1 Measures for location and dispersion of a sample


 Toby Hudson
 2 years ago
 Views:
Transcription
1 Statistical Geophysics WS 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 X Sample of size n Sample: x, x 2,..., x n Summary measures for the location or dispersion of empirical distributions. Measures for location Measures for location or central tendency Definition: Mode The most frequently occurring value or category of X Example: Mode of (2, 2, 3, 3, 4, 5, 5, 5) is 5 Perhaps not well defined: (2, 2, 2, 3, 4, 4, 4) has two modes Measures for location or central tendency Definition: Median Order the sample to get the Order Statistics: x, x 2,..., x n x () x (2)... x (n) Median divides ordered data values, such that 50% of the data values are lower than or equal to the median and 50% are greater than or equal to the median Calculate median x 0.5 as x 0.5 = { x( n+ 2 ) if n is odd 2 (x (n/2) + x (n/2 +) ) if n is even Measures for location or central tendency Definition: Arithmetic mean or average of a sample x = n The mean of a population is often denoted by µ with µ = N N x i x i
2 Measures for location or central tendency Other measures Geometric mean Harmonic mean Weighted mean/average Truncated or trimmed mean Winsorized mean Measures for location Definition: Quantile Generalization of median α [0, ] The αquantile divides the ordered data values such that nα% values are lower than or equal to the αquantile and n( α)% values are greater than or equal to the αquantile Calculation (usually software dependent, here the book version): x (k) if nα is not an integer, than x α = k is the smallest integer > nα 2 (x (nα) + x (nα+) ) if nα is integer Measures for location Special quantiles α {0., 0.2, 0.3,..., 0.9}: deciles α {0.25, 0.75}: first and third quartile α = 0: minimum α = : maximum.2 Definition: Variance of a sample The variance for a sample is defined as s 2 = n (x i x) 2 or s 2 n = n (x i x) 2 2
3 Loss of one degree of freedom, since n (x i x) = 0 x minimizes the average of the squared deviations The standard deviation s is then s = s 2 Note: s is not the same as Standard error of the mean (SEM) The variance of a population is σ 2 = N N (x i µ) 2 with µ = N N x i Definition: Variance decomposition k groups (x, x 2,..., x n,),, (x k, x 2k,..., x nk,k) with x j = x ij, j =,..., k and Then s 2 = (x ij x j ) 2, j =,..., k k k s 2 n = n j= with n = k j= and x = n k j= x j ( x j x) 2 + n j= s 2 Definition: Median absolute deviation The median absolute deviation (MAD) is MAD = n x i x 0.5 x 0.5 minimizes the average of the absolute deviations Definition: Range The range is Range = x (n) x () 3
4 Definition: Interquartile range (IQR) The IQR is IQR = x 0.75 x 0.25 Coefficient of variation Definition: Coefficient of variation v = s x. Assumption: X has positive values.3 Measure for skewness Skewness Definition: Skewness Figure : Distributions which are symmetric, negative skewed and positive skewed The skewness of a sample is g = n ( n (x i x) 3 ) 3 (x i x) 2.4 Graphical display, five point summary of a sample Five point summary: Minimum, first quartile, median, third quartile, maximum. version of a boxplot displays these measures The simple The extended version is given on the next slide 4
5 , extended version Calculate x 0.25, x 0.5, x 0.75 and IQR Draw a box bounded by x 0.25 and x 0.75, mark x 0.5 with a line Any data observation which lies more than.5 IQR lower than the first quartile or.5 IQR higher than the third quartile is considered an outlier. Indicate the smallest value that is not an outlier by connecting it to the box with a line or "whisker". Indicate outliers by open and closed dots (or stars). "Extreme" outliers, or those which lie more than 3 IQR below the first and above third quartiles respectively, are indicated by the presence of a closed dot or star. "Mild" outliers  that is, those observations which lie more than.5 IQR from the first and third quartile but are not also extreme outliers are indicated by the presence of a open dot. Design of a * o Extreme outlier (Mild) Outlier Whisker Third Quartile Median First Quartile Minimal value which is no outlier Magnitudes data 5
6 Noise data s: some notes s are useful to compare distributions (e.g. for different groups) s are more useful than error bars (e.g. x ± 2 SEM) s give a hint for the shape of the distribution (symmetric or not) Multiple modes can not be detected See for alternative forms s need to tuning values as e.g. the number of bins in a histogram or the bandwidth in a kernel density estimate 6
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 informationWe 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 informationChapter 3 Descriptive Statistics: Numerical Measures. Learning objectives
Chapter 3 Descriptive Statistics: Numerical Measures Slide 1 Learning objectives 1. Single variable Part I (Basic) 1.1. How to calculate and use the measures of location 1.. How to calculate and use the
More informationSTATS8: 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 informationSeminar paper Statistics
Seminar paper Statistics The seminar paper must contain:  the title page  the characterization of the data (origin, reason why you have chosen this analysis,...)  the list of the data (in the table)
More informationLecture 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 information1. 2. 3. 4. Find the mean and median. 5. 1, 2, 87 6. 3, 2, 1, 10. Bellwork 32315 Simplify each expression.
Bellwork 32315 Simplify each expression. 1. 2. 3. 4. Find the mean and median. 5. 1, 2, 87 6. 3, 2, 1, 10 1 Objectives Find measures of central tendency and measures of variation for statistical data.
More information103 Measures of Central Tendency and Variation
103 Measures of Central Tendency and Variation So far, we have discussed some graphical methods of data description. Now, we will investigate how statements of central tendency and variation can be used.
More informationDescriptive 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 informationF. 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 informationCenter: 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 informationChapter 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 informationStatistical Concepts and Market Return
Statistical Concepts and Market Return 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Some Fundamental Concepts... 2 3. Summarizing Data Using Frequency Distributions...
More informationNumerical Summarization of Data OPRE 6301
Numerical Summarization of Data OPRE 6301 Motivation... In the previous session, we used graphical techniques to describe data. For example: While this histogram provides useful insight, other interesting
More informationBNG 202 Biomechanics Lab. Descriptive statistics and probability distributions I
BNG 202 Biomechanics Lab Descriptive statistics and probability distributions I Overview The overall goal of this short course in statistics is to provide an introduction to descriptive and inferential
More informationDescriptive 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 informationA 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 informationHomework 3. Part 1. Name: Score: / null
Name: Score: / Homework 3 Part 1 null 1 For the following sample of scores, the standard deviation is. Scores: 7, 2, 4, 6, 4, 7, 3, 7 Answer Key: 2 2 For any set of data, the sum of the deviation scores
More informationx Measures of Central Tendency for Ungrouped Data Chapter 3 Numerical Descriptive Measures Example 31 Example 31: Solution
Chapter 3 umerical Descriptive Measures 3.1 Measures of Central Tendency for Ungrouped Data 3. Measures of Dispersion for Ungrouped Data 3.3 Mean, Variance, and Standard Deviation for Grouped Data 3.4
More informationTreatment and analysis of data Applied statistics Lecture 3: Sampling and descriptive statistics
Treatment and analysis of data Applied statistics Lecture 3: Sampling and descriptive statistics Topics covered: Parameters and statistics Sample mean and sample standard deviation Order statistics and
More informationExploratory 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 informationNumerical 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 informationMCQ S OF MEASURES OF CENTRAL TENDENCY
MCQ S OF MEASURES OF CENTRAL TENDENCY MCQ No 3.1 Any measure indicating the centre of a set of data, arranged in an increasing or decreasing order of magnitude, is called a measure of: (a) Skewness (b)
More information3: Summary Statistics
3: Summary Statistics Notation Let s start by introducing some notation. Consider the following small data set: 4 5 30 50 8 7 4 5 The symbol n represents the sample size (n = 0). The capital letter X denotes
More informationDescriptive 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 informationDescribing Data. We find the position of the central observation using the formula: position number =
HOSP 1207 (Business Stats) Learning Centre Describing Data This worksheet focuses on describing data through measuring its central tendency and variability. These measurements will give us an idea of what
More informationData Exploration Data Visualization
Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select
More informationThe 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 information1.3 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 informationChapter 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 information13.2 Measures of Central Tendency
13.2 Measures of Central Tendency Measures of Central Tendency For a given set of numbers, it may be desirable to have a single number to serve as a kind of representative value around which all the numbers
More informationIntroduction to Statistics for Psychology. Quantitative Methods for Human Sciences
Introduction to Statistics for Psychology and Quantitative Methods for Human Sciences Jonathan Marchini Course Information There is website devoted to the course at http://www.stats.ox.ac.uk/ marchini/phs.html
More informationCS6220: DATA MINING TECHNIQUES
CS6220: DATA MINING TECHNIQUES 2: Data PreProcessing Instructor: Yizhou Sun yzsun@ccs.neu.edu September 7, 2014 2: Data PreProcessing Getting to know your data Basic Statistical Descriptions of Data
More informationDescriptive Data Summarization
Descriptive Data Summarization (Understanding Data) First: Some data preprocessing problems... 1 Missing Values The approach of the problem of missing values adopted in SQL is based on nulls and threevalued
More informationFrequency distributions, central tendency & variability. Displaying data
Frequency distributions, central tendency & variability Displaying data Software SPSS Excel/Numbers/Google sheets Social Science Statistics website (socscistatistics.com) Creating and SPSS file Open the
More informationContent 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 informationExercise 1.12 (Pg. 2223)
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 informationvs. relative cumulative frequency
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...
More informationMeans, standard deviations and. and standard errors
CHAPTER 4 Means, standard deviations and standard errors 4.1 Introduction Change of units 4.2 Mean, median and mode Coefficient of variation 4.3 Measures of variation 4.4 Calculating the mean and standard
More informationLecture 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 informationExploratory 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 informationSTATISTICS FOR PSYCH MATH REVIEW GUIDE
STATISTICS FOR PSYCH MATH REVIEW GUIDE ORDER OF OPERATIONS Although remembering the order of operations as BEDMAS may seem simple, it is definitely worth reviewing in a new context such as statistics formulae.
More information4. Introduction to Statistics
Statistics for Engineers 41 4. Introduction to Statistics Descriptive Statistics Types of data A variate or random variable is a quantity or attribute whose value may vary from one unit of investigation
More informationChapter 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 informationModule 4: Data Exploration
Module 4: Data Exploration Now that you have your data downloaded from the Streams Project database, the detective work can begin! Before computing any advanced statistics, we will first use descriptive
More informationDescriptive 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 informationData Analysis. Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) SS Analysis of Experiments  Introduction
Data Analysis Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) Prof. Dr. Dr. h.c. Dieter Rombach Dr. Andreas Jedlitschka SS 2014 Analysis of Experiments  Introduction
More informationHistogram. Graphs, and measures of central tendency and spread. Alternative: density (or relative frequency ) plot /13/2004
Graphs, and measures of central tendency and spread 9.07 9/13/004 Histogram If discrete or categorical, bars don t touch. If continuous, can touch, should if there are lots of bins. Sum of bin heights
More informationCHINHOYI UNIVERSITY OF TECHNOLOGY
CHINHOYI UNIVERSITY OF TECHNOLOGY SCHOOL OF NATURAL SCIENCES AND MATHEMATICS DEPARTMENT OF MATHEMATICS MEASURES OF CENTRAL TENDENCY AND DISPERSION INTRODUCTION From the previous unit, the Graphical displays
More informationVariables. 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 informationSection 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 informationCH.6 Random Sampling and Descriptive Statistics
CH.6 Random Sampling and Descriptive Statistics Population vs Sample Random sampling Numerical summaries : sample mean, sample variance, sample range StemandLeaf Diagrams Median, quartiles, percentiles,
More informationBiostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY
Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY 1. Introduction Besides arriving at an appropriate expression of an average or consensus value for observations of a population, it is important to
More informationLearnStat MEASURES OF CENTRAL TENDENCY, Learning Statistics the Easy Way. Session on BUREAU OF LABOR AND EMPLOYMENT STATISTICS
LearnStat t Learning Statistics the Easy Way Session on MEASURES OF CENTRAL TENDENCY, DISPERSION AND SKEWNESS MEASURES OF CENTRAL TENDENCY, DISPERSION AND SKEWNESS OBJECTIVES At the end of the session,
More informationWhy Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012
Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization GENOME 560, Spring 2012 Data are interesting because they help us understand the world Genomics: Massive Amounts
More information4. DESCRIPTIVE STATISTICS. Measures of Central Tendency (Location) Sample Mean
4. DESCRIPTIVE STATISTICS Descriptive Statistics is a body of techniques for summarizing and presenting the essential information in a data set. Eg: Here are daily high temperatures for Jan 6, 29 in U.S.
More informationIntroduction to Descriptive Statistics
Mathematics Learning Centre Introduction to Descriptive Statistics Jackie Nicholas c 1999 University of Sydney Acknowledgements Parts of this booklet were previously published in a booklet of the same
More informationThe Big 50 Revision Guidelines for S1
The Big 50 Revision Guidelines for S1 If you can understand all of these you ll do very well 1. Know what is meant by a statistical model and the Modelling cycle of continuous refinement 2. Understand
More informationStatistical Foundations: Measures of Location and Central Tendency and Summation and Expectation
Statistical Foundations: and Central Tendency and and Lecture 4 September 5, 2006 Psychology 790 Lecture #49/05/2006 Slide 1 of 26 Today s Lecture Today s Lecture Where this Fits central tendency/location
More informationSampling Distribution of a Normal Variable
Ismor Fischer, 5/9/01 5.1 5. Formal Statement and Examples Comments: Sampling Distribution of a Normal Variable Given a random variable. Suppose that the population distribution of is known to be normal,
More informationGCSE HIGHER Statistics Key Facts
GCSE HIGHER Statistics Key Facts Collecting Data When writing questions for questionnaires, always ensure that: 1. the question is worded so that it will allow the recipient to give you the information
More informationProbability and Statistics Vocabulary List (Definitions for Middle School Teachers)
Probability and Statistics Vocabulary List (Definitions for Middle School Teachers) B Bar graph a diagram representing the frequency distribution for nominal or discrete data. It consists of a sequence
More informationUnit 21 Student s t Distribution in Hypotheses Testing
Unit 21 Student s t Distribution in Hypotheses Testing Objectives: To understand the difference between the standard normal distribution and the Student's t distributions To understand the difference between
More information1.5 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 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 informationStatistics 1040 Dr. Tom McGahagan DATA AND DESCRIPTIVE STATISTICS
Statistics 1040 Dr. Tom McGahagan DATA AND DESCRIPTIVE STATISTICS Data  information on a variable or group of variables, which may be either numeric (examples: income in dollars, weight in pounds) or
More informationBusiness Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGrawHill/Irwin, 2008, ISBN: 9780073319889. Required Computing
More informationLesson 4 Measures of Central Tendency
Outline Measures of a distribution s shape modality and skewness the normal distribution Measures of central tendency mean, median, and mode Skewness and Central Tendency Lesson 4 Measures of Central
More informationBox plots & ttests. Example
Box plots & ttests Box Plots Box plots are a graphical representation of your sample (easy to visualize descriptive statistics); they are also known as boxandwhisker diagrams. Any data that you can
More informationMeasures of Central Tendency. There are different types of averages, each has its own advantages and disadvantages.
Measures of Central Tendency According to Prof Bowley Measures of central tendency (averages) are statistical constants which enable us to comprehend in a single effort the significance of the whole. The
More informationDescriptive statistics parameters: Measures of centrality
Descriptive statistics parameters: Measures of centrality Contents Definitions... 3 Classification of descriptive statistics parameters... 4 More about central tendency estimators... 5 Relationship between
More informationSkew Dice TM Statistics Activities and Worksheets written by Robert Fathauer
Skew Dice TM Statistics Activities and Worksheets written by Robert Fathauer Teachers are given permission to print as many copies of the worksheets as needed for their own class. Individuals are given
More informationAP * 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 informationGeostatistics Exploratory Analysis
Instituto Superior de Estatística e Gestão de Informação Universidade Nova de Lisboa Master of Science in Geospatial Technologies Geostatistics Exploratory Analysis Carlos Alberto Felgueiras cfelgueiras@isegi.unl.pt
More informationImplications of Big Data for Statistics Instruction 17 Nov 2013
Implications of Big Data for Statistics Instruction 17 Nov 2013 Implications of Big Data for Statistics Instruction Mark L. Berenson Montclair State University MSMESB Mini Conference DSI Baltimore November
More informationQuantitative Methods for Finance
Quantitative Methods for Finance Module 1: The Time Value of Money 1 Learning how to interpret interest rates as required rates of return, discount rates, or opportunity costs. 2 Learning how to explain
More informationMeasures of Center Section 32 Definitions Mean (Arithmetic Mean)
Measures of Center Section 31 Mean (Arithmetic Mean) AVERAGE the number obtained by adding the values and dividing the total by the number of values 1 Mean as a Balance Point 3 Mean as a Balance Point
More informationDescriptive Statistics. Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion
Descriptive Statistics Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Statistics as a Tool for LIS Research Importance of statistics in research
More informationWeek 1. Exploratory Data Analysis
Week 1 Exploratory Data Analysis Practicalities This course ST903 has students from both the MSc in Financial Mathematics and the MSc in Statistics. Two lectures and one seminar/tutorial per week. Exam
More informationStatistical Analysis I
CTSI BERD Research Methods Seminar Series Statistical Analysis I Lan Kong, PhD Associate Professor Department of Public Health Sciences December 22, 2014 Biostatistics, Epidemiology, Research Design(BERD)
More informationExploratory 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 informationCourse Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics
Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGrawHill/Irwin, 2010, ISBN: 9780077384470 [This
More information( ) ( ) Central Tendency. Central Tendency
1 Central Tendency CENTRAL TENDENCY: A statistical measure that identifies a single score that is most typical or representative of the entire group Usually, a value that reflects the middle of the distribution
More information6. Methods 6.8. Methods related to outputs, Introduction
6. Methods 6.8. Methods related to outputs, Introduction In order to present the outcomes of statistical data collections to the users in a manner most users can easily understand, a variety of statistical
More informationMEAN 34 + 31 + 37 + 44 + 38 + 34 + 42 + 34 + 43 + 41 = 378 MEDIAN
MEASURES OF CENTRAL TENDENCY MEASURES OF CENTRAL TENDENCY The measures of central tendency are numbers that locate the center of a set of data. The three most common measures of center are mean, median
More informationDescriptive Statistics
Descriptive Statistics Suppose following data have been collected (heights of 99 fiveyearold boys) 117.9 11.2 112.9 115.9 18. 14.6 17.1 117.9 111.8 16.3 111. 1.4 112.1 19.2 11. 15.4 99.4 11.1 13.3 16.9
More informationBASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS
BASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi110 012 seema@iasri.res.in Genomics A genome is an organism s
More informationSession 1.6 Measures of Central Tendency
Session 1.6 Measures of Central Tendency Measures of location (Indices of central tendency) These indices locate the center of the frequency distribution curve. The mode, median, and mean are three indices
More informationUnit 24 Hypothesis Tests about Means
Unit 24 Hypothesis Tests about Means Objectives: To recognize the difference between a paired t test and a twosample t test To perform a paired t test To perform a twosample t test A measure of the amount
More informationData Analysis: Describing Data  Descriptive Statistics
WHAT IT IS Return to Table of ontents Descriptive statistics include the numbers, tables, charts, and graphs used to describe, organize, summarize, and present raw data. Descriptive statistics are most
More informationHome 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 informationMeasures of Central Tendency and Variability: Summarizing your Data for Others
Measures of Central Tendency and Variability: Summarizing your Data for Others 1 I. Measures of Central Tendency: Allow us to summarize an entire data set with a single value (the midpoint). 1. Mode :
More information= = = pages. = = =399 pages. = = 13 cm. 09 Measures of Center, Spread, and Position. Find the mean, median, and mode for each set of data.
Find the mean, median, and mode for each set of data. 1. number of pages in each novel assigned for summer reading: 224, 272, 374, 478, 960, 394, 404, 308, 480, 624 To find the mean divide the sum of all
More informationSummarizing Data: Measures of Variation
Summarizing Data: Measures of Variation One aspect of most sets of data is that the values are not all alike; indeed, the extent to which they are unalike, or vary among themselves, is of basic importance
More informationDescriptive 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 informationSummary of Formulas and Concepts. Descriptive Statistics (Ch. 14)
Summary of Formulas and Concepts Descriptive Statistics (Ch. 14) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume
More informationLab 6: Sampling Distributions and the CLT
Lab 6: Sampling Distributions and the CLT Objective: The objective of this lab is to give you a hands on discussion and understanding of sampling distributions and the Central Limit Theorem (CLT), a theorem
More information32 Measures of Central Tendency and Dispersion
32 Measures of Central Tendency and Dispersion In this section we discuss two important aspects of data which are its center and its spread. The mean, median, and the mode are measures of central tendency
More informationBasic Biostatistics for Clinical Research. Ramses F Sadek, PhD GRU Cancer Center
Basic Biostatistics for Clinical Research Ramses F Sadek, PhD GRU Cancer Center 1 1. Basic Concepts 2. Data & Their Presentation Part One 2 1. Basic Concepts Statistics Biostatistics Populations and samples
More informationDescribe what is meant by a placebo Contrast the doubleblind procedure with the singleblind procedure Review the structure for organizing a memo
Readings: Ha and Ha Textbook  Chapters 1 8 Appendix D & E (online) Plous  Chapters 10, 11, 12 and 14 Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability
More information