Lecture 2: Data Description
|
|
|
- Annabel Sharp
- 5 years ago
- Views:
Transcription
1 Lecture 2: Data Description Graham Elliott December 2008 Graham Elliott () December / 32
2 The Basic Objective The basic problem facing any analysis of data or presentation of results of some study - formal or informal - is a tradeo between A. Being able to get all the information out of a set of data, which one can potentially do if they have all the data, and B. Being able to actually see the information in the data, which is quite hard if you have large sets of data. Graham Elliott () December / 32
3 Some Examples Investing in a Mutual Fund. Barrons lists past returns (1,5 yr) but it runs many pages. Graham Elliott () December / 32
4 Some Examples Investing in a Mutual Fund. Barrons lists past returns (1,5 yr) but it runs many pages. Scholastic Acheivement Thousands of students in each cohort, how do you report how well they do vs other countries etc? Graham Elliott () December / 32
5 Some Examples Investing in a Mutual Fund. Barrons lists past returns (1,5 yr) but it runs many pages. Scholastic Acheivement Thousands of students in each cohort, how do you report how well they do vs other countries etc? Typical income of a US resident Are income gaps widening? Cannot tell easily from a full printout of IRS tax forms Graham Elliott () December / 32
6 What do we do? Descriptive Statistics: We examine informal methods of reducing and clarifying information in data. We regard these methods as informal as we do not give precise probabilistic answers to questions, but we move towards answers just the same. (and when we later add the formality, we use the same or similar statistics). Graham Elliott () December / 32
7 Outline Graphs with a Single Variable Graham Elliott () December / 32
8 Outline Graphs with a Single Variable Summary Statistics Graham Elliott () December / 32
9 Outline Graphs with a Single Variable Summary Statistics Graphs with Multiple Attributes Graham Elliott () December / 32
10 Outline Graphs with a Single Variable Summary Statistics Graphs with Multiple Attributes Summary Statistics with Multiple Attributes Graham Elliott () December / 32
11 1. Frequency Tables and Graphs e.g. Mutual Funds problem. The easiest way to reduce the information is to consider not the exact returns but classes of returns, i.e. if Firm 1 has a return of 20.1% and rm 2 has 21.2% we may lump them together and consider this as both being between 20 and 22%. We can then count up how many companies enter each class, and graph the classes versus the number of mutual funds in each class. Graham Elliott () December / 32
12 1. Frequency Tables and Graphs I have data on 194 mutual funds. The returns range from 10% to 38.6%. Take bins of every 5 from 9.99 to All the observations below into the bin etc, and all the ones over into the More bin (so the bin is etc). I get the following summary of the data in more manageable form. Graham Elliott () December / 32
13 Frequency Table Bin x < 10 10<= x <15 15<= x <20 20<= x <25 25<= x <30 30<= x <35 35<= x <40 40<= x <45 45<= x <50 x >=50 Frequency Graham Elliott () December / 32
14 Frequency Table We can read o quite quickly most funds are around the 25-40% return range (over half in fact), there are a few lousy performers and a few quite good performers. From the alphabetical listing in the newspaper such results are just not obvious. Frequency table since each number is an estimate/calculation of the frequency of members of that group. Graham Elliott () December / 32
15 Histogram An even clearer way to present these numbers is to graph them. Mutual Fund Returns number return Graham Elliott () December / 32
16 Histogram A key to drawing these carefully is to ensure that the areas of each block are compatible. Here I did this by making each category the same width (since they are for equal blocks of 5). Heights are also constructed so 50 is twice 25 etc. Not doing this leads to a visual misrepresentation of the data. Graham Elliott () December / 32
17 Histogram Consider changing this to percentages, i.e. divide the height by n=194. We can make the widths equal to one, which makes the area under the curve add up to one. (the reason is that since proportions add to one, and base is one, then base times height is one). Graham Elliott () December / 32
18 Histogram We can redraw the graph Frequency Graph Fequency More Category (<) Graham Elliott () December / 32
19 Categorical Data Categorical data is when the x value has no obvious ordering. Frequency graphs are still useful, either as we did them or alternatively as pie charts. The same ideas in terms of making areas proportional still matter, although it is basically impossible to fail at this for a pie chart. Graham Elliott () December / 32
20 Pie Charts US Fuel Consumption Graham Elliott () December / 32
21 Misrepresenting Data with Histograms It is important to mainstream media to trash younger generations (older readers love it!). The National Center for Education Statistics reports Trends in International Mathematics and Science Study (TIMMS). It is a cross country comparison. Graham Elliott () December / 32
22 International Science and Mathematics This summary appeared in the Atlantic Monthly. Graham Elliott () December / 32
23 International Science and Mathematics When we get the scale correct, a di erent picture emerges. Graham Elliott () December / 32
24 Picture Histograms The problem here is that the areas are not kept proportional (From Tufte (1983, p. 69) ). Graham Elliott () December / 32
25 Cumulative Frequency Tables Rather than compute for each bin, i.e. compute numbers where 10<=x<15, could compute the cumulative number of observations below any value. In this case we have entries like x<15, which simply sums all the values up to that point in the regular frequency table. Graham Elliott () December / 32
26 Cumulative Frequency Tables Bin x < 10 10<= x <15 15<= x <20 20<= x <25 25<= x <30 30<= x <35 35<= x <40 40<= x <45 45<= x <50 x >=50 Frequency Cumulative Frequency Graham Elliott () December / 32
27 Cumulative Frequency Graph We can obviousy graph this as well Cumulative Distribution % % 90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00%.00% return Graham Elliott () December / 32
28 Box Plots These are useful when we have Numerical data that is comparably across a few categories. e.g. Mutual Funds investing problem. Large cap, medium or small cap? Growth or Value orientation? Here we have six categories of numerical return data. Graham Elliott () December / 32
29 Boxplots Annual Return by Type Return Min 5 25% 0 Median % Type Max Graham Elliott () December / 32
30 Time Series Plots When data is ordered by time, it is often much more insightful to graph it against time. This is straightforward, however it can still lead to misleading results if you play around with the scaling. e.g. Manatee deaths in Florida Graham Elliott () December / 32
31 Manatee Deaths in Florida Manatees Killed 60 Number Killed Year Graham Elliott () December / 32
32 Power Boat Enthusiast Graph Manatees Killed 100 Number Killed Year Graham Elliott () December / 32
33 Environmentalist Graph Manatees Killed Number Killed Year Graham Elliott () December / 32
34 New Policing and Crime Homicides per 100, Year Graham Elliott () December / 32
35 Why the drop? The men and women of the NYPD are principally responsible for the dramatic crime decline that continues today... Bratton (1998) Graham Elliott () December / 32
36 Far reaching e ects Homicides per 100, Year Graham Elliott () December / 32
37 Very far reaching e ects Graham Elliott () December / 32
Lecture 3: Data Description - Multiple Attributes
Lecture 3: Data Description - Multiple Attributes Graham Elliott December 2008 Graham Elliott () December 2008 1 / 25 The Basic Objective Most interesting problems relate not to means etc. but to relationships
Summarising Data. Summarising Data. Examples of Types of Data. Types of Data
Summarising Data Summarising Data Mark Lunt Arthritis Research UK Epidemiology Unit University of Manchester Today we will consider Different types of data Appropriate ways to summarise these data 17/10/2017
Math 2311 Bekki George Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment
Math 2311 Bekki George bekki@math.uh.edu Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment Class webpage: http://www.math.uh.edu/~bekki/math2311.html Math 2311 Class
STAB22 section 1.3 and Chapter 1 exercises
STAB22 section 1.3 and Chapter 1 exercises 1.101 Go up and down two times the standard deviation from the mean. So 95% of scores will be between 572 (2)(51) = 470 and 572 + (2)(51) = 674. 1.102 Same idea
Prof. Thistleton MAT 505 Introduction to Probability Lecture 3
Sections from Text and MIT Video Lecture: Sections 2.1 through 2.5 http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systemsanalysis-and-applied-probability-fall-2010/video-lectures/lecture-1-probability-models-and-axioms/
2 Exploring Univariate Data
2 Exploring Univariate Data A good picture is worth more than a thousand words! Having the data collected we examine them to get a feel for they main messages and any surprising features, before attempting
Stat 101 Exam 1 - Embers Important Formulas and Concepts 1
1 Chapter 1 1.1 Definitions Stat 101 Exam 1 - Embers Important Formulas and Concepts 1 1. Data Any collection of numbers, characters, images, or other items that provide information about something. 2.
Math Take Home Quiz on Chapter 2
Math 116 - Take Home Quiz on Chapter 2 Show the calculations that lead to the answer. Due date: Tuesday June 6th Name Time your class meets Provide an appropriate response. 1) A newspaper surveyed its
Lecture 1: Review and Exploratory Data Analysis (EDA)
Lecture 1: Review and Exploratory Data Analysis (EDA) Ani Manichaikul amanicha@jhsph.edu 16 April 2007 1 / 40 Course Information I Office hours For questions and help When? I ll announce this tomorrow
Introduction to Descriptive Statistics
Introduction to Descriptive Statistics 17.871 Types of Variables ~Nominal (Quantitative) Nominal (Qualitative) categorical Ordinal Interval or ratio Describing data Moment Non-mean based measure Center
Stratification Analysis. Summarizing an Output Variable by a Grouping Input Variable
Stratification Analysis Summarizing an Output Variable by a Grouping Input Variable 1 Topics I. Stratification Analysis II. Stratification Analysis Tools Stratification Tables Bar Graphs / Pie Charts III.
Graphical and Tabular Methods in Descriptive Statistics. Descriptive Statistics
Graphical and Tabular Methods in Descriptive Statistics MATH 3342 Section 1.2 Descriptive Statistics n Graphs and Tables n Numerical Summaries Sections 1.3 and 1.4 1 Why graph data? n The amount of data
1. In a statistics class with 136 students, the professor records how much money each
so shows the data collected. student has in his or her possession during the first class of the semester. The histogram 1. In a statistics class with 136 students, the professor records how much money
Indices 2.2. Do you think the difference between this rate and the one from 1996 to 2001 is significant? Why or why not?
2.2 Indices In the previous section, you used tables and graphs of frequencies to summarize data. Indices are another way to summarize data and recognize trends. An index relates the value of a variable
A LEVEL MATHEMATICS ANSWERS AND MARKSCHEMES SUMMARY STATISTICS AND DIAGRAMS. 1. a) 45 B1 [1] b) 7 th value 37 M1 A1 [2]
![A LEVEL MATHEMATICS ANSWERS AND MARKSCHEMES SUMMARY STATISTICS AND DIAGRAMS. 1. a) 45 B1 [1] b) 7 th value 37 M1 A1 [2]](/thumbs/81/83043398.jpg "A LEVEL MATHEMATICS ANSWERS AND MARKSCHEMES SUMMARY STATISTICS AND DIAGRAMS. 1. a) 45 B1 [1] b) 7 th value 37 M1 A1 [2]")
1. a) 45 [1] b) 7 th value 37 [] n c) LQ : 4 = 3.5 4 th value so LQ = 5 3 n UQ : 4 = 9.75 10 th value so UQ = 45 IQR = 0 f.t. d) Median is closer to upper quartile Hence negative skew [] Page 1 . a) Orders
the display, exploration and transformation of the data are demonstrated and biases typically encountered are highlighted.
1 Insurance data Generalized linear modeling is a methodology for modeling relationships between variables. It generalizes the classical normal linear model, by relaxing some of its restrictive assumptions,
Lecture 2 Describing Data
Lecture 2 Describing Data Thais Paiva STA 111 - Summer 2013 Term II July 2, 2013 Lecture Plan 1 Types of data 2 Describing the data with plots 3 Summary statistics for central tendency and spread 4 Histograms
Exploring Data and Graphics
Exploring Data and Graphics Rick White Department of Statistics, UBC Graduate Pathways to Success Graduate & Postdoctoral Studies November 13, 2013 Outline Summarizing Data Types of Data Visualizing Data
Mathematics 1000, Winter 2008
Mathematics 1000, Winter 2008 Lecture 4 Sheng Zhang Department of Mathematics Wayne State University January 16, 2008 Announcement Monday is Martin Luther King Day NO CLASS Today s Topics Curves and Histograms
Lecture Week 4 Inspecting Data: Distributions
Lecture Week 4 Inspecting Data: Distributions Introduction to Research Methods & Statistics 2013 2014 Hemmo Smit So next week No lecture & workgroups But Practice Test on-line (BB) Enter data for your
STAT 157 HW1 Solutions
STAT 157 HW1 Solutions http://www.stat.ucla.edu/~dinov/courses_students.dir/10/spring/stats157.dir/ Problem 1. 1.a: (6 points) Determine the Relative Frequency and the Cumulative Relative Frequency (fill
Describing Data: One Quantitative Variable
STAT 250 Dr. Kari Lock Morgan The Big Picture Describing Data: One Quantitative Variable Population Sampling SECTIONS 2.2, 2.3 One quantitative variable (2.2, 2.3) Statistical Inference Sample Descriptive
NOTES TO CONSIDER BEFORE ATTEMPTING EX 2C BOX PLOTS
NOTES TO CONSIDER BEFORE ATTEMPTING EX 2C BOX PLOTS A box plot is a pictorial representation of the data and can be used to get a good idea and a clear picture about the distribution of the data. It shows
Construct a stem-and-leaf plot. Choose the correct answer below. D B A C. 0 79
1. The data to the right represent the number of grams of fat in breakfast meals offered at a certain restaurant. onstruct a stem-and-leaf plot and describe the shape of the distribution. 17 2 29 7 22
DATA SUMMARIZATION AND VISUALIZATION
APPENDIX DATA SUMMARIZATION AND VISUALIZATION PART 1 SUMMARIZATION 1: BUILDING BLOCKS OF DATA ANALYSIS 294 PART 2 PART 3 PART 4 VISUALIZATION: GRAPHS AND TABLES FOR SUMMARIZING AND ORGANIZING DATA 296
STAT:2010 Statistical Methods and Computing. Using density curves to describe the distribution of values of a quantitative
STAT:10 Statistical Methods and Computing Normal Distributions Lecture 4 Feb. 6, 17 Kate Cowles 374 SH, 335-0727 kate-cowles@uiowa.edu 1 2 Using density curves to describe the distribution of values of
y axis: Frequency or Density x axis: binned variable bins defined by: lower & upper limits midpoint bin width = upper-lower Histogram Frequency
Part 3 Displaying Data Histogram requency y axis: requency or Density x axis: binned variable bins defined by: lower & upper limits midpoint bin width = upper-lower 0 5 10 15 20 25 Density 0.000 0.002
UNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences. STAB22H3 Statistics I Duration: 1 hour and 45 minutes
UNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences STAB22H3 Statistics I Duration: 1 hour and 45 minutes Last Name: First Name: Student number: Aids allowed: - One handwritten
ATO Data Analysis on SMSF and APRA Superannuation Accounts
DATA61 ATO Data Analysis on SMSF and APRA Superannuation Accounts Zili Zhu, Thomas Sneddon, Alec Stephenson, Aaron Minney CSIRO Data61 CSIRO e-publish: EP157035 CSIRO Publishing: EP157035 Submitted on
Descriptive Statistics (Devore Chapter One)
Descriptive Statistics (Devore Chapter One) 1016-345-01 Probability and Statistics for Engineers Winter 2010-2011 Contents 0 Perspective 1 1 Pictorial and Tabular Descriptions of Data 2 1.1 Stem-and-Leaf
Exploratory Data Analysis
Exploratory Data Analysis Stemplots (or Stem-and-leaf plots) Stemplot and Boxplot T -- leading digits are called stems T -- final digits are called leaves STAT 74 Descriptive Statistics 2 Example: (number
Construction of the Maximum Employment Rate
Construction of the Maximum Employment Rate The maximum employment rate shows what the overall employment rate would be if each age group were to simultaneously achieve its peak employment rate. The peak
Chapter 3. Lecture 3 Sections
Chapter 3 Lecture 3 Sections 3.4 3.5 Measure of Position We would like to compare values from different data sets. We will introduce a z score or standard score. This measures how many standard deviation
2CORE. Summarising numerical data: the median, range, IQR and box plots
C H A P T E R 2CORE Summarising numerical data: the median, range, IQR and box plots How can we describe a distribution with just one or two statistics? What is the median, how is it calculated and what
Random variables The binomial distribution The normal distribution Other distributions. Distributions. Patrick Breheny.
Distributions February 11 Random variables Anything that can be measured or categorized is called a variable If the value that a variable takes on is subject to variability, then it the variable is a random
Categorical. A general name for non-numerical data; the data is separated into categories of some kind.
Chapter 5 Categorical A general name for non-numerical data; the data is separated into categories of some kind. Nominal data Categorical data with no implied order. Eg. Eye colours, favourite TV show,
Putting Things Together Part 2
Frequency Putting Things Together Part These exercise blend ideas from various graphs (histograms and boxplots), differing shapes of distributions, and values summarizing the data. Data for, and are in
Some estimates of the height of the podium
Some estimates of the height of the podium 24 36 40 40 40 41 42 44 46 48 50 53 65 98 1 5 number summary Inter quartile range (IQR) range = max min 2 1.5 IQR outlier rule 3 make a boxplot 24 36 40 40 40
SPSS I: Menu Basics Practice Exercises Target Software & Version: SPSS V Last Updated on January 17, 2007 Created by Jennifer Ortman
SPSS I: Menu Basics Practice Exercises Target Software & Version: SPSS V. 14.02 Last Updated on January 17, 2007 Created by Jennifer Ortman PRACTICE EXERCISES Exercise A Obtain descriptive statistics (mean,
Guide to buying an annuity
Guide to buying an annuity 2 Welcome to our guide to buying an annuity You now have more choice than ever before when it comes to using your pension savings. Of course having more options can make it difficult
MLC at Boise State Lines and Rates Activity 1 Week #2
Lines and Rates Activity 1 Week #2 This activity will use slopes to calculate marginal profit, revenue and cost of functions. What is Marginal? Marginal cost is the cost added by producing one additional
GovernmentAdda.com. Data Interpretation
Data Interpretation Data Interpretation problems can be solved with little ease. There are of course some other things to focus upon first before you embark upon solving DI questions. What other things?
Key: 18 5 = 1.85 cm. 5 a Stem Leaf. Key: 2 0 = 20 points. b Stem Leaf. Key: 2 0 = 20 cm. 6 a Stem Leaf. Key: 4 3 = 43 cm.
Answers EXERCISE. D D C B Numerical: a, b, c Categorical: c, d, e, f, g Discrete: c Continuous: a, b C C Categorical B A Categorical and ordinal Discrete Ordinal D EXERCISE. Stem Key: = Stem Key: = $ The
FINALS REVIEW BELL RINGER. Simplify the following expressions without using your calculator. 1) 6 2/3 + 1/2 2) 2 * 3(1/2 3/5) 3) 5/ /2 4
FINALS REVIEW BELL RINGER Simplify the following expressions without using your calculator. 1) 6 2/3 + 1/2 2) 2 * 3(1/2 3/5) 3) 5/3 + 7 + 1/2 4 4) 3 + 4 ( 7) + 3 + 4 ( 2) 1) 36/6 4/6 + 3/6 32/6 + 3/6 35/6
Fundamentals of Statistics
CHAPTER 4 Fundamentals of Statistics Expected Outcomes Know the difference between a variable and an attribute. Perform mathematical calculations to the correct number of significant figures. Construct
Using Recursion in Models and Decision Making: Relationships in Data IV.A Student Activity Sheet 1: Using Scatterplots in Reports
1. Consider the following graph. Who are the subjects in the study? What are the variables of interest? Thoroughly describe the information illustrated by the graph, choosing at least two data points to
Review of the US Department of Transportation Report The State of the National Pipeline Infrastructure
Review of the US Department of Transportation Report The State of the National Pipeline Infrastructure Analysis by Richard Stover, PhD August, 2013 The US Department of Transportation runs the Pipeline
Both the quizzes and exams are closed book. However, For quizzes: Formulas will be provided with quiz papers if there is any need.
Both the quizzes and exams are closed book. However, For quizzes: Formulas will be provided with quiz papers if there is any need. For exams (MD1, MD2, and Final): You may bring one 8.5 by 11 sheet of
EconS Supply and Demand
EconS 305 - Supply and Demand Eric Dunaway Washington State University eric.dunaway@wsu.edu August 28, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 2 August 28, 2015 1 / 54 Introduction When people talk
Review: Types of Summary Statistics
Review: Types of Summary Statistics We re often interested in describing the following characteristics of the distribution of a data series: Central tendency - where is the middle of the distribution?
Example: Histogram for US household incomes from 2015 Table:
1 Example: Histogram for US household incomes from 2015 Table: Income level Relative frequency $0 - $14,999 11.6% $15,000 - $24,999 10.5% $25,000 - $34,999 10% $35,000 - $49,999 12.7% $50,000 - $74,999
Full file at
Frequency CHAPTER 2 Descriptive Statistics: Tabular and Graphical Methods 2.1 Constructing either a frequency or a relative frequency distribution helps identify and quantify patterns in how often various
AP Statistics Unit 1 (Chapters 1-6) Extra Practice: Part 1
AP Statistics Unit 1 (Chapters 1-6) Extra Practice: Part 1 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,
Math 243 Lecture Notes
Assume the average annual rainfall for in Portland is 36 inches per year with a standard deviation of 9 inches. Also assume that the average wind speed in Chicago is 10 mph with a standard deviation of
Quantitative Literacy: Thinking Between the Lines
Quantitative Literacy: Thinking Between the Lines Crauder, Noell, Evans, Johnson Chapter 2: Analysis of Growth 2013 W. H. Freeman and Company 1 Chapter 2: Analysis of Growth Lesson Plan Measurements of
1 Variables and data types
1 Variables and data types The data in statistical studies come from observations. Each observation generally yields a variety data which produce values for different variables. Variables come in two basic
Basic Data Analysis. Stephen Turnbull Business Administration and Public Policy Lecture 3: April 25, Abstract
Basic Data Analysis Stephen Turnbull Business Administration and Public Policy Lecture 3: April 25, 2013 Abstract Review summary statistics and measures of location. Discuss the placement exam as an exercise
2 DESCRIPTIVE STATISTICS
Chapter 2 Descriptive Statistics 47 2 DESCRIPTIVE STATISTICS Figure 2.1 When you have large amounts of data, you will need to organize it in a way that makes sense. These ballots from an election are rolled
DATA HANDLING Five-Number Summary
DATA HANDLING Five-Number Summary The five-number summary consists of the minimum and maximum values, the median, and the upper and lower quartiles. The minimum and the maximum are the smallest and greatest
Discrete Probability Distributions
90 Discrete Probability Distributions Discrete Probability Distributions C H A P T E R 6 Section 6.2 4Example 2 (pg. 00) Constructing a Binomial Probability Distribution In this example, 6% of the human
STAT 113 Variability
STAT 113 Variability Colin Reimer Dawson Oberlin College September 14, 2017 1 / 48 Outline Last Time: Shape and Center Variability Boxplots and the IQR Variance and Standard Deviaton Transformations 2
Exotic Tea Prices. Year
Price, cents per pound UNDERSTANDING HOW TO READ GRAPHS Information is often presented in the form of a graph, a diagram that shows numerical data in a visual form. Graphs enable us to see relationships
STASTICAL METHODOLOGY FOR DEVELOPING TIME STANDARDS American Association for Respiratory Care 2011 All Rights Reserved
STASTICAL METHODOLOGY FOR DEVELOPING TIME STANDARDS American Association for Respiratory Care All Rights Reserved Formulas for Computing Standard Hours (time standards) There are three generally accepted
Comparison of U.S. Stock Indices
Magnus Erik Hvass Pedersen Hvass Laboratories Report HL-1503 First Edition September 30, 2015 Latest Revision www.hvass-labs.org/books Summary This paper compares stock indices for USA: Large-Cap stocks
Overview/Outline. Moving beyond raw data. PSY 464 Advanced Experimental Design. Describing and Exploring Data The Normal Distribution
PSY 464 Advanced Experimental Design Describing and Exploring Data The Normal Distribution 1 Overview/Outline Questions-problems? Exploring/Describing data Organizing/summarizing data Graphical presentations
CHAPTER 2 DESCRIBING DATA: FREQUENCY DISTRIBUTIONS AND GRAPHIC PRESENTATION
CHAPTER 2 DESCRIBING DATA: FREQUENCY DISTRIBUTIONS AND GRAPHIC PRESENTATION 1. Maxwell Heating & Air Conditioning far exceeds the other corporations in sales. Mancell Electric & Plumbing and Mizelle Roofing
Guide to. buying an annuity
Guide to buying an annuity 2 Guide to buying an annuity Welcome to our guide to buying an annuity You now have more flexibility than ever before when it comes to using your pension savings. Of course all
We will also use this topic to help you see how the standard deviation might be useful for distributions which are normally distributed.
We will discuss the normal distribution in greater detail in our unit on probability. However, as it is often of use to use exploratory data analysis to determine if the sample seems reasonably normally
Chapter 4-Describing Data: Displaying and Exploring Data
Chapter 4-Describing Data: Displaying and Exploring Data Jie Zhang, Ph.D. Student Account and Information Systems Department College of Business Administration The University of Texas at El Paso jzhang6@utep.edu
BUSINESS MATHEMATICS & QUANTITATIVE METHODS
BUSINESS MATHEMATICS & QUANTITATIVE METHODS FORMATION 1 EXAMINATION - AUGUST 2009 NOTES: You are required to answer 5 questions. (If you provide answers to all questions, you must draw a clearly distinguishable
Pennsylvania Municipal Retirement System
Pennsylvania Municipal Retirement System Experience Study Results and Recommendations For the period covering January 1, 2009 December 31, 2013 Produced by Cheiron July 2015 Table of Contents Section Page
We will use an example which will result in a paired t test regarding the labor force participation rate for women in the 60 s and 70 s.
Now let s review methods for one quantitative variable. We will use an example which will result in a paired t test regarding the labor force participation rate for women in the 60 s and 70 s. 17 The labor
Lecture 12. Some Useful Continuous Distributions. The most important continuous probability distribution in entire field of statistics.
ENM 207 Lecture 12 Some Useful Continuous Distributions Normal Distribution The most important continuous probability distribution in entire field of statistics. Its graph, called the normal curve, is
The Normal Distribution
Stat 6 Introduction to Business Statistics I Spring 009 Professor: Dr. Petrutza Caragea Section A Tuesdays and Thursdays 9:300:50 a.m. Chapter, Section.3 The Normal Distribution Density Curves So far we
2015 Life + Money Survey: What Americans Think About Most
Brought to you by 2015 Life + Money Survey: What Americans Think About Most v What Do Americans Think About Most? GOBankingRates surveyed 5,003 U.S. adults, asking, What do you think about most? The following
MA131 Lecture 8.2. The normal distribution curve can be considered as a probability distribution curve for normally distributed variables.
Normal distribution curve as probability distribution curve The normal distribution curve can be considered as a probability distribution curve for normally distributed variables. The area under the normal
Final Project Format
Final Project Format Liquidity & Leverage Ratio Analyses of Company A, Company B and Company C in Same Industry for FY 20X1, 20X2 & 20X3 (Bold, 16 font, Times New Roman style) A REPORT SUBMITTED TO THE
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level STATISTICS 4040/01
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level STATISTICS 4040/01 Paper 1 Additional Materials: Answer Booklet/Paper Graph paper (2 sheets) Mathematical
Generations at Work. March 2017
Generations at Work March 2017 1 Introduction Through our Generations at Work report we have explored the views of British workers on the multigenerational workforce. It s a fact that we have an ageing
Found under MATH NUM
While you wait Edit the last line of your z-score program : Disp round(z, 2) Found under MATH NUM Bluman, Chapter 6 1 Sec 6.2 Bluman, Chapter 6 2 Bluman, Chapter 6 3 6.2 Applications of the Normal Distributions
Continuous Probability Distributions
8.1 Continuous Probability Distributions Distributions like the binomial probability distribution and the hypergeometric distribution deal with discrete data. The possible values of the random variable
UNDERSTANDING RISK TOLERANCE CRITERIA. Paul Baybutt. Primatech Inc., Columbus, Ohio, USA.
UNDERSTANDING RISK TOLERANCE CRITERIA by Paul Baybutt Primatech Inc., Columbus, Ohio, USA www.primatech.com Introduction Various definitions of risk are used by risk analysts [1]. In process safety, risk
Link full download:
- Descriptive Statistics: Tabular and Graphical Method Chapter 02 Essentials of Business Statistics 5th Edition by Bruce L Bowerman Professor, Richard T O Connell Professor, Emily S. Murphree and J. Burdeane
STATISTICAL DISTRIBUTIONS AND THE CALCULATOR
STATISTICAL DISTRIBUTIONS AND THE CALCULATOR 1. Basic data sets a. Measures of Center - Mean ( ): average of all values. Characteristic: non-resistant is affected by skew and outliers. - Median: Either
MAS187/AEF258. University of Newcastle upon Tyne
MAS187/AEF258 University of Newcastle upon Tyne 2005-6 Contents 1 Collecting and Presenting Data 5 1.1 Introduction...................................... 5 1.1.1 Examples...................................
Week 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics.
Week 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics. Convergent validity: the degree to which results/evidence from different tests/sources, converge on the same conclusion.
Math 2200 Fall 2014, Exam 1 You may use any calculator. You may not use any cheat sheet.
1 Math 2200 Fall 2014, Exam 1 You may use any calculator. You may not use any cheat sheet. Warning to the Reader! If you are a student for whom this document is a historical artifact, be aware that the
Business Optimism Survey Report Summer 2017
Center for Economic and Business Research Business Optimism Survey Report Summer 2017 July 24, 2017 Student Author(s) Elena Rodriguez In Collaboration With Contents Executive Summary..3 Clarifying Notes
Toshiko Kaneda, PhD Population Reference Bureau (PRB) James Kirby, PhD Agency for Healthcare Research and Quality (AHRQ)
Disparities in Health Care Spending among Older Adults: Trends in Total and Out-of-Pocket Health Expenditures by Sex, Race/Ethnicity, and Income between 1996 and 21 Toshiko Kaneda, PhD Population Reference
MLC Written Answer Model Solutions Spring 2014
MLC Written Answer Model Solutions Spring 214 1. Learning Outcomes: (2a) (3a) (3b) (3d) Sources: Textbook references: 4.4, 5.6, 5.11, 6.5, 9.4 (a) Show that the expected present value of the death benefit
MAT 1371 Midterm. This is a closed book examination. However one sheet is permitted. Only non-programmable and non-graphic calculators are permitted.
MAT 1371 Midterm Duration: 80 minutes Professor G. Lamothe Student Number: Last Name: First Name: This is a closed book examination. However one sheet is permitted. Only non-programmable and non-graphic
Chapter 3: Displaying and Describing Quantitative Data Quiz A Name
Chapter 3: Displaying and Describing Quantitative Data Quiz A Name 3.1.1 Find summary statistics; create displays; describe distributions; determine 1. Following is a histogram of salaries (in $) for a
3) Marital status of each member of a randomly selected group of adults is an example of what type of variable?
MATH112 STATISTICS; REVIEW1 CH1,2,&3 Name CH1 Vocabulary 1) A statistics student wants to find some information about all college students who ride a bike. She collected data from other students in her
RETIREMENT A NEW BEGINNING
RETIREMENT A NEW BEGINNING 2 YOUR RETIREMENT. YOUR Contents More choice, more freedom, more decisions 4 Getting ready for retirement 6 Understanding what happens in the event of your death 7 Navigating
The Journal of Applied Business Research May/June 2009 Volume 25, Number 3
Risk Manage Capital Investment Decisions: A Lease vs. Purchase Illustration Thomas L. Zeller, PhD., CPA, Loyola University Chicago Brian B. Stanko, PhD., CPA, Loyola University Chicago ABSTRACT This paper
Termination, Retirement and SMP Experience Study for the Public Service Pension Plan
Termination, Retirement and SMP Experience Study for the Public Service Pension Plan June 2015 Risk. Reinsurance. Human Resources Table of Contents Executive Summary... 1 Section 1: Introduction... 2 Section
MVE051/MSG Lecture 7
MVE051/MSG810 2017 Lecture 7 Petter Mostad Chalmers November 20, 2017 The purpose of collecting and analyzing data Purpose: To build and select models for parts of the real world (which can be used for
Getting to know a data-set (how to approach data) Overview: Descriptives & Graphing
Overview: Descriptives & Graphing 1. Getting to know a data set 2. LOM & types of statistics 3. Descriptive statistics 4. Normal distribution 5. Non-normal distributions 6. Effect of skew on central tendency
Secure your future with guaranteed lifetime income
An Educational Guide for Consumers Secure your future with guaranteed lifetime income MassMutual RetireEase Choice SM Flexible Premium Deferred Income Annuity Table of contents 1 What does retirement mean
The following content is provided under a Creative Commons license. Your support
MITOCW Recitation 6 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make