Midrange: mean of highest and lowest scores. easy to compute, rough estimate, rarely used
|
|
- Homer Armstrong
- 6 years ago
- Views:
Transcription
1 Measures of Central Tendency Mode: most frequent score. best average for nominal data sometimes none or multiple modes in a sample bimodal or multimodal distributions indicate several groups included in sample easy to determine Midrange: mean of highest and lowest scores. easy to compute, rough estimate, rarely used Median: value at divides distribution in half. best average for ordinal data most appropriate average for skewed ratio or interval data or data on salaries difficult to compute because data must be sorted unaffected by extreme data Arimetic mean: centre of balance of data. sum of numbers divided by n best average for unskewed ratio or interval data easy to compute sample mean = population mean = Oer measures: harmonic mean, geometric mean, and quadratic mean, also called root mean square (RMS) RMS =
2 direction of skew is e direction of e tail positive direction of a number line is to e right, left is negative direction mean, mode and median (MD) are e same for symmetrical distributions Skewed Data notice mean is closest to e tail (i.e., more influenced by extreme values)
3 Measures of Variation Range: highest minus lowest values used for ordinal data R = highest lowest Interquartile range: 75 minus 25 percentile used for determining outliers IQR = Q Q 3 1 Variance: mean of squared differences between scores and e mean used on ratio or interval data used for advanced statistical analysis (ANOVAs) Standard deviation: has same units as raw data used on ratio or interval data most commonly used measure of variation Coefficient of variation: percentage of standard deviation to mean used to compare variability among data wi different units of measure
4 Biased and Unbiased Estimators sample mean is an unbiased estimate of e population mean variances and standard deviations are biased estimators because mean is used in eir computation Why? Last score can be determined from mean and all oer scores, erefore, it is not free to vary or add to variability. To compensate divide sums of squares by n 1 instead of n. Instead of using e standard formula a computing formula is used so at running totals of scores and scores squared may be used to compute variability. Computing Formulae 2 Variance: S = sample variance Standard deviation: S = sample standard deviation
5 Measures of Position Percentile: score which exceeds a specified percentage of e population. suitable for ordinal, ratio or interval data median (MD or Q 2) is 50 percentile first and ird quartiles (Q 1 and Q 3) are 25 and 75 percentiles easier for non-statisticians to understand an z-scores scores are all positive numbers Standard or z-scores: based on mean and standard deviation and e normal distribution suitable for ratio and interval numbers approximately 68% of scores are wiin 1 standard deviation of e mean, approximately 95% are wiin 2 standard deviations and approximately 99% are wiin 3 standard deviations half e scores are negative numbers mean score is zero excellent way of comparing measures or scores which have different units (i.e., heights vs. weights, metric vs. Imperial units, psychological vs. physiological measures)
6 Measures of Position and Outliers Oer measures of position: Deciles: 10, 20, percentiles (D 1, D 2,...D 10). often used in education or demographic studies Quartiles: 25, 50 and 75 percentiles (Q 1, Q 2, Q 3). frequently used for exploratory statistics and to determine outliers (Q is same as median) 2 Outliers: extreme values at adversely affect statistical measures of central tendency and variation Meod of determining outliers: compute interquartile range (IRQ) multiply IRQ by 1.5 lower bound is Q 1 minus 1.5 IRQ upper bound is Q 3 plus 1.5 IRQ values outside ese bounds are outliers and may be removed from e data set it is assumed at outliers are e result of errors in measurement or recording or were taken from an unrepresentative individual Alternate meod for normally distributed data: +/ 4 or 5 standard deviations
Chapter 3 Data Description
Chapter 3 Data Description Section 3.1: Measures of Central Tendency Section 3.2: Measures of Variation Section 3.3: Measures of Position Section 3.1: Measures of Central Tendency Definition of Average
More informationLecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series. Slide 1
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 3 Statistics for Describing, Exploring, and Comparing Data 3-1 Overview 3-2 Measures
More informationADMS2320.com. We Make Stats Easy. Chapter 4. ADMS2320.com Tutorials Past Tests. Tutorial Length 1 Hour 45 Minutes
We Make Stats Easy. Chapter 4 Tutorial Length 1 Hour 45 Minutes Tutorials Past Tests Chapter 4 Page 1 Chapter 4 Note The following topics will be covered in this chapter: Measures of central location Measures
More information2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 2 Methods for Describing Sets of Data Summary of Central Tendency Measures Measure Formula Description Mean x i / n Balance Point Median ( n +1) Middle Value
More informationLecture 11. Data Description Estimation
Lecture 11 Data Description Estimation Measures of Central Tendency (continued, see last lecture) Sample mean, population mean Sample mean for frequency distributions The median The mode The midrange 3-22
More informationLast Lecture. Distinguish Populations from Samples. Knowing different Sampling Techniques. Distinguish Parameters from Statistics
Last Lecture Distinguish Populations from Samples Importance of identifying a population and well chosen sample Knowing different Sampling Techniques Distinguish Parameters from Statistics Knowing different
More informationTastitsticsss? What s that? Principles of Biostatistics and Informatics. Variables, outcomes. Tastitsticsss? What s that?
Tastitsticsss? What s that? Statistics describes random mass phanomenons. Principles of Biostatistics and Informatics nd Lecture: Descriptive Statistics 3 th September Dániel VERES Data Collecting (Sampling)
More informationChapter 3. Data Description. McGraw-Hill, Bluman, 7 th ed, Chapter 3
Chapter 3 Data Description McGraw-Hill, Bluman, 7 th ed, Chapter 3 1 Chapter 3 Overview Introduction 3-1 Measures of Central Tendency 3-2 Measures of Variation 3-3 Measures of Position 3-4 Exploratory
More informationLecture 3: Chapter 3
Lecture 3: Chapter 3 C C Moxley UAB Mathematics 26 January 16 3.2 Measurements of Center Statistics involves describing data sets and inferring things about them. The first step in understanding a set
More informationAfter completing this chapter, you should be able to:
Chapter 2 Descriptive Statistics Chapter Goals After completing this chapter, you should be able to: Compute and interpret the mean, median, and mode for a set of data Find the range, variance, standard
More informationP8130: Biostatistical Methods I
P8130: Biostatistical Methods I Lecture 2: Descriptive Statistics Cody Chiuzan, PhD Department of Biostatistics Mailman School of Public Health (MSPH) Lecture 1: Recap Intro to Biostatistics Types of Data
More informationMATH 117 Statistical Methods for Management I Chapter Three
Jubail University College MATH 117 Statistical Methods for Management I Chapter Three This chapter covers the following topics: I. Measures of Center Tendency. 1. Mean for Ungrouped Data (Raw Data) 2.
More informationMeelis Kull Autumn Meelis Kull - Autumn MTAT Data Mining - Lecture 03
Meelis Kull meelis.kull@ut.ee Autumn 2017 1 Demo: Data science mini-project CRISP-DM: cross-industrial standard process for data mining Data understanding: Types of data Data understanding: First look
More informationChapter 3. Data Description
Chapter 3. Data Description Graphical Methods Pie chart It is used to display the percentage of the total number of measurements falling into each of the categories of the variable by partition a circle.
More informationLecture 2 and Lecture 3
Lecture 2 and Lecture 3 1 Lecture 2 and Lecture 3 We can describe distributions using 3 characteristics: shape, center and spread. These characteristics have been discussed since the foundation of statistics.
More informationSection 3. Measures of Variation
Section 3 Measures of Variation Range Range = (maximum value) (minimum value) It is very sensitive to extreme values; therefore not as useful as other measures of variation. Sample Standard Deviation The
More informationLecture Slides. Elementary Statistics Twelfth Edition. by Mario F. Triola. and the Triola Statistics Series. Section 3.1- #
Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series by Mario F. Triola Chapter 3 Statistics for Describing, Exploring, and Comparing Data 3-1 Review and Preview 3-2 Measures
More information3 Lecture 3 Notes: Measures of Variation. The Boxplot. Definition of Probability
3 Lecture 3 Notes: Measures of Variation. The Boxplot. Definition of Probability 3.1 Week 1 Review Creativity is more than just being different. Anybody can plan weird; that s easy. What s hard is to be
More informationPsychology 310 Exam1 FormA Student Name:
Psychology 310 Exam1 FormA Student Name: 1 Compute the sample mean X forthefollowing5numbers: 1,4,2,3,4 (a) 2. 8 (b) 3.00 (c) 2. 24 (d) 1. 4 (e) None of the above are correct 2 Compute the sample variance
More informationMEASURES OF CENTRAL TENDENCY
INTRODUCTION: MEASURES OF CENTRAL TENDENCY Often, one encounters e term Measures of central tendency in a book on statistics (or an examination). One may also find mention of e term in a description of
More informationChapter 4. Displaying and Summarizing. Quantitative Data
STAT 141 Introduction to Statistics Chapter 4 Displaying and Summarizing Quantitative Data Bin Zou (bzou@ualberta.ca) STAT 141 University of Alberta Winter 2015 1 / 31 4.1 Histograms 1 We divide the range
More informationPerhaps the most important measure of location is the mean (average). Sample mean: where n = sample size. Arrange the values from smallest to largest:
1 Chapter 3 - Descriptive stats: Numerical measures 3.1 Measures of Location Mean Perhaps the most important measure of location is the mean (average). Sample mean: where n = sample size Example: The number
More informationUnit 2. Describing Data: Numerical
Unit 2 Describing Data: Numerical Describing Data Numerically Describing Data Numerically Central Tendency Arithmetic Mean Median Mode Variation Range Interquartile Range Variance Standard Deviation Coefficient
More informationMath 120 Introduction to Statistics Mr. Toner s Lecture Notes 3.1 Measures of Central Tendency
Math 1 Introduction to Statistics Mr. Toner s Lecture Notes 3.1 Measures of Central Tendency The word average: is very ambiguous and can actually refer to the mean, median, mode or midrange. Notation:
More informationSlide 1. Slide 2. Slide 3. Pick a Brick. Daphne. 400 pts 200 pts 300 pts 500 pts 100 pts. 300 pts. 300 pts 400 pts 100 pts 400 pts.
Slide 1 Slide 2 Daphne Phillip Kathy Slide 3 Pick a Brick 100 pts 200 pts 500 pts 300 pts 400 pts 200 pts 300 pts 500 pts 100 pts 300 pts 400 pts 100 pts 400 pts 100 pts 200 pts 500 pts 100 pts 400 pts
More informationOBJECTIVES INTRODUCTION
M7 Chapter 3 Section 1 OBJECTIVES Suarize data using easures of central tendency, such as the ean, edian, ode, and idrange. Describe data using the easures of variation, such as the range, variance, and
More informationStatistics for Managers using Microsoft Excel 6 th Edition
Statistics for Managers using Microsoft Excel 6 th Edition Chapter 3 Numerical Descriptive Measures 3-1 Learning Objectives In this chapter, you learn: To describe the properties of central tendency, variation,
More information3.1 Measures of Central Tendency: Mode, Median and Mean. Average a single number that is used to describe the entire sample or population
. Measures of Central Tendency: Mode, Median and Mean Average a single number that is used to describe the entire sample or population. Mode a. Easiest to compute, but not too stable i. Changing just one
More informationDescribing distributions with numbers
Describing distributions with numbers A large number or numerical methods are available for describing quantitative data sets. Most of these methods measure one of two data characteristics: The central
More informationCHAPTER 4 VARIABILITY ANALYSES. Chapter 3 introduced the mode, median, and mean as tools for summarizing the
CHAPTER 4 VARIABILITY ANALYSES Chapter 3 introduced the mode, median, and mean as tools for summarizing the information provided in an distribution of data. Measures of central tendency are often useful
More information3.1 Measure of Center
3.1 Measure of Center Calculate the mean for a given data set Find the median, and describe why the median is sometimes preferable to the mean Find the mode of a data set Describe how skewness affects
More information200 participants [EUR] ( =60) 200 = 30% i.e. nearly a third of the phone bills are greater than 75 EUR
Ana Jerončić 200 participants [EUR] about half (71+37=108) 200 = 54% of the bills are small, i.e. less than 30 EUR (18+28+14=60) 200 = 30% i.e. nearly a third of the phone bills are greater than 75 EUR
More informationFurther Mathematics 2018 CORE: Data analysis Chapter 2 Summarising numerical data
Chapter 2: Summarising numerical data Further Mathematics 2018 CORE: Data analysis Chapter 2 Summarising numerical data Extract from Study Design Key knowledge Types of data: categorical (nominal and ordinal)
More informationStat 20: Intro to Probability and Statistics
Stat 20: Intro to Probability and Statistics Lecture 5: Summary Statistics Tessa L. Childers-Day UC Berkeley 30 June 2014 By the end of this lecture... You will be able to: Describe a data set by its:
More informationObjective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode.
Chapter 3 Numerically Summarizing Data Chapter 3.1 Measures of Central Tendency Objective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode. A1. Mean The
More informationProbabilities and Statistics Probabilities and Statistics Probabilities and Statistics
- Lecture 8 Olariu E. Florentin April, 2018 Table of contents 1 Introduction Vocabulary 2 Descriptive Variables Graphical representations Measures of the Central Tendency The Mean The Median The Mode Comparing
More informationDescribing distributions with numbers
Describing distributions with numbers A large number or numerical methods are available for describing quantitative data sets. Most of these methods measure one of two data characteristics: The central
More informationExample 2. Given the data below, complete the chart:
Statistics 2035 Quiz 1 Solutions Example 1. 2 64 150 150 2 128 150 2 256 150 8 8 Example 2. Given the data below, complete the chart: 52.4, 68.1, 66.5, 75.0, 60.5, 78.8, 63.5, 48.9, 81.3 n=9 The data is
More informationUnit Two Descriptive Biostatistics. Dr Mahmoud Alhussami
Unit Two Descriptive Biostatistics Dr Mahmoud Alhussami Descriptive Biostatistics The best way to work with data is to summarize and organize them. Numbers that have not been summarized and organized are
More informationChapter 3 Statistics for Describing, Exploring, and Comparing Data. Section 3-1: Overview. 3-2 Measures of Center. Definition. Key Concept.
Chapter 3 Statistics for Describing, Exploring, and Comparing Data 3-1 Overview 3- Measures of Center 3-3 Measures of Variation Section 3-1: Overview Descriptive Statistics summarize or describe the important
More informationReview for Exam #1. Chapter 1. The Nature of Data. Definitions. Population. Sample. Quantitative data. Qualitative (attribute) data
Review for Exam #1 1 Chapter 1 Population the complete collection of elements (scores, people, measurements, etc.) to be studied Sample a subcollection of elements drawn from a population 11 The Nature
More informationSTP 420 INTRODUCTION TO APPLIED STATISTICS NOTES
INTRODUCTION TO APPLIED STATISTICS NOTES PART - DATA CHAPTER LOOKING AT DATA - DISTRIBUTIONS Individuals objects described by a set of data (people, animals, things) - all the data for one individual make
More informationDescribing Distributions with Numbers
Topic 2 We next look at quantitative data. Recall that in this case, these data can be subject to the operations of arithmetic. In particular, we can add or subtract observation values, we can sort them
More informationDescriptive Data Summarization
Descriptive Data Summarization Descriptive data summarization gives the general characteristics of the data and identify the presence of noise or outliers, which is useful for successful data cleaning
More informationTopic Page: Central tendency
Topic Page: Central tendency Definition: measures of central tendency from Dictionary of Psychological Testing, Assessment and Treatment summary statistics which divide the data into two halves (i.e. half
More information1. Exploratory Data Analysis
1. Exploratory Data Analysis 1.1 Methods of Displaying Data A visual display aids understanding and can highlight features which may be worth exploring more formally. Displays should have impact and be
More informationLecture Slides. Elementary Statistics Eleventh Edition. by Mario F. Triola. and the Triola Statistics Series 3.1-1
Lecture Slides Elementary Statistics Eleventh Edition and the Triola Statistics Series by Mario F. Triola 3.1-1 Chapter 3 Statistics for Describing, Exploring, and Comparing Data 3-1 Review and Preview
More informationIntroduction to Statistics
Introduction to Statistics Data and Statistics Data consists of information coming from observations, counts, measurements, or responses. Statistics is the science of collecting, organizing, analyzing,
More informationStatistical Methods. by Robert W. Lindeman WPI, Dept. of Computer Science
Statistical Methods by Robert W. Lindeman WPI, Dept. of Computer Science gogo@wpi.edu Descriptive Methods Frequency distributions How many people were similar in the sense that according to the dependent
More informationLecture 6: Chapter 4, Section 2 Quantitative Variables (Displays, Begin Summaries)
Lecture 6: Chapter 4, Section 2 Quantitative Variables (Displays, Begin Summaries) Summarize with Shape, Center, Spread Displays: Stemplots, Histograms Five Number Summary, Outliers, Boxplots Cengage Learning
More informationMeasures of Central Tendency
Measures of Central Tendency Summary Measures Summary Measures Central Tendency Mean Median Mode Quartile Range Variance Variation Coefficient of Variation Standard Deviation Measures of Central Tendency
More informationIntroduction to Statistics
Introduction to Statistics By A.V. Vedpuriswar October 2, 2016 Introduction The word Statistics is derived from the Italian word stato, which means state. Statista refers to a person involved with the
More informationΣ x i. Sigma Notation
Sigma Notation The mathematical notation that is used most often in the formulation of statistics is the summation notation The uppercase Greek letter Σ (sigma) is used as shorthand, as a way to indicate
More informationMeasures of center. The mean The mean of a distribution is the arithmetic average of the observations:
Measures of center The mean The mean of a distribution is the arithmetic average of the observations: x = x 1 + + x n n n = 1 x i n i=1 The median The median is the midpoint of a distribution: the number
More informationChapter 4.notebook. August 30, 2017
Sep 1 7:53 AM Sep 1 8:21 AM Sep 1 8:21 AM 1 Sep 1 8:23 AM Sep 1 8:23 AM Sep 1 8:23 AM SOCS When describing a distribution, make sure to always tell about three things: shape, outliers, center, and spread
More informationSUMMARIZING MEASURED DATA. Gaia Maselli
SUMMARIZING MEASURED DATA Gaia Maselli maselli@di.uniroma1.it Computer Network Performance 2 Overview Basic concepts Summarizing measured data Summarizing data by a single number Summarizing variability
More informationMgtOp 215 Chapter 3 Dr. Ahn
MgtOp 215 Chapter 3 Dr. Ahn Measures of central tendency (center, location): measures the middle point of a distribution or data; these include mean and median. Measures of dispersion (variability, spread):
More informationNumerical Measures of Central Tendency
ҧ Numerical Measures of Central Tendency The central tendency of the set of measurements that is, the tendency of the data to cluster, or center, about certain numerical values; usually the Mean, Median
More informationF78SC2 Notes 2 RJRC. If the interest rate is 5%, we substitute x = 0.05 in the formula. This gives
F78SC2 Notes 2 RJRC Algebra It is useful to use letters to represent numbers. We can use the rules of arithmetic to manipulate the formula and just substitute in the numbers at the end. Example: 100 invested
More informationQuantitative Tools for Research
Quantitative Tools for Research KASHIF QADRI Descriptive Analysis Lecture Week 4 1 Overview Measurement of Central Tendency / Location Mean, Median & Mode Quantiles (Quartiles, Deciles, Percentiles) Measurement
More informationBNG 495 Capstone Design. Descriptive Statistics
BNG 495 Capstone Design Descriptive Statistics Overview The overall goal of this short course in statistics is to provide an introduction to descriptive and inferential statistical methods, with a focus
More informationDETAILED CONTENTS PART I INTRODUCTION AND DESCRIPTIVE STATISTICS. 1. Introduction to Statistics
DETAILED CONTENTS About the Author Preface to the Instructor To the Student How to Use SPSS With This Book PART I INTRODUCTION AND DESCRIPTIVE STATISTICS 1. Introduction to Statistics 1.1 Descriptive and
More informationChapter Four. Numerical Descriptive Techniques. Range, Standard Deviation, Variance, Coefficient of Variation
Chapter Four Numerical Descriptive Techniques 4.1 Numerical Descriptive Techniques Measures of Central Location Mean, Median, Mode Measures of Variability Range, Standard Deviation, Variance, Coefficient
More informationChapters 1 & 2 Exam Review
Problems 1-3 refer to the following five boxplots. 1.) To which of the above boxplots does the following histogram correspond? (A) A (B) B (C) C (D) D (E) E 2.) To which of the above boxplots does the
More informationPreliminary Statistics course. Lecture 1: Descriptive Statistics
Preliminary Statistics course Lecture 1: Descriptive Statistics Rory Macqueen (rm43@soas.ac.uk), September 2015 Organisational Sessions: 16-21 Sep. 10.00-13.00, V111 22-23 Sep. 15.00-18.00, V111 24 Sep.
More informationGlossary. The ISI glossary of statistical terms provides definitions in a number of different languages:
Glossary The ISI glossary of statistical terms provides definitions in a number of different languages: http://isi.cbs.nl/glossary/index.htm Adjusted r 2 Adjusted R squared measures the proportion of the
More informationDescriptive Statistics-I. Dr Mahmoud Alhussami
Descriptive Statistics-I Dr Mahmoud Alhussami Biostatistics What is the biostatistics? A branch of applied math. that deals with collecting, organizing and interpreting data using well-defined procedures.
More informationAverages How difficult is QM1? What is the average mark? Week 1b, Lecture 2
Averages How difficult is QM1? What is the average mark? Week 1b, Lecture 2 Topics: 1. Mean 2. Mode 3. Median 4. Order Statistics 5. Minimum, Maximum, Range 6. Percentiles, Quartiles, Interquartile Range
More informationCIVL 7012/8012. Collection and Analysis of Information
CIVL 7012/8012 Collection and Analysis of Information Uncertainty in Engineering Statistics deals with the collection and analysis of data to solve real-world problems. Uncertainty is inherent in all real
More informationREVIEW: Midterm Exam. Spring 2012
REVIEW: Midterm Exam Spring 2012 Introduction Important Definitions: - Data - Statistics - A Population - A census - A sample Types of Data Parameter (Describing a characteristic of the Population) Statistic
More informationCS 147: Computer Systems Performance Analysis
CS 147: Computer Systems Performance Analysis Summarizing Variability and Determining Distributions CS 147: Computer Systems Performance Analysis Summarizing Variability and Determining Distributions 1
More informationUnit 2: Numerical Descriptive Measures
Unit 2: Numerical Descriptive Measures Summation Notation Measures of Central Tendency Measures of Dispersion Chebyshev's Rule Empirical Rule Measures of Relative Standing Box Plots z scores Jan 28 10:48
More informationVariables, distributions, and samples (cont.) Phil 12: Logic and Decision Making Fall 2010 UC San Diego 10/18/2010
Variables, distributions, and samples (cont.) Phil 12: Logic and Decision Making Fall 2010 UC San Diego 10/18/2010 Review Recording observations - Must extract that which is to be analyzed: coding systems,
More informationMeasures of average are called measures of central tendency and include the mean, median, mode, and midrange.
CHAPTER 3 Data Description Objectives Suarize data using easures of central tendency, such as the ean, edian, ode, and idrange. Describe data using the easures of variation, such as the range, variance,
More informationDescribing Distributions with Numbers
Describing Distributions with Numbers Using graphs, we could determine the center, spread, and shape of the distribution of a quantitative variable. We can also use numbers (called summary statistics)
More informationUNIT 3 CONCEPT OF DISPERSION
UNIT 3 CONCEPT OF DISPERSION Structure 3.0 Introduction 3.1 Objectives 3.2 Concept of Dispersion 3.2.1 Functions of Dispersion 3.2.2 Measures of Dispersion 3.2.3 Meaning of Dispersion 3.2.4 Absolute Dispersion
More informationSummarizing Measured Data
Summarizing Measured Data 12-1 Overview Basic Probability and Statistics Concepts: CDF, PDF, PMF, Mean, Variance, CoV, Normal Distribution Summarizing Data by a Single Number: Mean, Median, and Mode, Arithmetic,
More informationMeasures of the Location of the Data
Measures of the Location of the Data 1. 5. Mark has 51 films in his collection. Each movie comes with a rating on a scale from 0.0 to 10.0. The following table displays the ratings of the aforementioned
More informationFinal Exam STAT On a Pareto chart, the frequency should be represented on the A) X-axis B) regression C) Y-axis D) none of the above
King Abdul Aziz University Faculty of Sciences Statistics Department Final Exam STAT 0 First Term 49-430 A 40 Name No ID: Section: You have 40 questions in 9 pages. You have 90 minutes to solve the exam.
More informationRange The range is the simplest of the three measures and is defined now.
Measures of Variation EXAMPLE A testing lab wishes to test two experimental brands of outdoor paint to see how long each will last before fading. The testing lab makes 6 gallons of each paint to test.
More informationZ score indicates how far a raw score deviates from the sample mean in SD units. score Mean % Lower Bound
1 EDUR 8131 Chat 3 Notes 2 Normal Distribution and Standard Scores Questions Standard Scores: Z score Z = (X M) / SD Z = deviation score divided by standard deviation Z score indicates how far a raw score
More informationDescriptive Statistics C H A P T E R 5 P P
Descriptive Statistics C H A P T E R 5 P P 1 1 0-130 Graphing data Frequency distributions Bar graphs Qualitative variable (categories) Bars don t touch Histograms Frequency polygons Quantitative variable
More informationTOPIC: Descriptive Statistics Single Variable
TOPIC: Descriptive Statistics Single Variable I. Numerical data summary measurements A. Measures of Location. Measures of central tendency Mean; Median; Mode. Quantiles - measures of noncentral tendency
More informationIntroduction and Descriptive Statistics p. 1 Introduction to Statistics p. 3 Statistics, Science, and Observations p. 5 Populations and Samples p.
Preface p. xi Introduction and Descriptive Statistics p. 1 Introduction to Statistics p. 3 Statistics, Science, and Observations p. 5 Populations and Samples p. 6 The Scientific Method and the Design of
More information2.0 Lesson Plan. Answer Questions. Summary Statistics. Histograms. The Normal Distribution. Using the Standard Normal Table
2.0 Lesson Plan Answer Questions 1 Summary Statistics Histograms The Normal Distribution Using the Standard Normal Table 2. Summary Statistics Given a collection of data, one needs to find representations
More informationMeasures of Central Tendency:
Measures of Central Tendency: Mean, Median, Mode CasperWendy Measures of Central Tendency Measure of central tendency provides a very convenient way of describing a set of scores with a single number that
More informationStatistics and parameters
Statistics and parameters Tables, histograms and other charts are used to summarize large amounts of data. Often, an even more extreme summary is desirable. Statistics and parameters are numbers that characterize
More informationSTATISTICS. 1. Measures of Central Tendency
STATISTICS 1. Measures o Central Tendency Mode, median and mean For a sample o discrete data, the mode is the observation, x with the highest requency,. 1 N F For grouped data in a cumulative requency
More informationDetermining the Spread of a Distribution Variance & Standard Deviation
Determining the Spread of a Distribution Variance & Standard Deviation 1.3 Cathy Poliak, Ph.D. cathy@math.uh.edu Department of Mathematics University of Houston Lecture 3 Lecture 3 1 / 32 Outline 1 Describing
More informationCHAPTER 2 Description of Samples and Populations
Chapter 2 27 CHAPTER 2 Description of Samples and Populations 2.1.1 (a) i) Molar width ii) Continuous variable iii) A molar iv) 36 (b) i) Birthweight, date of birth, and race ii) Birthweight is continuous,
More information2/2/2015 GEOGRAPHY 204: STATISTICAL PROBLEM SOLVING IN GEOGRAPHY MEASURES OF CENTRAL TENDENCY CHAPTER 3: DESCRIPTIVE STATISTICS AND GRAPHICS
Spring 2015: Lembo GEOGRAPHY 204: STATISTICAL PROBLEM SOLVING IN GEOGRAPHY CHAPTER 3: DESCRIPTIVE STATISTICS AND GRAPHICS Descriptive statistics concise and easily understood summary of data set characteristics
More informationSTAT 200 Chapter 1 Looking at Data - Distributions
STAT 200 Chapter 1 Looking at Data - Distributions What is Statistics? Statistics is a science that involves the design of studies, data collection, summarizing and analyzing the data, interpreting the
More informationSection 3.2 Measures of Central Tendency
Section 3.2 Measures of Central Tendency 1 of 149 Section 3.2 Objectives Determine the mean, median, and mode of a population and of a sample Determine the weighted mean of a data set and the mean of a
More informationTopic-1 Describing Data with Numerical Measures
Topic-1 Describing Data with Numerical Measures Central Tendency (Center) and Dispersion (Variability) Central tendency: measures of the degree to which scores are clustered around the mean of a distribution
More informationChapter 3: Displaying and summarizing quantitative data p52 The pattern of variation of a variable is called its distribution.
Chapter 3: Displaying and summarizing quantitative data p52 The pattern of variation of a variable is called its distribution. 1 Histograms p53 The breakfast cereal data Study collected data on nutritional
More informationChapter 3. Measuring data
Chapter 3 Measuring data 1 Measuring data versus presenting data We present data to help us draw meaning from it But pictures of data are subjective They re also not susceptible to rigorous inference Measuring
More informationØ Set of mutually exclusive categories. Ø Classify or categorize subject. Ø No meaningful order to categorization.
Statistical Tools in Evaluation HPS 41 Dr. Joe G. Schmalfeldt Types of Scores Continuous Scores scores with a potentially infinite number of values. Discrete Scores scores limited to a specific number
More informationMath 14 Lecture Notes Ch Percentile
.3 Measures of the Location of the Data Percentile g A measure of position, the percentile, p, is an integer (1 p 99) such that the p th percentile is the position of a data value where p% of the data
More informationStat Lecture Slides Exploring Numerical Data. Yibi Huang Department of Statistics University of Chicago
Stat 22000 Lecture Slides Exploring Numerical Data Yibi Huang Department of Statistics University of Chicago Outline In this slide, we cover mostly Section 1.2 & 1.6 in the text. Data and Types of Variables
More informationDescriptive Statistics
Sherif Khalifa Sherif Khalifa () Descriptive Statistics 1 / 34 Definition Measures of central tendency yield information about the center, or middle part, of a group of numbers. Mode Median Mean Percentiles
More information