Statistics Chapter 2

Size: px
Start display at page:

Download "Statistics Chapter 2"

Transcription

1 Statistics Chapter 2 Frequency Tables A frequency table organizes quantitative data. partitions data into classes (intervals). shows how many data values are in each class. Test Score Number of Students A frequency table partitions data into classes or intervals and shows how many data values are in each class. The classes or intervals are constructed so that each data falls into exactly one class. If the frequency is converted into percentage of individuals then we have a relative frequency table. Data Classes and Class Frequency Class: an interval of values. Example: 61 x 70 Frequency: the number of data values that fall within a class. Four data fall within the class 61 x 70. Relative Frequency: the proportion of data values that fall within a class. 11.7% of the data fall within the class 61 x 70. Structure of a Data Class A data class is basically an interval on a number line. It has: A lower limit a and an upper limit b. A width. A lower boundary and an upper boundary (integer data). A midpoint. 1 P a g e

2 Example - If a = 60 and b = 69 for integer data, what is the value of the lower boundary? a). 60 b) c). 9 d) Constructing Data Classes Find the class width largest data values smallest data values class width Desired number of classes Increase the computed value to the next higher whole number. Find the class limits. The lower limit of the leftmost class is set equal to the smallest value in the data set. The lower class limit is the lowest data values that can fit in a class. The upper class limit is the highest data values that can fit in a class. The class width is the difference between the lower class limit of one class and the lower class limit of the next class. Find the class boundaries (integer data). Subtract 0.5 from the lower class limit and add 0.5 to the upper class limit. Example - For a certain data set, the minimum value is 25 and the maximum value is 58. If you wish to partition the data into 5 classes, what would be the class width? a). 5 b). 6 c). 7 d). 8 Building a Frequency Table Find the class width, class limits, and class boundaries of the data. Use Tally marks to count the data in each class. Record the frequencies (and relative frequencies if desired) on the table. class frequency Relative Frequency total of all frequency 2 P a g e

3 Example - A task force to encourage car pooling conducted a study of one-way commuting distances of workers in the downtown Dallas area. A random sample of 60 of these workers was taken. The commuting distances of the workers in the sample in miles are as follows Make a frequency table for these data with six classes. 3 P a g e

4 Histograms Histogram graphical summary of a frequency table. Uses bars to plot the data classes versus the class frequencies. A graphical representation of this information can be useful. A histogram uses bars to represent each class, where the width of the bar is the class width and the height of the bar is the class frequency. Making a Histogram Make a frequency table. Place class boundaries on horizontal axis. Place frequencies on vertical axis. For each class, draw a bar with height equal to the class frequency Example Use the data from the commuting distances of workers in the downtown Dallas area, to make a histogram. 4 P a g e

5 Distribution Shapes Critical Thinking A bimodal distribution shape might indicate that the data are from two different populations. Outliers data values that are very different from other values in the data set. Outliers may indicate data recording errors. Outliers in a data set are data values that are very different from other measurements in the data set. They many indicate that an error occurred or the data may be an actual data point. Do you include Outliers in statistical analysis? It depends, any decision about outliers should include people what are familiar with the field and the purpose of the study. Exploratory Data Analysis EDA is the process of learning about a data set by creating graphs. EDA specifically looks for patterns and trends in the data. EDA also identifies extreme values. Graphical Displays represent the data. induce the viewer to think about the substance of the graphic. should avoid distorting the message of the data. 5 P a g e

6 Bar Graphs Used for qualitative or quantitative data. Can be vertical or horizontal. Bars are uniformly spaced and have equal widths. Length/height of bars indicate counts or percentages of the variable. Good practice requires including titles and units and labeling axes. Below is an example of a cluster bar graph because there are two bars for year of birth. One bar represents the life expectancy of men and the other represents the life expectancy of women. The height of each bar represents the life expectancy in years. Pareto Charts A bar chart with two specific features: Heights of bars represent frequencies. Bars are vertical and are ordered from tallest to shortest. All graphs need the following: Title, both axis labeled, both axis have a scale. 6 P a g e

7 Example The data below represents student s responses for reasons for being late for the months of September October. Make a bar Pareto graph showing the causes for lateness. Cause Frequency Snoozing after alarm goes off 15 Car trouble 5 Too long of breakfast 13 Last-minute studying 20 Finding something to wear 8 Talking too long with roommate 9 Other 3 Circle Graphs/Pie Charts Used for qualitative data Wedges of the circle represent proportions of the data that share a common characteristic. Good practice requires including a title and either wedge labels or legend. 7 P a g e

8 Example The following data comes from a survey reported in USA Today. How long do we spend talking on the phone in the evening (after 5pm)? 500 people were surveyed. Time Number Fractional Part Percentage Number of Degrees <30 Minutes / * 360 = min. 1 hour 83 83/ * 360 = 60 >1 hour 121 Total Fill in the above table, and draw a circle graph representing the data. Time-Series Shows data measurements in chronological order. Data are plotted in order of occurrence at regular intervals over a period of time. Example Suppose you have been in the walking/jogging exercise program for 20 weeks, and for each week you have recorded the distance you covered in 30 minutes. Week Distance Make a Time series graph for the above table 8 P a g e

9 Critical Thinking Which type of graph to use? Bar graphs are useful for quantitative or qualitative data. Pareto charts identify the frequency in decreasing order. Circle graphs display how a total is dispersed into several categories. Time-series graphs display how data change over time. Example - What type of graph would be best for showing the ice cream flavor preferences of a group of 100 children? a). Histogram c). Time series graph b). Pareto graph d). Circle graph Stem and Leaf Plots Displays the distribution of the data while maintaining the actual data values. Each data value is split into a stem and a leaf. A stem-and-leaf display is a method of exploratory data analysis that is used to rank-order and arrange data into groups. Stem-and-leaf displays organize numbers in much the same way alphabetization organizes words. 9 P a g e

10 Stem and Leaf Plot Construction Critical Thinking- By looking at the stem-and-leaf display sideways, we can see the distribution shape of the data. Large gaps between stems containing leaves, especially at the top or bottom, suggest the existence of outliers. Watch the outliers are they data errors or simply unusual data values? 10 P a g e

11 Example For the below table of data points from the winning scores of the conference championship games over the last 35 years make a stem-and-leaf plot of the data P a g e

Chapter 2: Frequency Distributions and Graphs

Chapter 2: Frequency Distributions and Graphs Chapter 2: Frequency Distributions and Graphs Learning Objectives Upon completion of Chapter 2, you will be able to: Organize the data into a table or chart (called a frequency distribution) Construct

More information

Summarizing and Displaying Categorical Data

Summarizing and Displaying Categorical Data Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency

More information

Exploratory data analysis (Chapter 2) Fall 2011

Exploratory data analysis (Chapter 2) Fall 2011 Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,

More information

Variables. Exploratory Data Analysis

Variables. Exploratory Data Analysis Exploratory Data Analysis Exploratory Data Analysis involves both graphical displays of data and numerical summaries of data. A common situation is for a data set to be represented as a matrix. There is

More information

Diagrams and Graphs of Statistical Data

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

More information

Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics

Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),

More information

Statistics and Probability

Statistics and Probability Statistics and Probability TABLE OF CONTENTS 1 Posing Questions and Gathering Data. 2 2 Representing Data. 7 3 Interpreting and Evaluating Data 13 4 Exploring Probability..17 5 Games of Chance 20 6 Ideas

More information

Visualizing Data. Contents. 1 Visualizing Data. Anthony Tanbakuchi Department of Mathematics Pima Community College. Introductory Statistics Lectures

Visualizing Data. Contents. 1 Visualizing Data. Anthony Tanbakuchi Department of Mathematics Pima Community College. Introductory Statistics Lectures Introductory Statistics Lectures Visualizing Data Descriptive Statistics I Department of Mathematics Pima Community College Redistribution of this material is prohibited without written permission of the

More information

Northumberland Knowledge

Northumberland Knowledge Northumberland Knowledge Know Guide How to Analyse Data - November 2012 - This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about

More information

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

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

More information

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

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)

More information

Descriptive Statistics

Descriptive Statistics Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web

More information

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

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

More information

Appendix 2.1 Tabular and Graphical Methods Using Excel

Appendix 2.1 Tabular and Graphical Methods Using Excel Appendix 2.1 Tabular and Graphical Methods Using Excel 1 Appendix 2.1 Tabular and Graphical Methods Using Excel The instructions in this section begin by describing the entry of data into an Excel spreadsheet.

More information

Statistics Revision Sheet Question 6 of Paper 2

Statistics Revision Sheet Question 6 of Paper 2 Statistics Revision Sheet Question 6 of Paper The Statistics question is concerned mainly with the following terms. The Mean and the Median and are two ways of measuring the average. sumof values no. of

More information

Week 1. Exploratory Data Analysis

Week 1. Exploratory Data Analysis Week 1 Exploratory Data Analysis Practicalities This course ST903 has students from both the MSc in Financial Mathematics and the MSc in Statistics. Two lectures and one seminar/tutorial per week. Exam

More information

Practice#1(chapter1,2) Name

Practice#1(chapter1,2) Name Practice#1(chapter1,2) Name Solve the problem. 1) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics? A) inferential statistics

More information

STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI

STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI STATS8: Introduction to Biostatistics Data Exploration Babak Shahbaba Department of Statistics, UCI Introduction After clearly defining the scientific problem, selecting a set of representative members

More information

Drawing a histogram using Excel

Drawing a histogram using Excel Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to

More information

Exercise 1.12 (Pg. 22-23)

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.

More information

Sta 309 (Statistics And Probability for Engineers)

Sta 309 (Statistics And Probability for Engineers) Instructor: Prof. Mike Nasab Sta 309 (Statistics And Probability for Engineers) Chapter 2 Organizing and Summarizing Data Raw Data: When data are collected in original form, they are called raw data. The

More information

Descriptive Statistics

Descriptive Statistics CHAPTER Descriptive Statistics.1 Distributions and Their Graphs. More Graphs and Displays.3 Measures of Central Tendency. Measures of Variation Case Study. Measures of Position Uses and Abuses Real Statistics

More information

Common Tools for Displaying and Communicating Data for Process Improvement

Common Tools for Displaying and Communicating Data for Process Improvement Common Tools for Displaying and Communicating Data for Process Improvement Packet includes: Tool Use Page # Box and Whisker Plot Check Sheet Control Chart Histogram Pareto Diagram Run Chart Scatter Plot

More information

Visualizations. Cyclical data. Comparison. What would you like to show? Composition. Simple share of total. Relative and absolute differences matter

Visualizations. Cyclical data. Comparison. What would you like to show? Composition. Simple share of total. Relative and absolute differences matter Visualizations Variable width chart Table or tables with embedded charts Bar chart horizontal Circular area chart per item Many categories Cyclical data Non-cyclical data Single or few categories Many

More information

Exploratory Data Analysis

Exploratory Data Analysis Exploratory Data Analysis Johannes Schauer johannes.schauer@tugraz.at Institute of Statistics Graz University of Technology Steyrergasse 17/IV, 8010 Graz www.statistics.tugraz.at February 12, 2008 Introduction

More information

CRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide

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

More information

Mathematics. Probability and Statistics Curriculum Guide. Revised 2010

Mathematics. Probability and Statistics Curriculum Guide. Revised 2010 Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction

More information

Exploratory Data Analysis

Exploratory Data Analysis Exploratory Data Analysis Learning Objectives: 1. After completion of this module, the student will be able to explore data graphically in Excel using histogram boxplot bar chart scatter plot 2. After

More information

CSU, Fresno - Institutional Research, Assessment and Planning - Dmitri Rogulkin

CSU, Fresno - Institutional Research, Assessment and Planning - Dmitri Rogulkin My presentation is about data visualization. How to use visual graphs and charts in order to explore data, discover meaning and report findings. The goal is to show that visual displays can be very effective

More information

Intro to Statistics 8 Curriculum

Intro to Statistics 8 Curriculum Intro to Statistics 8 Curriculum Unit 1 Bar, Line and Circle Graphs Estimated time frame for unit Big Ideas 8 Days... Essential Question Concepts Competencies Lesson Plans and Suggested Resources Bar graphs

More information

Section 1.1 Exercises (Solutions)

Section 1.1 Exercises (Solutions) Section 1.1 Exercises (Solutions) HW: 1.14, 1.16, 1.19, 1.21, 1.24, 1.25*, 1.31*, 1.33, 1.34, 1.35, 1.38*, 1.39, 1.41* 1.14 Employee application data. The personnel department keeps records on all employees

More information

Chapter 1: Exploring Data

Chapter 1: Exploring Data Chapter 1: Exploring Data Chapter 1 Review 1. As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student

More information

Lecture 1: Review and Exploratory Data Analysis (EDA)

Lecture 1: Review and Exploratory Data Analysis (EDA) Lecture 1: Review and Exploratory Data Analysis (EDA) Sandy Eckel seckel@jhsph.edu Department of Biostatistics, The Johns Hopkins University, Baltimore USA 21 April 2008 1 / 40 Course Information I Course

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. Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

More information

4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"

4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: What do the data look like? Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses

More information

Section 1.3 Exercises (Solutions)

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

More information

Tutorial 3: Graphics and Exploratory Data Analysis in R Jason Pienaar and Tom Miller

Tutorial 3: Graphics and Exploratory Data Analysis in R Jason Pienaar and Tom Miller Tutorial 3: Graphics and Exploratory Data Analysis in R Jason Pienaar and Tom Miller Getting to know the data An important first step before performing any kind of statistical analysis is to familiarize

More information

Chapter 4 Displaying Quantitative Data

Chapter 4 Displaying Quantitative Data Chapter 4 Displaying Quantitative Data Chapter 4 Displaying Quantitative Data 27 1. Statistics in print. Answers will vary. 2. Not a histogram. Answers will vary. 3. Thinking about shape. a) The distribution

More information

AP * Statistics Review. Descriptive Statistics

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

More information

HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

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

More information

Pie Charts. proportion of ice-cream flavors sold annually by a given brand. AMS-5: Statistics. Cherry. Cherry. Blueberry. Blueberry. Apple.

Pie Charts. proportion of ice-cream flavors sold annually by a given brand. AMS-5: Statistics. Cherry. Cherry. Blueberry. Blueberry. Apple. Graphical Representations of Data, Mean, Median and Standard Deviation In this class we will consider graphical representations of the distribution of a set of data. The goal is to identify the range of

More information

Describing, Exploring, and Comparing Data

Describing, Exploring, and Comparing Data 24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter

More information

Variable: characteristic that varies from one individual to another in the population

Variable: characteristic that varies from one individual to another in the population Goals: Recognize variables as: Qualitative or Quantitative Discrete Continuous Study Ch. 2.1, # 1 13 : Prof. G. Battaly, Westchester Community College, NY Study Ch. 2.1, # 1 13 Variable: characteristic

More information

Continuous Random Variables

Continuous Random Variables Chapter 5 Continuous Random Variables 5.1 Continuous Random Variables 1 5.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Recognize and understand continuous

More information

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

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

More information

Classify the data as either discrete or continuous. 2) An athlete runs 100 meters in 10.5 seconds. 2) A) Discrete B) Continuous

Classify the data as either discrete or continuous. 2) An athlete runs 100 meters in 10.5 seconds. 2) A) Discrete B) Continuous Chapter 2 Overview Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify as categorical or qualitative data. 1) A survey of autos parked in

More information

Basic Tools for Process Improvement

Basic Tools for Process Improvement What is a Histogram? A Histogram is a vertical bar chart that depicts the distribution of a set of data. Unlike Run Charts or Control Charts, which are discussed in other modules, a Histogram does not

More information

Exploratory Spatial Data Analysis

Exploratory Spatial Data Analysis Exploratory Spatial Data Analysis Part II Dynamically Linked Views 1 Contents Introduction: why to use non-cartographic data displays Display linking by object highlighting Dynamic Query Object classification

More information

DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS

DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi - 110 012 seema@iasri.res.in 1. Descriptive Statistics Statistics

More information

Demographics of Atlanta, Georgia:

Demographics of Atlanta, Georgia: Demographics of Atlanta, Georgia: A Visual Analysis of the 2000 and 2010 Census Data 36-315 Final Project Rachel Cohen, Kathryn McKeough, Minnar Xie & David Zimmerman Ethnicities of Atlanta Figure 1: From

More information

A Picture Really Is Worth a Thousand Words

A Picture Really Is Worth a Thousand Words 4 A Picture Really Is Worth a Thousand Words Difficulty Scale (pretty easy, but not a cinch) What you ll learn about in this chapter Why a picture is really worth a thousand words How to create a histogram

More information

Interpreting Data in Normal Distributions

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,

More information

Consolidation of Grade 3 EQAO Questions Data Management & Probability

Consolidation of Grade 3 EQAO Questions Data Management & Probability Consolidation of Grade 3 EQAO Questions Data Management & Probability Compiled by Devika William-Yu (SE2 Math Coach) GRADE THREE EQAO QUESTIONS: Data Management and Probability Overall Expectations DV1

More information

MBA 611 STATISTICS AND QUANTITATIVE METHODS

MBA 611 STATISTICS AND QUANTITATIVE METHODS MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain

More information

Dimension: Data Handling Module: Organization and Representation of data Unit: Construction and Interpretation of Simple Diagrams and Graphs

Dimension: Data Handling Module: Organization and Representation of data Unit: Construction and Interpretation of Simple Diagrams and Graphs Topic: Stem and Leaf Diagrams S1 Topic 13 Level: Key Stage 3 Dimension: Data Handling Module: Organization and Representation of data Unit: Construction and Interpretation of Simple Diagrams and Graphs

More information

STAB22 section 1.1. total = 88(200/100) + 85(200/100) + 77(300/100) + 90(200/100) + 80(100/100) = 176 + 170 + 231 + 180 + 80 = 837,

STAB22 section 1.1. total = 88(200/100) + 85(200/100) + 77(300/100) + 90(200/100) + 80(100/100) = 176 + 170 + 231 + 180 + 80 = 837, STAB22 section 1.1 1.1 Find the student with ID 104, who is in row 5. For this student, Exam1 is 95, Exam2 is 98, and Final is 96, reading along the row. 1.2 This one involves a careful reading of the

More information

SECTION 2-1: OVERVIEW SECTION 2-2: FREQUENCY DISTRIBUTIONS

SECTION 2-1: OVERVIEW SECTION 2-2: FREQUENCY DISTRIBUTIONS SECTION 2-1: OVERVIEW Chapter 2 Describing, Exploring and Comparing Data 19 In this chapter, we will use the capabilities of Excel to help us look more carefully at sets of data. We can do this by re-organizing

More information

Data Exploration Data Visualization

Data Exploration Data Visualization Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select

More information

Darton College Online Math Center Statistics. Chapter 2: Frequency Distributions and Graphs. Presenting frequency distributions as graphs

Darton College Online Math Center Statistics. Chapter 2: Frequency Distributions and Graphs. Presenting frequency distributions as graphs Chapter : Frequency Distributions and Graphs 1 Presenting frequency distributions as graphs In a statistical study, researchers gather data that describe the particular variable under study. To present

More information

Describing Data: Frequency Distributions and Graphic Presentation

Describing Data: Frequency Distributions and Graphic Presentation Chapter 2 Describing Data: Frequency Distributions and Graphic Presentation GOALS When you have completed this chapter, you will be able to: Organize raw data into a frequency distribution Produce a histogram,

More information

2: Frequency Distributions

2: Frequency Distributions 2: Frequency Distributions Stem-and-Leaf Plots (Stemplots) The stem-and-leaf plot (stemplot) is an excellent way to begin an analysis. Consider this small data set: 218 426 53 116 309 504 281 270 246 523

More information

Key Concept. Density Curve

Key Concept. Density Curve MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 6 Normal Probability Distributions 6 1 Review and Preview 6 2 The Standard Normal Distribution 6 3 Applications of Normal

More information

Algebra 1 Course Information

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

More information

Chapter 4. Probability Distributions

Chapter 4. Probability Distributions Chapter 4 Probability Distributions Lesson 4-1/4-2 Random Variable Probability Distributions This chapter will deal the construction of probability distribution. By combining the methods of descriptive

More information

Determine whether the data are qualitative or quantitative. 8) the colors of automobiles on a used car lot Answer: qualitative

Determine whether the data are qualitative or quantitative. 8) the colors of automobiles on a used car lot Answer: qualitative Name Score: Math 227 Review Exam 1 Chapter 2& Fall 2011 ********************************************************************************************************************** SHORT ANSWER. Show work on

More information

Exploratory Data Analysis. Psychology 3256

Exploratory Data Analysis. Psychology 3256 Exploratory Data Analysis Psychology 3256 1 Introduction If you are going to find out anything about a data set you must first understand the data Basically getting a feel for you numbers Easier to find

More information

Keystone National Middle School Math Level 7 Placement Exam

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

More information

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics. Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

More information

Performance evaluation

Performance evaluation Visualization of experimental data Jean-Marc Vincent MESCAL-INRIA Project Laboratoire d Informatique de Grenoble Universities of Grenoble, France {Jean-Marc.Vincent}@imag.fr This work was partially supported

More information

2 Describing, Exploring, and

2 Describing, Exploring, and 2 Describing, Exploring, and Comparing Data This chapter introduces the graphical plotting and summary statistics capabilities of the TI- 83 Plus. First row keys like \ R (67$73/276 are used to obtain

More information

Lesson 2: Constructing Line Graphs and Bar Graphs

Lesson 2: Constructing Line Graphs and Bar Graphs Lesson 2: Constructing Line Graphs and Bar Graphs Selected Content Standards Benchmarks Assessed: D.1 Designing and conducting statistical experiments that involve the collection, representation, and analysis

More information

Chapter 32 Histograms and Bar Charts. Chapter Table of Contents VARIABLES...470 METHOD...471 OUTPUT...472 REFERENCES...474

Chapter 32 Histograms and Bar Charts. Chapter Table of Contents VARIABLES...470 METHOD...471 OUTPUT...472 REFERENCES...474 Chapter 32 Histograms and Bar Charts Chapter Table of Contents VARIABLES...470 METHOD...471 OUTPUT...472 REFERENCES...474 467 Part 3. Introduction 468 Chapter 32 Histograms and Bar Charts Bar charts are

More information

Directions for Frequency Tables, Histograms, and Frequency Bar Charts

Directions for Frequency Tables, Histograms, and Frequency Bar Charts Directions for Frequency Tables, Histograms, and Frequency Bar Charts Frequency Distribution Quantitative Ungrouped Data Dataset: Frequency_Distributions_Graphs-Quantitative.sav 1. Open the dataset containing

More information

Density Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties:

Density Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: Density Curve A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: 1. The total area under the curve must equal 1. 2. Every point on the curve

More information

Introduction to Environmental Statistics. The Big Picture. Populations and Samples. Sample Data. Examples of sample data

Introduction to Environmental Statistics. The Big Picture. Populations and Samples. Sample Data. Examples of sample data A Few Sources for Data Examples Used Introduction to Environmental Statistics Professor Jessica Utts University of California, Irvine jutts@uci.edu 1. Statistical Methods in Water Resources by D.R. Helsel

More information

Introducing the. Tools for. Continuous Improvement

Introducing the. Tools for. Continuous Improvement Introducing the Tools for Continuous Improvement The Concept In today s highly competitive business environment it has become a truism that only the fittest survive. Organisations invest in many different

More information

AP Statistics Solutions to Packet 2

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

More information

Chapter 6: Constructing and Interpreting Graphic Displays of Behavioral Data

Chapter 6: Constructing and Interpreting Graphic Displays of Behavioral Data Chapter 6: Constructing and Interpreting Graphic Displays of Behavioral Data Chapter Focus Questions What are the benefits of graphic display and visual analysis of behavioral data? What are the fundamental

More information

Bar Graphs and Dot Plots

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

More information

Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics

Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This

More information

SPSS Manual for Introductory Applied Statistics: A Variable Approach

SPSS Manual for Introductory Applied Statistics: A Variable Approach SPSS Manual for Introductory Applied Statistics: A Variable Approach John Gabrosek Department of Statistics Grand Valley State University Allendale, MI USA August 2013 2 Copyright 2013 John Gabrosek. All

More information

Unit 9. Unit 10. Unit 11. Unit 12. Introduction Busy Ant Maths Year 2 Medium-Term Plans. Number - Geometry - Position & direction

Unit 9. Unit 10. Unit 11. Unit 12. Introduction Busy Ant Maths Year 2 Medium-Term Plans. Number - Geometry - Position & direction Busy Ant Maths Year Medium-Term Plans Unit 9 Geometry - Position & direction Unit 0 ( Temperature) Unit Statistics Unit Fractions (time) 8 Busy Ant Maths Year Medium-Term Plans Introduction Unit Geometry

More information

Iris Sample Data Set. Basic Visualization Techniques: Charts, Graphs and Maps. Summary Statistics. Frequency and Mode

Iris Sample Data Set. Basic Visualization Techniques: Charts, Graphs and Maps. Summary Statistics. Frequency and Mode Iris Sample Data Set Basic Visualization Techniques: Charts, Graphs and Maps CS598 Information Visualization Spring 2010 Many of the exploratory data techniques are illustrated with the Iris Plant data

More information

6. Decide which method of data collection you would use to collect data for the study (observational study, experiment, simulation, or survey):

6. Decide which method of data collection you would use to collect data for the study (observational study, experiment, simulation, or survey): MATH 1040 REVIEW (EXAM I) Chapter 1 1. For the studies described, identify the population, sample, population parameters, and sample statistics: a) The Gallup Organization conducted a poll of 1003 Americans

More information

The Comparisons. Grade Levels Comparisons. Focal PSSM K-8. Points PSSM CCSS 9-12 PSSM CCSS. Color Coding Legend. Not Identified in the Grade Band

The Comparisons. Grade Levels Comparisons. Focal PSSM K-8. Points PSSM CCSS 9-12 PSSM CCSS. Color Coding Legend. Not Identified in the Grade Band Comparison of NCTM to Dr. Jim Bohan, Ed.D Intelligent Education, LLC Intel.educ@gmail.com The Comparisons Grade Levels Comparisons Focal K-8 Points 9-12 pre-k through 12 Instructional programs from prekindergarten

More information

Introduction to Statistics for Psychology. Quantitative Methods for Human Sciences

Introduction to Statistics for Psychology. Quantitative Methods for Human Sciences Introduction to Statistics for Psychology and Quantitative Methods for Human Sciences Jonathan Marchini Course Information There is website devoted to the course at http://www.stats.ox.ac.uk/ marchini/phs.html

More information

Descriptive Statistics. Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion

Descriptive Statistics. Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Descriptive Statistics Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Statistics as a Tool for LIS Research Importance of statistics in research

More information

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 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

More information

AMS 7L LAB #2 Spring, 2009. Exploratory Data Analysis

AMS 7L LAB #2 Spring, 2009. Exploratory Data Analysis AMS 7L LAB #2 Spring, 2009 Exploratory Data Analysis Name: Lab Section: Instructions: The TAs/lab assistants are available to help you if you have any questions about this lab exercise. If you have any

More information

Unit 19: Probability Models

Unit 19: Probability Models Unit 19: Probability Models Summary of Video Probability is the language of uncertainty. Using statistics, we can better predict the outcomes of random phenomena over the long term from the very complex,

More information

Lecture 2: Descriptive Statistics and Exploratory Data Analysis

Lecture 2: Descriptive Statistics and Exploratory Data Analysis Lecture 2: Descriptive Statistics and Exploratory Data Analysis Further Thoughts on Experimental Design 16 Individuals (8 each from two populations) with replicates Pop 1 Pop 2 Randomly sample 4 individuals

More information

6.4 Normal Distribution

6.4 Normal Distribution Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under

More information

Name: Date: Use the following to answer questions 2-3:

Name: Date: Use the following to answer questions 2-3: Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student

More information

Common Core Unit Summary Grades 6 to 8

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

More information

Descriptive Statistics Practice Problems (Total 6 marks) (Total 8 marks) (Total 8 marks) (Total 8 marks) (1)

Descriptive Statistics Practice Problems (Total 6 marks) (Total 8 marks) (Total 8 marks) (Total 8 marks) (1) Descriptive Statistics Practice Problems 1. The age in months at which a child first starts to walk is observed for a random group of children from a town in Brazil. The results are 14.3, 11.6, 12.2, 14.,

More information

Data exploration with Microsoft Excel: univariate analysis

Data exploration with Microsoft Excel: univariate analysis Data exploration with Microsoft Excel: univariate analysis Contents 1 Introduction... 1 2 Exploring a variable s frequency distribution... 2 3 Calculating measures of central tendency... 16 4 Calculating

More information

BNG 202 Biomechanics Lab. Descriptive statistics and probability distributions I

BNG 202 Biomechanics Lab. Descriptive statistics and probability distributions I BNG 202 Biomechanics Lab Descriptive statistics and probability distributions I Overview The overall goal of this short course in statistics is to provide an introduction to descriptive and inferential

More information

Bar Charts, Histograms, Line Graphs & Pie Charts

Bar Charts, Histograms, Line Graphs & Pie Charts Bar Charts and Histograms Bar charts and histograms are commonly used to represent data since they allow quick assimilation and immediate comparison of information. Normally the bars are vertical, but

More information

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques

More information

Gestation Period as a function of Lifespan

Gestation Period as a function of Lifespan This document will show a number of tricks that can be done in Minitab to make attractive graphs. We work first with the file X:\SOR\24\M\ANIMALS.MTP. This first picture was obtained through Graph Plot.

More information