vs. relative cumulative frequency

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "vs. relative cumulative frequency"

Transcription

1 Variable - what we are measuring Quantitative - numerical where mathematical operations make sense. These have UNITS Categorical - puts individuals into categories Numbers don't always mean Quantitative... Frequency vs. Relative Frequency vs. cumulative frequency vs. relative cumulative frequency

2 Two-Way Tables and Marginal Distributions Distributions are of VARIABLES, not individual values!!! To examine a marginal distribution, 1) Use the data in the table to calculate the marginal distribution (in percents) of the row or column totals. 2) Make a graph to display the marginal distribution. Note: Percents are often more informative than counts, especially when comparing groups of different sizes.

3 A Conditional Distribution of a variable describes the values of that variable among individuals who have a specidic value of another variable. To examine or compare conditional distributions, 1) Select the row(s) or column(s) of interest. 2) Use the data in the table to calculate the conditional distribution (in percents) of the row(s) or column(s). 3) Make a graph to display the conditional distribution. Use a side-by-side bar graph or segmented bar graph to compare distributions. There are three main ways to display quantitative data: -Dotplots -Stemplots -split -back-to-back -Histograms

4 How to create a dotplot: 1) Draw a horizontal axis (a number line) and label it with the variable name. 2) Scale the axis from the minimum to the maximum value. 3) Mark a dot above the location on the horizontal axis corresponding to each data value. How to make a stemplot: 1) Separate each observation into a stem (all but the Linal digit) and a leaf (the Linal digit). 2) Write all possible stems from the smallest to the largest in a vertical column and draw a vertical line to the right of the column. 3) Write each leaf in the row to the right of its stem. Arrange the leaves in increasing order out from the stem. 4) Provide a key that explains in context what the stems and leaves represent. Splitting Stems and Back-to-Back Stemplots When data values are bunched up, we can get a better picture of the distribution by splitting stems. Two distributions of the same quantitative variable can be compared using a back-to-back stemplot with common stems. How to make a histogram: 1) Divide the range of data into classes of equal width. 2) Find the count (frequency) or percent (relative frequency) of individuals in each class. 3) Label and scale your axes and draw the histogram. The height of the bar equals its frequency. Adjacent bars should touch, unless a class contains no individuals.

5 (Using your calculator) 1. Enter the data into L 1. (press the STAT button, highlight EDIT and choice #1 and press ENTER). 2. Turn on the stat-plot. (press 2 nd and the Y= button to select STAT PLOT, highlight choice #1 and press ENTER, select ON and press enter, select the histogram under TYPE and press enter) 3. Adjust your window. (press the WINDOW button; enter your minimum value (smaller than the smallest observation) for Xmin, enter your maximum value (larger than the largest observation) for Xmax, enter the length of your classes for Xscl (i.e. what you are counting by to get from Xmin to Xmax), adjust your Ymin = 0 and Ymax appropriately) OR Go to ZOOM and select #9ZoomStat Using Histograms Wisely Here are several cautions based on common mistakes students make when using histograms. 1) Don t confuse histograms and bar graphs. 2) Don t use counts (in a frequency table) or percents (in a relative frequency table) as data. 3) Use percents instead of counts on the vertical axis when comparing distributions with different numbers of observations. 4) Just because a graph looks nice, it s not necessarily a meaningful display of data.

6 Relative Frequency Histogram This type of histogram displays proportions or percents rather than counts. Cumulative Frequency Histogram (Ogive) Examine the Distribution Look for the OVERALL pattern and any striking DEVIATIONS from that pattern Describe the shape, center, and spread and determine if there are any outliers (don't forget your SOCS!) Shape Skewed or symmetric? Symmetric - the left and right hand sides of the histogram are approximately mirror images of each other Skewed right - the right side of the histogram extends MUCH farther out than the left side ("tail" goes to the right) Skewed left - the left side of the histogram extends MUCH farther out than the right side ("tail" goes to the left) Uniform distribution - doesn't appear to have any modes - pretty much the same height across the whole distribution

7 Measures of Center We have two ways of numerically measuring the center of a quantitative data set - the Median and the Mean. Both of these can be considered to give us the "average" of a data set. Some issues with notation: There are two ways to write the mean The choice depends on whether you are talking about the entire POPULATION of interest or just a SAMPLE from the entire population. Unless you are 100% positive you have the data from the ENTIRE population, use μ. If you see being used, then the data must be from the entire population. Comparing the Mean and Median In a symmetric distribution the mean and median are VERY close together. In a skewed distribution the mean will be greater than or less than the median, depending upon the skew. The larger the difference between the two, the greater the skew. If the mean is greater than the median, the distribution is skewed right If the mean is smaller than the median, the distribution is skewed left

8 Measures of Spread As with measures of center, we have two different ways to measure the spread in quantitative data - quartiles and IQR and the standard deviation and variance. Standard Deviation - (written as σ - population or s - sample) and Variance - (written as σ 2 - population or s 2 - sample) The standard deviation gives a measure of the "average" distance that data points fall from the mean s = 0 ONLY when there is NO SPREAD - this only happens when every observation is the SAME otherwise s > 0 The more spread out the observations are the greater s will be s has the same units of measurement as the observations do Like we saw with the mean, s is not resistant Choosing measures of center of spread 1. FIVE-NUMBER SUMMARY or Median and IQR The Five-Number Summary gives a quick summary of both the center and spread of your data. Some people also consider giving the IQR with the Median to be a suflicient measure of center and spread. It contains the Minimum observation, Q 1, the Median, Q 3, and the Maximum observation. Use when the distribution is skewed or has strong outliers Used to create another graphical display of quantitative data - the BOXPLOT 2. The Mean and Standard Deviation Use for reasonably symmetric distribution that are free of outliers

9 Boxplot A graph of the Dive-number summary A central box spans the quartiles, Q 1 and Q 3 with a line marking the median, M. Lines extend from the edge of the box ( Q 1 and Q 3 ) out to the minimum and maximum values, respectively. IF THERE ARE OUTLIERS: DO NOT extend the lines to outliers. Only extend to the minimum and maximum values that are NOT outliers. Mark outliers with an asterisk. How to use the calculator for numerical summaries and boxplots: (Using your calculator) 1. Enter the data into L 1. (press the STAT button, highlight EDIT and choice #1 and press ENTER). For Numerical Summaries: 2. Press the STAT button, arrow over to CALC 3. Select 1-Var Stats 4. You will get a list of values on your main screen. Arrow through to find all necessary values. mean standard deviation Minimum Observation Q 1 Median Q 3 Maximum For Boxplot: 2. Turn on the stat-plot. (press 2 nd and the Y= button to select STAT PLOT, highlight choice #1 and press ENTER, select ON and press enter) 3. Select the FIRST boxplot option under "TYPE" - this one graphs outliers 4. Adjust your window. (ZOOM, select #9ZoomStat)

10

Chapter 2: Exploring Data with Graphs and Numerical Summaries. Graphical Measures- Graphs are used to describe the shape of a data set.

Chapter 2: Exploring Data with Graphs and Numerical Summaries. Graphical Measures- Graphs are used to describe the shape of a data set. Page 1 of 16 Chapter 2: Exploring Data with Graphs and Numerical Summaries Graphical Measures- Graphs are used to describe the shape of a data set. Section 1: Types of Variables In general, variable can

More information

Chapter 2. Objectives. Tabulate Qualitative Data. Frequency Table. Descriptive Statistics: Organizing, Displaying and Summarizing Data.

Chapter 2. Objectives. Tabulate Qualitative Data. Frequency Table. Descriptive Statistics: Organizing, Displaying and Summarizing Data. Objectives Chapter Descriptive Statistics: Organizing, Displaying and Summarizing Data Student should be able to Organize data Tabulate data into frequency/relative frequency tables Display data graphically

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

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

Chapter 2 - Graphical Summaries of Data

Chapter 2 - Graphical Summaries of Data Chapter 2 - Graphical Summaries of Data Data recorded in the sequence in which they are collected and before they are processed or ranked are called raw data. Raw data is often difficult to make sense

More information

TYPES OF DATA TYPES OF VARIABLES

TYPES OF DATA TYPES OF VARIABLES TYPES OF DATA Univariate data Examines the distribution features of one variable. Bivariate data Explores the relationship between two variables. Univariate and bivariate analysis will be revised separately.

More information

The Big Picture. Describing Data: Categorical and Quantitative Variables Population. Descriptive Statistics. Community Coalitions (n = 175)

The Big Picture. Describing Data: Categorical and Quantitative Variables Population. Descriptive Statistics. Community Coalitions (n = 175) Describing Data: Categorical and Quantitative Variables Population The Big Picture Sampling Statistical Inference Sample Exploratory Data Analysis Descriptive Statistics In order to make sense of data,

More information

Chapter 1: Looking at Data Distributions. Dr. Nahid Sultana

Chapter 1: Looking at Data Distributions. Dr. Nahid Sultana Chapter 1: Looking at Data Distributions Dr. Nahid Sultana Chapter 1: Looking at Data Distributions 1.1 Displaying Distributions with Graphs 1.2 Describing Distributions with Numbers 1.3 Density Curves

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

Creating a Box and Whisker Plot TI-73

Creating a Box and Whisker Plot TI-73 TI-73 1. Press É. 2. Press 3. If data is in the columns, you will need to clear the data by moving the cursor to the top with the arrow keys until L 1 is highlighted, press then e. Repeat to clear all

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

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

A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes

A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes together with the number of data values from the set that

More information

Visual Display of Data in Stata

Visual Display of Data in Stata Lab 2 Visual Display of Data in Stata In this lab we will try to understand data not only through numerical summaries, but also through graphical summaries. The data set consists of a number of variables

More information

Lecture I. Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions.

Lecture I. Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions. Lecture 1 1 Lecture I Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions. It is a process consisting of 3 parts. Lecture

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

Descriptive Statistics. Frequency Distributions and Their Graphs 2.1. Frequency Distributions. Chapter 2

Descriptive Statistics. Frequency Distributions and Their Graphs 2.1. Frequency Distributions. Chapter 2 Chapter Descriptive Statistics.1 Frequency Distributions and Their Graphs Frequency Distributions A frequency distribution is a table that shows classes or intervals of data with a count of the number

More information

1.3 Measuring Center & Spread, The Five Number Summary & Boxplots. Describing Quantitative Data with Numbers

1.3 Measuring Center & Spread, The Five Number Summary & Boxplots. Describing Quantitative Data with Numbers 1.3 Measuring Center & Spread, The Five Number Summary & Boxplots Describing Quantitative Data with Numbers 1.3 I can n Calculate and interpret measures of center (mean, median) in context. n Calculate

More information

Chapter 3: Data Description Numerical Methods

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,

More information

CHAPTER 3 AVERAGES AND VARIATION

CHAPTER 3 AVERAGES AND VARIATION CHAPTER 3 AVERAGES AND VARIATION ONE-VARIABLE STATISTICS (SECTIONS 3.1 AND 3.2 OF UNDERSTANDABLE STATISTICS) The TI-83 Plus and TI-84 Plus graphing calculators support many of the common descriptive measures

More information

F. Farrokhyar, MPhil, PhD, PDoc

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

More information

+ Chapter 1 Exploring Data

+ Chapter 1 Exploring Data Chapter 1 Exploring Data Introduction: Data Analysis: Making Sense of Data 1.1 Analyzing Categorical Data 1.2 Displaying Quantitative Data with Graphs 1.3 Describing Quantitative Data with Numbers Introduction

More information

Chapter 2 Summarizing and Graphing Data

Chapter 2 Summarizing and Graphing Data Chapter 2 Summarizing and Graphing Data 2-1 Review and Preview 2-2 Frequency Distributions 2-3 Histograms 2-4 Graphs that Enlighten and Graphs that Deceive Preview Characteristics of Data 1. Center: A

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

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

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

More information

Copyright 2013 by Laura Schultz. All rights reserved. Page 1 of 7

Copyright 2013 by Laura Schultz. All rights reserved. Page 1 of 7 Using Your TI-NSpire Calculator: Descriptive Statistics Dr. Laura Schultz Statistics I This handout is intended to get you started using your TI-Nspire graphing calculator for statistical applications.

More information

Desciptive Statistics Qualitative data Quantitative data Graphical methods Numerical methods

Desciptive Statistics Qualitative data Quantitative data Graphical methods Numerical methods Desciptive Statistics Qualitative data Quantitative data Graphical methods Numerical methods Qualitative data Data are classified in categories Non numerical (although may be numerically codified) Elements

More information

MAKING A BOX AND WHISKER PLOT USING YOUR TI-83 CALCULATOR

MAKING A BOX AND WHISKER PLOT USING YOUR TI-83 CALCULATOR MAKING A BOX AND WHISKER PLOT USING YOUR TI-83 CALCULATOR Shaunna Knepp Step 1: Turn on the calculator! Step 2: Input the following data into L1: 12, 34, 27, 29, 15, 38, 22, 19, 31, 36 To do this press

More information

Math Lesson 3: Displaying Data Graphically

Math Lesson 3: Displaying Data Graphically Math Lesson 3: Displaying Data Graphically Hawaii DOE Content Standards: Math standard: [Data Analysis, Statistics, and Probability]-Pose questions and collect, organize, and represent data to answer those

More information

Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 4-1

Copyright 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Slide 4-1 Slide 4-1 Chapter 4 Displaying Quantitative Data Dealing With a Lot of Numbers Summarizing the data will help us when we look at large sets of quantitative data. Without summaries of the data, it s hard

More information

Technology Step-by-Step Using StatCrunch

Technology Step-by-Step Using StatCrunch Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate

More information

Data Mining Part 2. Data Understanding and Preparation 2.1 Data Understanding Spring 2010

Data Mining Part 2. Data Understanding and Preparation 2.1 Data Understanding Spring 2010 Data Mining Part 2. and Preparation 2.1 Spring 2010 Instructor: Dr. Masoud Yaghini Introduction Outline Introduction Measuring the Central Tendency Measuring the Dispersion of Data Graphic Displays References

More information

Center: Finding the Median. Median. Spread: Home on the Range. Center: Finding the Median (cont.)

Center: Finding the Median. Median. Spread: Home on the Range. Center: Finding the Median (cont.) Center: Finding the Median When we think of a typical value, we usually look for the center of the distribution. For a unimodal, symmetric distribution, it s easy to find the center it s just the center

More information

a. mean b. interquartile range c. range d. median

a. mean b. interquartile range c. range d. median 3. Since 4. The HOMEWORK 3 Due: Feb.3 1. A set of data are put in numerical order, and a statistic is calculated that divides the data set into two equal parts with one part below it and the other part

More information

III. GRAPHICAL METHODS

III. GRAPHICAL METHODS Pie Charts and Bar Charts: III. GRAPHICAL METHODS Pie charts and bar charts are used for depicting frequencies or relative frequencies. We compare examples of each using the same data. Sources: AT&T (1961)

More information

Chapter 2: Frequency Distributions and Graphs (or making pretty tables and pretty pictures)

Chapter 2: Frequency Distributions and Graphs (or making pretty tables and pretty pictures) Chapter 2: Frequency Distributions and Graphs (or making pretty tables and pretty pictures) Example: Titanic passenger data is available for 1310 individuals for 14 variables, though not all variables

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

Minitab Guide. This packet contains: A Friendly Guide to Minitab. Minitab Step-By-Step

Minitab Guide. This packet contains: A Friendly Guide to Minitab. Minitab Step-By-Step Minitab Guide This packet contains: A Friendly Guide to Minitab An introduction to Minitab; including basic Minitab functions, how to create sets of data, and how to create and edit graphs of different

More information

Stats on the TI-84+ 9/15/2014. Stats on the TI-84+

Stats on the TI-84+ 9/15/2014. Stats on the TI-84+ Topics Stats on the TI-84+ Notation Problems and Errors Lists and Matrices Enter a new list Edit an existing list Clear a list Enter or edit a matrix Descriptive statistics Find the mean or median Find

More information

SPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)

SPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer

More information

Chapter 2. The Normal Distribution

Chapter 2. The Normal Distribution Chapter 2 The Normal Distribution Lesson 2-1 Density Curve Review Graph the data Calculate a numerical summary of the data Describe the shape, center, spread and outliers of the data Histogram with Curve

More information

MTH 140 Statistics Videos

MTH 140 Statistics Videos MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative

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

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

Numerical Summaries. Chapter 2. Mean or Average. Median (M) Basic Practice of Statistics - 3rd Edition

Numerical Summaries. Chapter 2. Mean or Average. Median (M) Basic Practice of Statistics - 3rd Edition Numerical Summaries Chapter 2 Describing Distributions with Numbers Center of the data mean median Variation range quartiles (interquartile range) variance standard deviation BPS - 5th Ed. Chapter 2 1

More information

Section 3.1 Measures of Central Tendency: Mode, Median, and Mean

Section 3.1 Measures of Central Tendency: Mode, Median, and Mean Section 3.1 Measures of Central Tendency: Mode, Median, and Mean One number can be used to describe the entire sample or population. Such a number is called an average. There are many ways to compute averages,

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

TI-82 / TI-83 Summary of Commands

TI-82 / TI-83 Summary of Commands TI-82 / TI-83 Summary of Commands Getting Started Turn on the calculator 1: Press the [On] button, located at the bottom right corner of the calculator 2: If necessary you can adjust the contrast: - to

More information

Mathematics. GSE Algebra II/ Advanced Algebra Unit 7: Inferences & Conclusions from Data

Mathematics. GSE Algebra II/ Advanced Algebra Unit 7: Inferences & Conclusions from Data Georgia Standards of Excellence Curriculum Frameworks Mathematics GSE Algebra II/ Advanced Algebra Unit 7: Inferences & Conclusions from Data These materials are for nonprofit educational purposes only.

More information

We will use the following data sets to illustrate measures of center. DATA SET 1 The following are test scores from a class of 20 students:

We will use the following data sets to illustrate measures of center. DATA SET 1 The following are test scores from a class of 20 students: MODE The mode of the sample is the value of the variable having the greatest frequency. Example: Obtain the mode for Data Set 1 77 For a grouped frequency distribution, the modal class is the class having

More information

Home Runs, Statistics, and Probability

Home Runs, Statistics, and Probability NATIONAL MATH + SCIENCE INITIATIVE Mathematics American League AL Central AL West AL East National League NL West NL East Level 7 th grade in a unit on graphical displays Connection to AP* Graphical Display

More information

WHICH TYPE OF GRAPH SHOULD YOU CHOOSE?

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

More information

Box-and-Whisker Plots

Box-and-Whisker Plots Mathematics Box-and-Whisker Plots About this Lesson This is a foundational lesson for box-and-whisker plots (boxplots), a graphical tool used throughout statistics for displaying data. During the lesson,

More information

Instructions for Using the Calculator for Statistics

Instructions for Using the Calculator for Statistics Descriptive Statistics Entering Data General Statistics mean, median, stdev, quartiles, etc Five Number Summary Box Plot with Outliers Histogram Distributions: Normal, Student t Area under a normal curve

More information

Chapter 6: Continuous Probability Distributions

Chapter 6: Continuous Probability Distributions Chapter 6: Continuous Probability Distributions Chapter 5 dealt with probability distributions arising from discrete random variables. Mostly that chapter focused on the binomial experiment. There are

More information

Obtaining Summary Statistics with SPSS. Math 260

Obtaining Summary Statistics with SPSS. Math 260 Obtaining Summary Statistics with SPSS Math 260 Open the New York Travel Times data from Exercise 2.2 File eg02-03.sav. Your data should have n=20 rows Explore Procedure Select Analyze Descriptive Statistics

More information

Content DESCRIPTIVE STATISTICS. Data & Statistic. Statistics. Example: DATA VS. STATISTIC VS. STATISTICS

Content DESCRIPTIVE STATISTICS. Data & Statistic. Statistics. Example: DATA VS. STATISTIC VS. STATISTICS Content DESCRIPTIVE STATISTICS Dr Najib Majdi bin Yaacob MD, MPH, DrPH (Epidemiology) USM Unit of Biostatistics & Research Methodology School of Medical Sciences Universiti Sains Malaysia. Introduction

More information

M 225 Test 1 A Name (1 point) SHOW YOUR WORK FOR FULL CREDIT!

M 225 Test 1 A Name (1 point) SHOW YOUR WORK FOR FULL CREDIT! M 225 Test 1 A Name (1 point) SHOW YOUR WORK FOR FULL CREDIT! Problem Max. Points Your Points 1-14 14 15 3 16 5 17 4 18 4 19 11 20 9 21 8 22 16 Total 75 1 Multiple choice questions (1 point each) 1. Look

More information

2. Describing Data. We consider 1. Graphical methods 2. Numerical methods 1 / 56

2. Describing Data. We consider 1. Graphical methods 2. Numerical methods 1 / 56 2. Describing Data We consider 1. Graphical methods 2. Numerical methods 1 / 56 General Use of Graphical and Numerical Methods Graphical methods can be used to visually and qualitatively present data and

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

TI 83/84 Graphing Calculator Manual. Stephen M. Kokoska

TI 83/84 Graphing Calculator Manual. Stephen M. Kokoska TI 83/84 Graphing Calculator Manual Stephen M. Kokoska February 28, 2006 2 Contents 1 Introduction to the TI 83 Plus 1 2... Single Variable Data 9 2.1 Graphic Presentation of Data................. 9 2.2

More information

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

Descriptive Statistics

Descriptive Statistics Chapter 2 Descriptive Statistics 2.1 Descriptive Statistics 1 2.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Display data graphically and interpret graphs:

More information

Slides by. JOHN LOUCKS St. Edward s University

Slides by. JOHN LOUCKS St. Edward s University s by JOHN LOUCKS St. Edward s University 1 Chapter 2, Part A Descriptive Statistics: Tabular and Graphical Presentations Summarizing Qualitative Data Summarizing Quantitative Data 2 Summarizing Qualitative

More information

Graphical and Tabular. Summarization of Data OPRE 6301

Graphical and Tabular. Summarization of Data OPRE 6301 Graphical and Tabular Summarization of Data OPRE 6301 Introduction and Re-cap... Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that useful information

More information

1.5 NUMERICAL REPRESENTATION OF DATA (Sample Statistics)

1.5 NUMERICAL REPRESENTATION OF DATA (Sample Statistics) 1.5 NUMERICAL REPRESENTATION OF DATA (Sample Statistics) As well as displaying data graphically we will often wish to summarise it numerically particularly if we wish to compare two or more data sets.

More information

Using SPSS, Chapter 2: Descriptive Statistics

Using SPSS, Chapter 2: Descriptive Statistics 1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,

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

How Does My TI-84 Do That

How Does My TI-84 Do That How Does My TI-84 Do That A guide to using the TI-84 for statistics Austin Peay State University Clarksville, Tennessee How Does My TI-84 Do That A guide to using the TI-84 for statistics Table of Contents

More information

How to interpret scientific & statistical graphs

How to interpret scientific & statistical graphs How to interpret scientific & statistical graphs Theresa A Scott, MS Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott 1 A brief introduction Graphics:

More information

AP Statistics Chapter 1 Test - Multiple Choice

AP Statistics Chapter 1 Test - Multiple Choice AP Statistics Chapter 1 Test - Multiple Choice Name: 1. The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph, we may conclude

More information

Graphing Calculator. The Viewing Rectangle. Xscl. Xmin

Graphing Calculator. The Viewing Rectangle. Xscl. Xmin s or graphing software packages for computers are referred to as graphing utilities or graphers. Below you will find the viewing rectangle. 1 The meaning of the terms is demonstrated at right. This is

More information

The right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median

The right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median CONDENSED LESSON 2.1 Box Plots In this lesson you will create and interpret box plots for sets of data use the interquartile range (IQR) to identify potential outliers and graph them on a modified box

More information

909 responses responded via telephone survey in U.S. Results were shown by political affiliations (show graph on the board)

909 responses responded via telephone survey in U.S. Results were shown by political affiliations (show graph on the board) 1 2-1 Overview Chapter 2: Learn the methods of organizing, summarizing, and graphing sets of data, ultimately, to understand the data characteristics: Center, Variation, Distribution, Outliers, Time. (Computer

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

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

Numerical Measures of Central Tendency

Numerical Measures of Central Tendency Numerical Measures of Central Tendency Often, it is useful to have special numbers which summarize characteristics of a data set These numbers are called descriptive statistics or summary statistics. A

More information

Introduction to Stata: Graphic Displays of Data and Correlation

Introduction to Stata: Graphic Displays of Data and Correlation Math 143 Lab #1 Introduction to Stata: Graphic Displays of Data and Correlation Overview Thus far in the course, you have produced most of our graphical displays by hand, calculating summaries and correlations

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

Cents and the Central Limit Theorem Overview of Lesson GAISE Components Common Core State Standards for Mathematical Practice

Cents and the Central Limit Theorem Overview of Lesson GAISE Components Common Core State Standards for Mathematical Practice Cents and the Central Limit Theorem Overview of Lesson In this lesson, students conduct a hands-on demonstration of the Central Limit Theorem. They construct a distribution of a population and then construct

More information

NUMERICAL AND GRAPHICAL SUMMARIES OF QUANTITATIVE DATA: FREQUENCY DISTRIBUTIONS AND HISTOGRAMS

NUMERICAL AND GRAPHICAL SUMMARIES OF QUANTITATIVE DATA: FREQUENCY DISTRIBUTIONS AND HISTOGRAMS Frequency (Number of Plants) Relative Frequency (Number of Plants) NUMERICAL AND GRAPHICAL SUMMARIES OF QUANTITATIVE DATA: FREQUENCY DISTRIBUTIONS AND HISTOGRAMS Numerical data may be presented individually

More information

Organizing & Graphing Data

Organizing & Graphing Data AGSC 320 Statistical Methods Organizing & Graphing Data 1 DATA Numerical representation of reality Raw data: Data recorded in the sequence in which they are collected and before any processing Qualitative

More information

GRAPHING ON THE TI CALCULATORS. 1. Enter your equation. Equation must be solved for y: y = 3x - 4, y = x 2 +7x -1, etc.

GRAPHING ON THE TI CALCULATORS. 1. Enter your equation. Equation must be solved for y: y = 3x - 4, y = x 2 +7x -1, etc. GRAPHING ON THE TI CALCULATORS 1. Enter your equation. Equation must be solved for y: y = 3x - 4, y = x 2 +7x -1, etc. TI-83: Use y= button under screen, at left. When entering equation, use the X,T,θ

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 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

Math Tools Cell Phone Plans

Math Tools Cell Phone Plans NATIONAL PARTNERSHIP FOR QUALITY AFTERSCHOOL LEARNING www.sedl.org/afterschool/toolkits Math Tools Cell Phone Plans..............................................................................................

More information

SPECIAL FEATURES OF THE TI-83 PLUS CALCULATOR

SPECIAL FEATURES OF THE TI-83 PLUS CALCULATOR SPECIAL FEATURES OF THE TI-83 PLUS CALCULATOR The TI-83 Plus uses Flash technology: This will let you update to future software versions from the Internet, without buying a new calculator. 184k bytes of

More information

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

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

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

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

Graphical methods for presenting data

Graphical methods for presenting data Chapter 2 Graphical methods for presenting data 2.1 Introduction We have looked at ways of collecting data and then collating them into tables. Frequency tables are useful methods of presenting data; they

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 3 (b) 51

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 3 (b) 51 Chapter 2- Problems to look at Use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class. 1) Height (in inches) 1)

More information

Chapter 7 What to do when you have the data

Chapter 7 What to do when you have the data Chapter 7 What to do when you have the data We saw in the previous chapters how to collect data. We will spend the rest of this course looking at how to analyse the data that we have collected. Stem and

More information

1 Measures for location and dispersion of a sample

1 Measures for location and dispersion of a sample Statistical Geophysics WS 2008/09 7..2008 Christian Heumann und Helmut Küchenhoff Measures for location and dispersion of a sample Measures for location and dispersion of a sample In the following: Variable

More information

Statistics Chapter 3 Averages and Variations

Statistics Chapter 3 Averages and Variations Statistics Chapter 3 Averages and Variations Measures of Central Tendency Average a measure of the center value or central tendency of a distribution of values. Three types of average: Mode Median Mean

More information

Descriptive Statistics. Understanding Data: Categorical Variables. Descriptive Statistics. Dataset: Shellfish Contamination

Descriptive Statistics. Understanding Data: Categorical Variables. Descriptive Statistics. Dataset: Shellfish Contamination Descriptive Statistics Understanding Data: Dataset: Shellfish Contamination Location Year Species Species2 Method Metals Cadmium (mg kg - ) Chromium (mg kg - ) Copper (mg kg - ) Lead (mg kg - ) Mercury

More information

Academic Support Center. Using the TI-83/84+ Graphing Calculator PART II

Academic Support Center. Using the TI-83/84+ Graphing Calculator PART II Academic Support Center Using the TI-83/84+ Graphing Calculator PART II Designed and Prepared by The Academic Support Center Revised June 2012 1 Using the Graphing Calculator (TI-83+ or TI-84+) Table of

More information

How Do You Measure Up?

How Do You Measure Up? . Name Date A c t i v i t y 3 How Do You Measure Up? Height Arm Span Does increasing the amount of time practicing a sport increase performance levels in that sport? Does decreasing the speed at which

More information

Introductory Statistics Notes

Introductory Statistics Notes Introductory Statistics Notes Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone: (205) 348-4431 Fax: (205) 348-8648 August

More information

In this course, we will consider the various possible types of presentation of data and justification for their use in given situations.

In this course, we will consider the various possible types of presentation of data and justification for their use in given situations. PRESENTATION OF DATA 1.1 INTRODUCTION Once data has been collected, it has to be classified and organised in such a way that it becomes easily readable and interpretable, that is, converted to information.

More information