics Goal: Data Analysis, Statistics, and Probability

DesCartes (Combined) Subject: Mathematics Goal: Data Analysis, Statistics, and Probability RIT Score Range: Below 171 Below 171 171-180 Data Analysis and Statistics Data Analysis and Statistics Solves

F. Farrokhyar, MPhil, PhD, PDoc

Learning objectives Descriptive Statistics F. Farrokhyar, MPhil, PhD, PDoc To recognize different types of variables To learn how to appropriately explore your data How to display data using graphs How

Section 1.3 Exercises (Solutions)

Section 1.3 Exercises (s) 1.109, 1.110, 1.111, 1.114*, 1.115, 1.119*, 1.122, 1.125, 1.127*, 1.128*, 1.131*, 1.133*, 1.135*, 1.137*, 1.139*, 1.145*, 1.146-148. 1.109 Sketch some normal curves. (a) Sketch

Chapter 3: Data Description Numerical Methods

Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,

Correlation key concepts:

CORRELATION Correlation key concepts: Types of correlation Methods of studying correlation a) Scatter diagram b) Karl pearson s coefficient of correlation c) Spearman s Rank correlation coefficient d)

HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

Mathematics Revision Guides Histograms, Cumulative Frequency and Box Plots Page 1 of 25 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

CRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide

Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Thursday, August 16, 2012 8:30 to 11:30 a.m.

INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name

Diagrams and Graphs of Statistical Data

Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in

POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a

Maths Targets Year 1 Addition and Subtraction Measures. N / A in year 1.

Number and place value Maths Targets Year 1 Addition and Subtraction Count to and across 100, forwards and backwards beginning with 0 or 1 or from any given number. Count, read and write numbers to 100

Elementary Statistics. Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination

Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination What is a Scatter Plot? A Scatter Plot is a plot of ordered pairs (x, y) where the horizontal axis is used

PARCC Grade 08 Mathematics Practice Test Released April, 2014 http://practice.parcc.testnav.com/#

Non-Calculator Part 1. Solve for. Enter your answer in the space provided. Enter only your solution. ( ) ( ) 2. Which decimal is equivalent to? Select your answer. A. B. C. D. 3. Two lines are graphed

Pennsylvania System of School Assessment

Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read

Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013

A Correlation of Prentice Hall Mathematics Courses 1-3 Common Core Edition 2013 to the Topics & Lessons of Pearson A Correlation of Courses 1, 2 and 3, Common Core Introduction This document demonstrates

10-3 Measures of Central Tendency and Variation

10-3 Measures of Central Tendency and Variation So far, we have discussed some graphical methods of data description. Now, we will investigate how statements of central tendency and variation can be used.

ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only

ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The

2. Simple Linear Regression

Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

MyMathLab ecourse for Developmental Mathematics

MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and

College of the Canyons Math 140 Exam 1 Amy Morrow. Name:

Name: Answer the following questions NEATLY. Show all necessary work directly on the exam. Scratch paper will be discarded unread. One point each part unless otherwise marked. 1. Owners of an exercise

Interpreting Data in Normal Distributions

Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,

New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and Quick Review Math Handbook Book 1

New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and The lessons that address each Performance Indicator are listed, and those in which the Performance Indicator

Chapter 10 - Practice Problems 1

Chapter 10 - Practice Problems 1 1. A researcher is interested in determining if one could predict the score on a statistics exam from the amount of time spent studying for the exam. In this study, the

TEST A CHAPTER 6, EQUATIONS, INEQUALITIES, PROBLEM SOLVING. 1. Factor x 2-5x + 6. 2. Factor x 2-4x - 5.

TEST A CHAPTER 6, EQUATIONS, INEQUALITIES, PROBLEM SOLVING. Factor x 2-5x + 6. 2. Factor x 2-4x - 5. 3. Solve: (x + 2)(x - 3) = 0 x(x - 3)(x + 4) = 0 4. Solve by factoring: x 2 + x + 2 = 0. 5. Solve by

Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs

Types of Variables Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Quantitative (numerical)variables: take numerical values for which arithmetic operations make sense (addition/averaging)

Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),

Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables

COMMON CORE STATE STANDARDS FOR

COMMON CORE STATE STANDARDS FOR Mathematics (CCSSM) High School Statistics and Probability Mathematics High School Statistics and Probability Decisions or predictions are often based on data numbers in

Algebra 1 Course Information

Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through

with functions, expressions and equations which follow in units 3 and 4.

Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model

Common Core State Standards for Mathematics Accelerated 7th Grade

A Correlation of 2013 To the to the Introduction This document demonstrates how Mathematics Accelerated Grade 7, 2013, meets the. Correlation references are to the pages within the Student Edition. Meeting

Numerical Summarization of Data OPRE 6301

Numerical Summarization of Data OPRE 6301 Motivation... In the previous session, we used graphical techniques to describe data. For example: While this histogram provides useful insight, other interesting

Relationships Between Two Variables: Scatterplots and Correlation

Relationships Between Two Variables: Scatterplots and Correlation Example: Consider the population of cars manufactured in the U.S. What is the relationship (1) between engine size and horsepower? (2)

Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

Worksheet A5: Slope Intercept Form

Name Date Worksheet A5: Slope Intercept Form Find the Slope of each line below 1 3 Y - - - - - - - - - - Graph the lines containing the point below, then find their slopes from counting on the graph!.

Students will understand 1. use numerical bases and the laws of exponents

Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?

Bar Graphs and Dot Plots

CONDENSED L E S S O N 1.1 Bar Graphs and Dot Plots In this lesson you will interpret and create a variety of graphs find some summary values for a data set draw conclusions about a data set based on graphs

GRADES 7, 8, AND 9 BIG IDEAS

Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for

Module 3: Correlation and Covariance

Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis

McDougal Littell California:

McDougal Littell California: Pre-Algebra Algebra 1 correlated to the California Math Content s Grades 7 8 McDougal Littell California Pre-Algebra Components: Pupil Edition (PE), Teacher s Edition (TE),

Mathematics Pre-Test Sample Questions A. { 11, 7} B. { 7,0,7} C. { 7, 7} D. { 11, 11}

Mathematics Pre-Test Sample Questions 1. Which of the following sets is closed under division? I. {½, 1,, 4} II. {-1, 1} III. {-1, 0, 1} A. I only B. II only C. III only D. I and II. Which of the following

, has mean A) 0.3. B) the smaller of 0.8 and 0.5. C) 0.15. D) which cannot be determined without knowing the sample results.

BA 275 Review Problems - Week 9 (11/20/06-11/24/06) CD Lessons: 69, 70, 16-20 Textbook: pp. 520-528, 111-124, 133-141 An SRS of size 100 is taken from a population having proportion 0.8 of successes. An

Volume and Surface Area of a Sphere

Volume and Surface rea of a Sphere Reteaching 111 Math ourse, Lesson 111 The relationship between the volume of a cylinder, the volume of a cone, and the volume of a sphere is a special one. If the heights

Lesson 4 Measures of Central Tendency

Outline Measures of a distribution s shape -modality and skewness -the normal distribution Measures of central tendency -mean, median, and mode Skewness and Central Tendency Lesson 4 Measures of Central

How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

The Point-Slope Form

7. The Point-Slope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope

Infinite Algebra 1 supports the teaching of the Common Core State Standards listed below.

Infinite Algebra 1 Kuta Software LLC Common Core Alignment Software version 2.05 Last revised July 2015 Infinite Algebra 1 supports the teaching of the Common Core State Standards listed below. High School

MATHS LEVEL DESCRIPTORS

MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and

AP * Statistics Review. Descriptive Statistics

AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

Keystone National Middle School Math Level 7 Placement Exam

Keystone National Middle School Math Level 7 Placement Exam ) Erica bought a car for \$,000. She had to add Pennsylvania s sales tax of 6%. The total price of the car is closest to? \$,00 \$6,000 \$,000 \$,000

Algebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions.

Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables.

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 119 STATISTICS AND ELEMENTARY ALGEBRA 5 Lecture Hours, 2 Lab Hours, 3 Credits Pre-

Chapter 9 Descriptive Statistics for Bivariate Data

9.1 Introduction 215 Chapter 9 Descriptive Statistics for Bivariate Data 9.1 Introduction We discussed univariate data description (methods used to eplore the distribution of the values of a single variable)

Chapter 15 Multiple Choice Questions (The answers are provided after the last question.)

Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) 1. What is the median of the following set of scores? 18, 6, 12, 10, 14? a. 10 b. 14 c. 18 d. 12 2. Approximately

Florida Department of Education/Office of Assessment January 2012. Grade 7 FCAT 2.0 Mathematics Achievement Level Descriptions

Florida Department of Education/Office of Assessment January 2012 Grade 7 FCAT 2.0 Mathematics Grade 7 FCAT 2.0 Mathematics Reporting Category Geometry and Measurement Students performing at the mastery

DesCartes (Combined) Subject: Mathematics 2-5 Goal: Data Analysis, Statistics, and Probability

DesCartes (Combined) Subject: Mathematics 2-5 Goal: Data Analysis, Statistics, and Probability RIT Score Range: Below 171 Below 171 Data Analysis and Statistics Solves simple problems based on data from

Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

Stats Review Chapters 3-4

Stats Review Chapters 3-4 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

Math 2015 Lesson 21. We discuss the mean and the median, two important statistics about a distribution. p(x)dx = 0.5

ean and edian We discuss the mean and the median, two important statistics about a distribution. The edian The median is the halfway point of a distribution. It is the point where half the population has

Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

The correlation coefficient

The correlation coefficient Clinical Biostatistics The correlation coefficient Martin Bland Correlation coefficients are used to measure the of the relationship or association between two quantitative

Central Tendency. n Measures of Central Tendency: n Mean. n Median. n Mode

Central Tendency Central Tendency n A single summary score that best describes the central location of an entire distribution of scores. n Measures of Central Tendency: n Mean n The sum of all scores divided

Premaster Statistics Tutorial 4 Full solutions

Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125,000 + 150. b. What is the prediction for

Report of for Chapter 2 pretest

Report of for Chapter 2 pretest Exam: Chapter 2 pretest Category: Organizing and Graphing Data 1. "For our study of driving habits, we recorded the speed of every fifth vehicle on Drury Lane. Nearly every

Rectangle Square Triangle

HFCC Math Lab Beginning Algebra - 15 PERIMETER WORD PROBLEMS The perimeter of a plane geometric figure is the sum of the lengths of its sides. In this handout, we will deal with perimeter problems involving

Graphical Presentation of Data

Graphical Presentation of Data Guidelines for Making Graphs Titles should tell the reader exactly what is graphed Remove stray lines, legends, points, and any other unintended additions by the computer

Chapter 8 Graphs and Functions:

Chapter 8 Graphs and Functions: Cartesian axes, coordinates and points 8.1 Pictorially we plot points and graphs in a plane (flat space) using a set of Cartesian axes traditionally called the x and y axes

Homework 8 Solutions

Math 17, Section 2 Spring 2011 Homework 8 Solutions Assignment Chapter 7: 7.36, 7.40 Chapter 8: 8.14, 8.16, 8.28, 8.36 (a-d), 8.38, 8.62 Chapter 9: 9.4, 9.14 Chapter 7 7.36] a) A scatterplot is given below.

Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year.

Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 2014-2015 school year. Goal The goal of the summer math program is to help students

of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

What is the purpose of this document? What is in the document? How do I send Feedback?

This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Statistics

Inferential Statistics

Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

Assessment Anchors and Eligible Content

M07.A-N The Number System M07.A-N.1 M07.A-N.1.1 DESCRIPTOR Assessment Anchors and Eligible Content Aligned to the Grade 7 Pennsylvania Core Standards Reporting Category Apply and extend previous understandings

PowerTeaching i3: Algebra I Mathematics

PowerTeaching i3: Algebra I Mathematics Alignment to the Common Core State Standards for Mathematics Standards for Mathematical Practice and Standards for Mathematical Content for Algebra I Key Ideas and

Math Grade 11 Assessment Anchors and Eligible Content

Math Grade 11 Assessment Anchors and Eligible Content Pennsylvania Department of Education www.pde.state.pa.us Updated August 2010 M11.A Numbers and Operations M11.A.1 Demonstrate an understanding of numbers,

Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade

Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements

Enduring Understandings: Some basic math skills are required to be reviewed in preparation for the course.

HADDONFIELD PUBLIC SCHOOLS Curriculum Map for Functions, Statistics and Trigonometry September 5 Days Targeted NJ Core Curriculum Content Standards: N-Q.1, N-Q.2, N-Q.3, A-CED.1, A-REI.1, A-REI.3 Enduring

Developmental Math Course Outcomes and Objectives

Developmental Math Course Outcomes and Objectives I. Math 0910 Basic Arithmetic/Pre-Algebra Upon satisfactory completion of this course, the student should be able to perform the following outcomes and

WHICH TYPE OF GRAPH SHOULD YOU CHOOSE?

PRESENTING GRAPHS WHICH TYPE OF GRAPH SHOULD YOU CHOOSE? CHOOSING THE RIGHT TYPE OF GRAPH You will usually choose one of four very common graph types: Line graph Bar graph Pie chart Histograms LINE GRAPHS

Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for