Stat 20: Intro to Probability and Statistics

Size: px
Start display at page:

Download "Stat 20: Intro to Probability and Statistics"

Transcription

1 Stat 20: Intro to Probability and Statistics Lecture 4: Data Displays (cont.) Tessa L. Childers-Day UC Berkeley 26 June 2014

2 By the end of this lecture... You will be able to: Comprehend displays of quantitative data Construct a histogram 2 / 18

3 Example: High School Hobbies (Hypothetical:) Imagine we are interested in exploring what kinds of hobbies high school students have below. We construct a survey: (1) Circle your gender: Female Male (2) Circle your class level: Fresh Soph Jr Sr (3) What is your GPA ( )? (4) What is your height in inches? (5) What is your weight in pounds? (6) What is your favorite hobby? 3 / 18

4 Example: High School Hobbies (cont.) A selection of the hypothetical raw data appear below: obs gender class level gpa height weight hobbies 1 male jr watching tv 2 female soph facebook 3 female jr baseball 4 male jr soccer 5 male sr yearbook 6 female jr baseball 7 male sr facebook 8 female fresh gymnastics 9 male sr hanging out 10 male jr reading 4 / 18

5 Ways to classify data Level of Measurement: Qualitative Nominal Ordinal Quantitative Interval Ratio Countability: Discrete Continuous 5 / 18

6 Displaying Qualitative Data Helps to summarize/organize raw data visually Data Tables Distribution Tables Contingency Tables Pie Charts Bar Charts Word Clouds How can we make this work for quantitative data as well? 6 / 18

7 Quantitative Data Displays Today: Quantitative Data Stem and Leaf Plot Scatterplot Histogram Frequency Density Smoothed Histogram Will not work for qualitative data 7 / 18

8 Stem and Leaf Plot A stem and leaf plot breaks the numbers into groups/classes, usually based on the first (several) digits. This is the stem. The last digit is the leaf. The data gets sorted, and each data point gets put onto a leaf. GPA stem leaf ones tenths What is good about this display? What is bad? 8 / 18

9 Scatterplots A scatterplot represents each data point by a dot, and plots the dots on a pair of axes Height of High Schoolers Observation Height (inches) Height of High Schoolers Rank Height (inches) 9 / 18

10 Scatterplots (cont.) Here we have two data types plotted together Plot the pair (x,y) = (height, weight) for each student But we say we ve plotted y vs. x or weight vs. height or weight against height Weight vs. Height of High Schoolers Height (inches) Weight (pounds) What is good about this display? What is bad? 10 / 18

11 Histogram A histogram is like a bar chart, but is intended for quantitative data, instead of qualitative data. Data broken into mutually exclusive, exhaustive classes Numerically adjoining classes are connected Need to know the endpoint convention Pretends data is spread evenly over class interval 11 / 18

12 Histogram (cont.) Frequency Histogram Height represents frequency of observations which fall into each class Sum of all frequencies = total number of observations Class widths are equal just compare heights/frequencies Frequency Histogram of Weight of High Schoolers Weight (pounds) 12 / 18

13 Histogram (cont.) Density Histogram Area represents the percentage of data in a class Histogram of Weight of High Schoolers area = base height = percentage height = percentage base = % per unit of x = density Height represents density (crowding) of observations in each class Density (% per pound) Weight (pounds) 13 / 18

14 Histogram (cont.) Density Histogram Total area = 100% If class widths equal, compare heights percentage in a class = density class width Can add percentages No fixed number of classes Density (% per pound) Histogram of Weight of High Schoolers Weight (pounds) 14 / 18

15 Histogram (cont.) Histogram of Weight of High Schoolers Histogram of Weight of High Schoolers Density (% per pound) Density (% per pound) Weight (pounds) Weight (pounds) What is good about this kind of display? What is bad? 15 / 18

16 Smoothed Histogram With the advent of computers, it became possible to smooth a histogram (estimate a density) Smoothed Histogram Basically take class width to zero Total area = 100% Smooths histogram to reflect continuity of data Have to pick bandwidth (amount of smoothing) Doesn t pretend data is spread evenly over class interval Density (% per pound) Smoothed Histogram of Weight of High Schoolers Weight (pounds) 16 / 18

17 Smoothed Histogram (cont.) Smoothed Histogram of Weight of High Schoolers Smoothed Histogram of Weight of High Schoolers Density (% per pound) Density (% per pound) Weight (pounds) What is good about this display? What is bad? Weight (pounds) 17 / 18

18 Important Takeaways Need to display data hard to understand raw data, especially in large amounts Quantitative Data Displays Stem and Leaf Plot Scatterplot Histogram (frequency and density) Smoothed Histogram Next time: Summary Statistics 18 / 18

Notes: Displaying Quantitative Data

Notes: Displaying Quantitative Data Notes: Displaying Quantitative Data Stats: Modeling the World Chapter 4 A or is often used to display categorical data. These types of displays, however, are not appropriate for quantitative data. Quantitative

More information

Chapter 3. Graphical Methods for Describing Data. Copyright 2005 Brooks/Cole, a division of Thomson Learning, Inc.

Chapter 3. Graphical Methods for Describing Data. Copyright 2005 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 3 Graphical Methods for Describing Data 1 Frequency Distribution Example The data in the column labeled vision for the student data set introduced in the slides for chapter 1 is the answer to the

More information

Chapter Displaying Graphical Data. Frequency Distribution Example. Graphical Methods for Describing Data. Vision Correction Frequency Relative

Chapter Displaying Graphical Data. Frequency Distribution Example. Graphical Methods for Describing Data. Vision Correction Frequency Relative Chapter 3 Graphical Methods for Describing 3.1 Displaying Graphical Distribution Example The data in the column labeled vision for the student data set introduced in the slides for chapter 1 is the answer

More information

This Chapter s Topics

This Chapter s Topics This Chapter s Topics Today, we re going to talk about three things: Frequency distributions Graphs Charts Frequency distributions, graphs, and charts 1 Frequency distributions Frequency distributions

More information

Chapter 4. September 08, appstats 4B.notebook. Displaying Quantitative Data. Aug 4 9:13 AM. Aug 4 9:13 AM. Aug 27 10:16 PM.

Chapter 4. September 08, appstats 4B.notebook. Displaying Quantitative Data. Aug 4 9:13 AM. Aug 4 9:13 AM. Aug 27 10:16 PM. Objectives: Students will: Chapter 4 1. Be able to identify an appropriate display for any quantitative variable: stem leaf plot, time plot, histogram and dotplot given a set of quantitative data. 2. Be

More information

Outline. Drawing the Graph. 1 Homework Review. 2 Introduction. 3 Histograms. 4 Histograms on the TI Assignment

Outline. Drawing the Graph. 1 Homework Review. 2 Introduction. 3 Histograms. 4 Histograms on the TI Assignment Lecture 14 Section 4.4.4 on Hampden-Sydney College Fri, Sep 18, 2009 Outline 1 on 2 3 4 on 5 6 Even-numbered on Exercise 4.25, p. 249. The following is a list of homework scores for two students: Student

More information

10 Wyner Statistics Fall 2013

10 Wyner Statistics Fall 2013 1 Wyner Statistics Fall 213 CHAPTER TWO: GRAPHS Summary Terms Objectives For research to be valuable, it must be shared. The fundamental aspect of a good graph is that it makes the results clear at a glance.

More information

Section 1.5 Graphs and Describing Distributions

Section 1.5 Graphs and Describing Distributions Section 1.5 Graphs and Describing Distributions Data can be displayed using graphs. Some of the most common graphs used in statistics are: Bar graph Pie Chart Dot plot Histogram Stem and leaf plot Box

More information

Business Statistics:

Business Statistics: Department of Quantitative Methods & Information Systems Business Statistics: Chapter 2 Graphs, Charts, and Tables Describing Your Data QMIS 120 Dr. Mohammad Zainal Chapter Goals After completing this

More information

Stat 20: Intro to Probability and Statistics

Stat 20: Intro to Probability and Statistics Stat 20: Intro to Probability and Statistics Lecture 17: Using the Normal Curve with Box Models Tessa L. Childers-Day UC Berkeley 23 July 2014 By the end of this lecture... You will be able to: Draw and

More information

Chapter 2. Organizing Data. Slide 2-2. Copyright 2012, 2008, 2005 Pearson Education, Inc.

Chapter 2. Organizing Data. Slide 2-2. Copyright 2012, 2008, 2005 Pearson Education, Inc. Chapter 2 Organizing Data Slide 2-2 Section 2.1 Variables and Data Slide 2-3 Definition 2.1 Variables Variable: A characteristic that varies from one person or thing to another. Qualitative variable: A

More information

Going back to the definition of Biostatistics. Organizing and Presenting Data. Learning Objectives. Nominal Data 10/10/2016. Tabulation and Graphs

Going back to the definition of Biostatistics. Organizing and Presenting Data. Learning Objectives. Nominal Data 10/10/2016. Tabulation and Graphs 1/1/1 Organizing and Presenting Data Tabulation and Graphs Introduction to Biostatistics Haleema Masud Going back to the definition of Biostatistics The collection, organization, summarization, analysis,

More information

Numerical: Data with quantity Discrete: whole number answers Example: How many siblings do you have?

Numerical: Data with quantity Discrete: whole number answers Example: How many siblings do you have? Types of data Numerical: Data with quantity Discrete: whole number answers Example: How many siblings do you have? Continuous: Answers can fall anywhere in between two whole numbers. Usually any type of

More information

Chapter 10. Definition: Categorical Variables. Graphs, Good and Bad. Distribution

Chapter 10. Definition: Categorical Variables. Graphs, Good and Bad. Distribution Chapter 10 Graphs, Good and Bad Chapter 10 3 Distribution Definition: Tells what values a variable takes and how often it takes these values Can be a table, graph, or function Categorical Variables Places

More information

Introduction. Descriptive Statistics. Problem Solving. Inferential Statistics. Chapter1 Slides. Maurice Geraghty

Introduction. Descriptive Statistics. Problem Solving. Inferential Statistics. Chapter1 Slides. Maurice Geraghty Inferential Statistics and Probability a Holistic Approach Chapter 1 Displaying and Analyzing Data with Graphs This Course Material by Maurice Geraghty is licensed under a Creative Commons Attribution-ShareAlike

More information

11 Wyner Statistics Fall 2018

11 Wyner Statistics Fall 2018 11 Wyner Statistics Fall 218 CHAPTER TWO: GRAPHS Review September 19 Test September 28 For research to be valuable, it must be shared, and a graph can be an effective way to do so. The fundamental aspect

More information

Statistics for Managers using Microsoft Excel 3 rd Edition

Statistics for Managers using Microsoft Excel 3 rd Edition Statistics for Managers using Microsoft Excel 3 rd Edition Chapter 2 Presenting Data in Tables and Charts 22 Prentice-Hall, Inc. Chap 2-1 Chapter Topics Organizing numerical data The ordered array and

More information

Elementary Statistics. Graphing Data

Elementary Statistics. Graphing Data Graphing Data What have we learned so far? 1 Randomly collect data. 2 Sort the data. 3 Compute the class width for specific number of classes. 4 Complete a frequency distribution table with the following

More information

Chapter 2 Frequency Distributions and Graphs

Chapter 2 Frequency Distributions and Graphs Chapter 2 Frequency Distributions and Graphs Outline 2-1 Organizing Data 2-2 Histograms, Frequency Polygons, and Ogives 2-3 Other Types of Graphs Objectives Organize data using a frequency distribution.

More information

Chapter 4. Displaying and Summarizing Quantitative Data. Copyright 2012, 2008, 2005 Pearson Education, Inc.

Chapter 4. Displaying and Summarizing Quantitative Data. Copyright 2012, 2008, 2005 Pearson Education, Inc. Chapter 4 Displaying and Summarizing Quantitative Data Copyright 2012, 2008, 2005 Pearson Education, Inc. Dealing With a Lot of Numbers Summarizing the data will help us when we look at large sets of quantitative

More information

GRAPHS & CHARTS. Prof. Rahul C. Basole CS/MGT 8803-DV > January 23, 2017 INFOVIS 8803DV > SPRING 17

GRAPHS & CHARTS. Prof. Rahul C. Basole CS/MGT 8803-DV > January 23, 2017 INFOVIS 8803DV > SPRING 17 GRAPHS & CHARTS Prof. Rahul C. Basole CS/MGT 8803-DV > January 23, 2017 HW2: DataVis Examples Tumblr 47 students = 47 VIS of the Day submissions Random Order We will start next week Stay tuned Tufte Seminar

More information

Notes 5C: Statistical Tables and Graphs

Notes 5C: Statistical Tables and Graphs Notes 5C: Statistical Tables and Graphs Frequency Tables A frequency table is an easy way to display raw data. A frequency table typically has between two to four columns: The first column lists all the

More information

DESCRIBING DATA. Frequency Tables, Frequency Distributions, and Graphic Presentation

DESCRIBING DATA. Frequency Tables, Frequency Distributions, and Graphic Presentation DESCRIBING DATA Frequency Tables, Frequency Distributions, and Graphic Presentation Raw Data A raw data is the data obtained before it is being processed or arranged. 2 Example: Raw Score A raw score is

More information

15-388/688 - Practical Data Science: Visualization and Data Exploration. J. Zico Kolter Carnegie Mellon University Spring 2018

15-388/688 - Practical Data Science: Visualization and Data Exploration. J. Zico Kolter Carnegie Mellon University Spring 2018 15-388/688 - Practical Data Science: Visualization and Data Exploration J. Zico Kolter Carnegie Mellon University Spring 2018 1 Outline Basics of visualization Data types and visualization types Software

More information

Univariate Descriptive Statistics

Univariate Descriptive Statistics Univariate Descriptive Statistics Displays: pie charts, bar graphs, box plots, histograms, density estimates, dot plots, stemleaf plots, tables, lists. Example: sea urchin sizes Boxplot Histogram Urchin

More information

Statistics 101 Reviewer for Final Examination

Statistics 101 Reviewer for Final Examination Statistics 101 Reviewer for Final Examination Elementary Statistics S101-FE-003 TRUE or FALSE. Write True, if the statement is correct, and False, if otherwise. (20 pts.) 1. A sample is a subset of the

More information

Chapter 1: Stats Starts Here Chapter 2: Data

Chapter 1: Stats Starts Here Chapter 2: Data Chapter 1: Stats Starts Here Chapter 2: Data Statistics data, datum variation individual respondent subject participant experimental unit observation variable categorical quantitative Calculator Skills:

More information

Chapter 2. The Excel functions, Excel Analysis ToolPak Add-ins or Excel PHStat2 Add-ins needed to create frequency distributions are:

Chapter 2. The Excel functions, Excel Analysis ToolPak Add-ins or Excel PHStat2 Add-ins needed to create frequency distributions are: I. Organizing Data in Tables II. Describing Data by Graphs Chapter 2 I. Tables: 1. Frequency Distribution (Nominal or Ordinal) 2. Grouped Frequency Distribution (Interval or Ratio data) 3. Joint Frequency

More information

General tips for all graphs Choosing the right kind of graph scatter graph bar graph

General tips for all graphs Choosing the right kind of graph scatter graph bar graph Excerpted and adapted from: McDonald, J.H. 2014. Handbook of Biological Statistics (3rd ed.). Sparky House Publishing, Baltimore, MD. (http://www.biostathandbook.com/graph.html) Guide to fairly good graphs

More information

Chapter 4 Displaying and Describing Quantitative Data

Chapter 4 Displaying and Describing Quantitative Data Chapter 4 Displaying and Describing Quantitative Data Overview Key Concepts Be able to identify an appropriate display for any quantitative variable. Be able to guess the shape of the distribution of a

More information

Review. In an experiment, there is one variable that is of primary interest. There are several other factors, which may affect the measured result.

Review. In an experiment, there is one variable that is of primary interest. There are several other factors, which may affect the measured result. Review Observational study vs experiment Experimental designs In an experiment, there is one variable that is of primary interest. There are several other factors, which may affect the measured result.

More information

Stat 20: Intro to Probability and Statistics

Stat 20: Intro to Probability and Statistics Stat 20: Intro to Probability and Statistics Lecture 12: More Probability Tessa L. Childers-Day UC Berkeley 10 July 2014 By the end of this lecture... You will be able to: Use the theory of equally likely

More information

Sidcot intranet - Firefly. Useful links: Instant classroom. MyMaths. Objectives

Sidcot intranet - Firefly. Useful links: Instant classroom. MyMaths. Objectives Useful links: Sidcot intranet - Firefly Instant classroom MyMaths Objectives Objectives To revise scatter graphs To use them to make estimations Scatter Graphs Revision powerpoint Now make some revision

More information

UNCORRECTED PAGE PROOFS

UNCORRECTED PAGE PROOFS Topic 14 Representing and interpreting data 14.1 Overview Why learn this? Understanding data helps us to make sense of graphs, charts and advertising material. The media often present statistics such as

More information

Data Presentation. Esra Akdeniz. February 12th, 2016

Data Presentation. Esra Akdeniz. February 12th, 2016 Data Presentation Esra Akdeniz February 12th, 2016 HOW TO DO RESEARCH? Question. Literature research. Hypothesis. Collect data. Analyze data. Interpret and present results. HOW TO DO RESEARCH? Analyze

More information

Learning Log Title: CHAPTER 2: ARITHMETIC STRATEGIES AND AREA. Date: Lesson: Chapter 2: Arithmetic Strategies and Area

Learning Log Title: CHAPTER 2: ARITHMETIC STRATEGIES AND AREA. Date: Lesson: Chapter 2: Arithmetic Strategies and Area Chapter 2: Arithmetic Strategies and Area CHAPTER 2: ARITHMETIC STRATEGIES AND AREA Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 2: Arithmetic Strategies and Area Date: Lesson:

More information

Chapter 1. Picturing Distributions with Graphs

Chapter 1. Picturing Distributions with Graphs Chapter 1. Picturing Distributions with Graphs 1 Chapter 1. Picturing Distributions with Graphs Definition. Individuals are the objects described by a set of data. Individuals may be people, but they may

More information

Statistics. Graphing Statistics & Data. What is Data?. Data is organized information. It can be numbers, words, measurements,

Statistics. Graphing Statistics & Data. What is Data?. Data is organized information. It can be numbers, words, measurements, Statistics Graphing Statistics & Data What is Data?. Data is organized information. It can be numbers, words, measurements, observations or even just descriptions of things. Qualitative vs Quantitative.

More information

Chapter 2 Descriptive Statistics: Tabular and Graphical Methods

Chapter 2 Descriptive Statistics: Tabular and Graphical Methods Chapter Descriptive Statistics http://nscc-webctdev.northweststate.edu/script/sta_sp/scripts/student/serve_page... Page of 7 /7/9 Chapter Descriptive Statistics: Tabular and Graphical Methods Data can

More information

Section 1: Data (Major Concept Review)

Section 1: Data (Major Concept Review) Section 1: Data (Major Concept Review) Individuals = the objects described by a set of data variable = characteristic of an individual weight height age IQ hair color eye color major social security #

More information

Chapter 1. Statistics. Individuals and Variables. Basic Practice of Statistics - 3rd Edition. Chapter 1 1. Picturing Distributions with Graphs

Chapter 1. Statistics. Individuals and Variables. Basic Practice of Statistics - 3rd Edition. Chapter 1 1. Picturing Distributions with Graphs Chapter 1 Picturing Distributions with Graphs BPS - 3rd Ed. Chapter 1 1 Statistics Statistics is a science that involves the extraction of information from numerical data obtained during an experiment

More information

3. Data and sampling. Plan for today

3. Data and sampling. Plan for today 3. Data and sampling Business Statistics Plan for today Reminders and introduction Data: qualitative and quantitative Quantitative data: discrete and continuous Qualitative data discussion Samples and

More information

Sampling, Part 2. AP Statistics Chapter 12

Sampling, Part 2. AP Statistics Chapter 12 Sampling, Part 2 AP Statistics Chapter 12 bias error Sampling error is just sampling variation! Bias vs Error BIAS is something that causes your measurements to systematically miss in the same direction,

More information

Displaying Distributions with Graphs

Displaying Distributions with Graphs Displaying Distributions with Graphs Recall that the distribution of a variable indicates two things: (1) What value(s) a variable can take, and (2) how often it takes those values. Example 1: Weights

More information

Female Height. Height (inches)

Female Height. Height (inches) Math 111 Normal distribution NAME: Consider the histogram detailing female height. The mean is 6 and the standard deviation is 2.. We will use it to introduce and practice the ideas of normal distributions.

More information

APPENDIX 2.3: RULES OF PROBABILITY

APPENDIX 2.3: RULES OF PROBABILITY The frequentist notion of probability is quite simple and intuitive. Here, we ll describe some rules that govern how probabilities are combined. Not all of these rules will be relevant to the rest of this

More information

TJP TOP TIPS FOR IGCSE STATS & PROBABILITY

TJP TOP TIPS FOR IGCSE STATS & PROBABILITY TJP TOP TIPS FOR IGCSE STATS & PROBABILITY Dr T J Price, 2011 First, some important words; know what they mean (get someone to test you): Mean the sum of the data values divided by the number of items.

More information

Describing Data Visually. Describing Data Visually. Describing Data Visually 9/28/12. Applied Statistics in Business & Economics, 4 th edition

Describing Data Visually. Describing Data Visually. Describing Data Visually 9/28/12. Applied Statistics in Business & Economics, 4 th edition A PowerPoint Presentation Package to Accompany Applied Statistics in Business & Economics, 4 th edition David P. Doane and Lori E. Seward Prepared by Lloyd R. Jaisingh Describing Data Visually Chapter

More information

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation. Chapter 2

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation. Chapter 2 Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation Chapter 2 Learning Objectives Organize qualitative data into a frequency table. Present a frequency table as a bar chart

More information

not human choice is used to select the sample.

not human choice is used to select the sample. [notes for days 2 and 3] Random Sampling All statistical sampling designs have in common the idea that chance not human choice is used to select the sample. Randomize let chance do the choosing! Randomization

More information

Using Figures - The Basics

Using Figures - The Basics Using Figures - The Basics by David Caprette, Rice University OVERVIEW To be useful, the results of a scientific investigation or technical project must be communicated to others in the form of an oral

More information

Principles of Graphical Excellence Best Paper: ALAIR April 5 6, 2001 AIR: June 2-5, 2002, Toronto Focus-IR, February 21, 2003

Principles of Graphical Excellence Best Paper: ALAIR April 5 6, 2001 AIR: June 2-5, 2002, Toronto Focus-IR, February 21, 2003 Anna T. Waggener, Ph.D. Institutional Assessment United States Army War College Principles of Graphical Excellence Best Paper: ALAIR April 5 6, 2001 AIR: June 2-5, 2002, Toronto Focus-IR, February 21,

More information

Line Graphs. Name: The independent variable is plotted on the x-axis. This axis will be labeled Time (days), and

Line Graphs. Name: The independent variable is plotted on the x-axis. This axis will be labeled Time (days), and Name: Graphing Review Graphs and charts are great because they communicate information visually. For this reason graphs are often used in newspapers, magazines, and businesses around the world. Sometimes,

More information

Symmetric (Mean and Standard Deviation)

Symmetric (Mean and Standard Deviation) Summary: Unit 2 & 3 Distributions for Quantitative Data Topics covered in Module 2: How to calculate the Mean, Median, IQR Shapes of Histograms, Dotplots, Boxplots Know the difference between categorical

More information

Frequency Distribution and Graphs

Frequency Distribution and Graphs Chapter 2 Frequency Distribution and Graphs 2.1 Organizing Qualitative Data Denition 2.1.1 A categorical frequency distribution lists the number of occurrences for each category of data. Example 2.1.1

More information

Data 1 Assessment Calculator allowed for all questions

Data 1 Assessment Calculator allowed for all questions Foundation Higher Data Assessment Calculator allowed for all questions MATHSWATCH All questions Time for the test: 45 minutes Name: MATHSWATCH ANSWERS Grade Title of clip Marks Score Percentage Clip 4

More information

Learning Objectives. Describing Data: Displaying and Exploring Data. Dot Plot. Dot Plot 12/9/2015

Learning Objectives. Describing Data: Displaying and Exploring Data. Dot Plot. Dot Plot 12/9/2015 Describing Data: Displaying and Exploring Data Chapter 4 Learning Objectives Develop and interpret a dot plot. Develop and interpret a stem-and-leaf display. Compute and understand quartiles. Construct

More information

Describing Data: Displaying and Exploring Data. Chapter 4

Describing Data: Displaying and Exploring Data. Chapter 4 Describing Data: Displaying and Exploring Data Chapter 4 Learning Objectives Develop and interpret a dot plot. Develop and interpret a stem-and-leaf display. Compute and understand quartiles. Construct

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Practice for Final Exam Name Identify the following variable as either qualitative or quantitative and explain why. 1) The number of people on a jury A) Qualitative because it is not a measurement or a

More information

(3 pts) 1. Which statements are usually true of a left-skewed distribution? (circle all that are correct)

(3 pts) 1. Which statements are usually true of a left-skewed distribution? (circle all that are correct) STAT 451 - Practice Exam I Name (print): Section: This is a practice exam - it s a representative sample of problems that may appear on the exam and also substantially longer than the in-class exam. It

More information

Statistics is the study of the collection, organization, analysis, interpretation and presentation of data.

Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. What is Data? Data is a collection of facts, such as values or measurements. It can be numbers,

More information

AWM 11 UNIT 1 WORKING WITH GRAPHS

AWM 11 UNIT 1 WORKING WITH GRAPHS AWM 11 UNIT 1 WORKING WITH GRAPHS Assignment Title Work to complete Complete 1 Introduction to Statistics Read the introduction no written assignment 2 Bar Graphs Bar Graphs 3 Double Bar Graphs Double

More information

Objective: Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.

Objective: Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes. Lesson 5 Objective: Investigate patterns in vertical and horizontal lines, and interpret Suggested Lesson Structure Application Problem Fluency Practice Concept Development Student Debrief Total Time (7

More information

Chapter 10. Re-expressing Data: Get it Straight! Copyright 2012, 2008, 2005 Pearson Education, Inc.

Chapter 10. Re-expressing Data: Get it Straight! Copyright 2012, 2008, 2005 Pearson Education, Inc. Chapter 10 Re-expressing Data: Get it Straight! Copyright 2012, 2008, 2005 Pearson Education, Inc. Straight to the Point We cannot use a linear model unless the relationship between the two variables is

More information

MAT Midterm Review

MAT Midterm Review MAT 120 - Midterm Review Name Identify the population and the sample. 1) When 1094 American households were surveyed, it was found that 67% of them owned two cars. Identify whether the statement describes

More information

Exam #1. Good luck! Page 1 of 7

Exam #1. Good luck! Page 1 of 7 Exam # Total: 00 points Date: July, 008 Time: :00 :0 You have hour and 0 minutes to finish the exam. Please read the question carefully and assign your time smartly. Please PRINIT your name on each page

More information

NCSS Statistical Software

NCSS Statistical Software Chapter 147 Introduction A mosaic plot is a graphical display of the cell frequencies of a contingency table in which the area of boxes of the plot are proportional to the cell frequencies of the contingency

More information

Chpt 2. Frequency Distributions and Graphs. 2-3 Histograms, Frequency Polygons, Ogives / 35

Chpt 2. Frequency Distributions and Graphs. 2-3 Histograms, Frequency Polygons, Ogives / 35 Chpt 2 Frequency Distributions and Graphs 2-3 Histograms, Frequency Polygons, Ogives 1 Chpt 2 Homework 2-3 Read pages 48-57 p57 Applying the Concepts p58 2-4, 10, 14 2 Chpt 2 Objective Represent Data Graphically

More information

Why Should We Care? Everyone uses plotting But most people ignore or are unaware of simple principles Default plotting tools are not always the best

Why Should We Care? Everyone uses plotting But most people ignore or are unaware of simple principles Default plotting tools are not always the best Elementary Plots Why Should We Care? Everyone uses plotting But most people ignore or are unaware of simple principles Default plotting tools are not always the best More importantly, it is easy to lie

More information

2. Let E and F be two events of the same sample space. If P (E) =.55, P (F ) =.70, and

2. Let E and F be two events of the same sample space. If P (E) =.55, P (F ) =.70, and c Dr. Patrice Poage, August 23, 2017 1 1324 Exam 1 Review NOTE: This review in and of itself does NOT prepare you for the test. You should be doing this review in addition to all your suggested homework,

More information

Tables and Figures. Germination rates were significantly higher after 24 h in running water than in controls (Fig. 4).

Tables and Figures. Germination rates were significantly higher after 24 h in running water than in controls (Fig. 4). Tables and Figures Text: contrary to what you may have heard, not all analyses or results warrant a Table or Figure. Some simple results are best stated in a single sentence, with data summarized parenthetically:

More information

Scientific Investigation Use and Interpret Graphs Promotion Benchmark 3 Lesson Review Student Copy

Scientific Investigation Use and Interpret Graphs Promotion Benchmark 3 Lesson Review Student Copy Scientific Investigation Use and Interpret Graphs Promotion Benchmark 3 Lesson Review Student Copy Vocabulary Data Table A place to write down and keep track of data collected during an experiment. Line

More information

Chapter 3: Probability (Part 1)

Chapter 3: Probability (Part 1) Chapter 3: Probability (Part 1) 3.1: Basic Concepts of Probability and Counting Types of Probability There are at least three different types of probability Subjective Probability is found through people

More information

INTRODUCTORY STATISTICS LECTURE 4 PROBABILITY

INTRODUCTORY STATISTICS LECTURE 4 PROBABILITY INTRODUCTORY STATISTICS LECTURE 4 PROBABILITY THE GREAT SCHLITZ CAMPAIGN 1981 Superbowl Broadcast of a live taste pitting Against key competitor: Michelob Subjects: 100 Michelob drinkers REF: SCHLITZBREWING.COM

More information

Data and its representation

Data and its representation 2 Data and its representation A microphone in the sidewalk would provide an eavesdropper with a cacophony of clocks, seemingly random like the noise from a Geiger counter. But the right kind of person

More information

Mathematics Expectations Page 1 Grade 04

Mathematics Expectations Page 1 Grade 04 Mathematics Expectations Page 1 Problem Solving Mathematical Process Expectations 4m1 develop, select, and apply problem-solving strategies as they pose and solve problems and conduct investigations, to

More information

CHAPTER 1 Exploring Data

CHAPTER 1 Exploring Data CHAPTER 1 Exploring Data 1.1 Analyzing Categorical Data The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Analyzing Categorical Data Learning Objectives

More information

A Visual Display. A graph is a visual display of information or data. This is a graph that shows a girl walking her dog. Communicating with Graphs

A Visual Display. A graph is a visual display of information or data. This is a graph that shows a girl walking her dog. Communicating with Graphs A Visual Display A graph is a visual display of information or data. This is a graph that shows a girl walking her dog. A Visual Display The horizontal axis, or the x-axis, measures time. Time is the independent

More information

!"#$%&'("&)*("*+,)-(#'.*/$'-0%$1$"&-!!!"#$%&'(!"!!"#$%"&&'()*+*!

!#$%&'(&)*(*+,)-(#'.*/$'-0%$1$&-!!!#$%&'(!!!#$%&&'()*+*! !"#$%&'("&)*("*+,)-(#'.*/$'-0%$1$"&-!!!"#$%&'(!"!!"#$%"&&'()*+*! In this Module, we will consider dice. Although people have been gambling with dice and related apparatus since at least 3500 BCE, amazingly

More information

DECISION TREE TUTORIAL

DECISION TREE TUTORIAL Kardi Teknomo DECISION TREE TUTORIAL Revoledu.com Decision Tree Tutorial by Kardi Teknomo Copyright 2008-2012 by Kardi Teknomo Published by Revoledu.com Online edition is available at Revoledu.com Last

More information

Key Stage 3 Mathematics. Common entrance revision

Key Stage 3 Mathematics. Common entrance revision Key Stage 3 Mathematics Key Facts Common entrance revision Number and Algebra Solve the equation x³ + x = 20 Using trial and improvement and give your answer to the nearest tenth Guess Check Too Big/Too

More information

MDM4U Some Review Questions

MDM4U Some Review Questions 1. Expand and simplify the following expressions. a) ( y 1) 7 b) ( 3x 2) 6 2x + 3 5 2. In the expansion of ( ) 9 MDM4U Some Review Questions, find a) the 6 th term b) 12 the term containing x n + 7 n +

More information

Page Solve all cards in library pocket. 2.Complete Multiple Representations of Number Puzzle (in front pocket)

Page Solve all cards in library pocket. 2.Complete Multiple Representations of Number Puzzle (in front pocket) Page 1 1. Solve all cards in library pocket 2.Complete Multiple Representations of Number Puzzle (in front pocket) Page 2 1. Write name of symbols under flaps on Comparison Symbols foldable 2. Cards in

More information

NUMERICAL DATA and OUTLIERS

NUMERICAL DATA and OUTLIERS ESSENTIAL MATHEMATICS 2 WEEK 2 NOTES AND EXERCISES NUMERICAL DATA and OUTLIERS Example Peter asked eight friends about the amount of pocket money they received each week. The results were: $20 $32 $32

More information

STAT Chapter 14 From Randomness to Probability

STAT Chapter 14 From Randomness to Probability STAT 203 - Chapter 14 From Randomness to Probability This is the topic that started my love affair with statistics, although I should mention that we will only skim the surface of Probability. Let me tell

More information

Variables. Lecture 13 Sections Wed, Sep 16, Hampden-Sydney College. Displaying Distributions - Quantitative.

Variables. Lecture 13 Sections Wed, Sep 16, Hampden-Sydney College. Displaying Distributions - Quantitative. - - Lecture 13 Sections 4.4.1-4.4.3 Hampden-Sydney College Wed, Sep 16, 2009 Outline - 1 2 3 4 5 6 7 Even-numbered - Exercise 4.7, p. 226. According to the National Center for Health Statistics, in the

More information

Sections Descriptive Statistics for Numerical Variables

Sections Descriptive Statistics for Numerical Variables Math 243 Sections 2.1.2-2.2.5 Descriptive Statistics for Numerical Variables A framework to describe quantitative data: Describe the Shape, Center and Spread, and Unusual Features Shape How is the data

More information

CPM Educational Program

CPM Educational Program CC COURSE 3 ETOOLS Table of Contents General etools... 4 Algebra Tiles (CPM)... 5 Pattern Tile & Dot Tool (CPM)... 8 Base Ten Blocks (CPM)...10 Area and Perimeter (CPM)...12 Desmos Graphing Calculator...15

More information

Unit Nine Precalculus Practice Test Probability & Statistics. Name: Period: Date: NON-CALCULATOR SECTION

Unit Nine Precalculus Practice Test Probability & Statistics. Name: Period: Date: NON-CALCULATOR SECTION Name: Period: Date: NON-CALCULATOR SECTION Vocabulary: Define each word and give an example. 1. discrete mathematics 2. dependent outcomes 3. series Short Answer: 4. Describe when to use a combination.

More information

Chapter 6: Descriptive Statistics

Chapter 6: Descriptive Statistics Chapter 6: Descriptive Statistics Problem (01): Make a frequency distribution table for the following data using 5 classes. 5 10 7 19 25 12 15 7 6 8 17 17 22 21 7 7 24 5 6 5 Problem (02): Annual Salaries

More information

Chapter Test Form A. mean median mode. 187 Holt Algebra 1. Name Date Class. Select the best answer.

Chapter Test Form A. mean median mode. 187 Holt Algebra 1. Name Date Class. Select the best answer. Select the best answer. 1. Use this bar graph to identify how many more candies are blue than red. A 3 B 6 C 9 D 15 Form A 2. Which type of graph would be best for displaying this data? Board Members Opinions

More information

Why Should We Care? More importantly, it is easy to lie or deceive people with bad plots

Why Should We Care? More importantly, it is easy to lie or deceive people with bad plots Elementary Plots Why Should We Care? Everyone uses plotting But most people ignore or are unaware of simple principles Default plotting tools (or default settings) are not always the best More importantly,

More information

A B C. 142 D. 96

A B C. 142 D. 96 Data Displays and Analysis 1. stem leaf 900 3 3 4 5 7 9 901 1 1 1 2 4 5 6 7 8 8 8 9 9 902 1 3 3 3 4 6 8 9 9 903 1 2 2 3 3 3 4 7 8 9 904 1 1 2 4 5 6 8 8 What is the range of the data shown in the stem-and-leaf

More information

PSY 307 Statistics for the Behavioral Sciences. Chapter 2 Describing Data with Tables and Graphs

PSY 307 Statistics for the Behavioral Sciences. Chapter 2 Describing Data with Tables and Graphs PSY 307 Statistics for the Behavioral Sciences Chapter 2 Describing Data with Tables and Graphs Class Progress To-Date Math Readiness Descriptives Midterm next Monday Frequency Distributions One of the

More information

TO PLOT OR NOT TO PLOT?

TO PLOT OR NOT TO PLOT? Graphic Examples This document provides examples of a number of graphs that might be used in understanding or presenting data. Comments with each example are intended to help you understand why the data

More information

Mrs. Ambre s Math Notebook

Mrs. Ambre s Math Notebook Mrs. Ambre s Math Notebook Almost everything you need to know for 7 th grade math Plus a little about 6 th grade math And a little about 8 th grade math 1 Table of Contents by Outcome Outcome Topic Page

More information

Introduction to Graphs

Introduction to Graphs Introduction to Graphs INTRODUCTION TO GRAPHS 231 CHAPTER 15 15.1 Introduction Have you seen graphs in the newspapers, television, magazines, books etc.? The purpose of the graph is to show numerical facts

More information

GCSE MATHEMATICS 43601H. Higher Tier Unit 1 Statistics and Number. Morning. (JUN H01) WMP/Jun16/E4

GCSE MATHEMATICS 43601H. Higher Tier Unit 1 Statistics and Number. Morning. (JUN H01) WMP/Jun16/E4 Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature GCSE H MATHEMATICS Higher Tier Unit 1 Statistics and Number Thursday 26 May 2016 Materials

More information

ESP 171 Urban and Regional Planning. Demographic Report. Due Tuesday, 5/10 at noon

ESP 171 Urban and Regional Planning. Demographic Report. Due Tuesday, 5/10 at noon ESP 171 Urban and Regional Planning Demographic Report Due Tuesday, 5/10 at noon Purpose The starting point for planning is an assessment of current conditions the answer to the question where are we now.

More information

MAT 1272 STATISTICS LESSON STATISTICS AND TYPES OF STATISTICS

MAT 1272 STATISTICS LESSON STATISTICS AND TYPES OF STATISTICS MAT 1272 STATISTICS LESSON 1 1.1 STATISTICS AND TYPES OF STATISTICS WHAT IS STATISTICS? STATISTICS STATISTICS IS THE SCIENCE OF COLLECTING, ANALYZING, PRESENTING, AND INTERPRETING DATA, AS WELL AS OF MAKING

More information