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


 Bernadette McCoy
 7 years ago
 Views:
Transcription
1 Descriptive Statistics Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion
2 Statistics as a Tool for LIS Research Importance of statistics in research Summarize observations to provide answers to research questions and hypotheses Make general conclusions based on specific study observations Objectively evaluate reliability of study conclusions
3 Statistics as a Tool for LIS Research Main purposes of statistics in research Describe central point in a set of data/observations Describe how broad, diversified, or variable the data in a set is Indicate whether specfic features of a set of data are related, and how closely they are related Indicate probability of features of data being influenced by factors other than simply chance
4 Statistics as a Tool for LIS Research Two main types or branches of statistics Descriptive statistics Characterizing or summarizing data set Presenting data in charts and tables to clarify characteristics No inference, just describing a particular group of observations Inferential statistics Using sample data to make generalizations (inferences) or estimates about a population Statements made in terms of probability
5 Statistics as a Tool for LIS Research Descriptive and inferential statistics not mutually exclusive Overlap in what can be called descriptive and what can be called inferential Intent is important: Group of observations intended to describe an event: descriptive Group of observations collected from a sample and intended to predict what a larger population is like: inferential
6 Statistics as a Tool for LIS Research Choosing statistical methods Type of data collected largely determines choice of statistical analysis techniques Decisions about how and what type of data is collected will determine the specific statistical tests that can be performed to analyze the data Data collected should determine statistical tests used, not the other way around But consideration of how you want to analyze data should be done as part of research design to ensure study can produce the type of conclusions you want to make
7 Descriptive Statistics Commonly used in LIS research Cannot test causal relationships Primary strength is describing and summarizing data: Describing data in terms of frequency distributions Describing most typical value in data set  measures of central tendency Describing variability of data  measures of dispersion
8 Frequency Distributions Describing data in terms of frequency distributions Counts of totals by value or category for each measured variable Can be presented as absolute totals, cumulative totals, percentages, grouped totals Books checked out Often a first step in statistical analysis of data Usually presented in tables or charts (histogram, bar graph, etc.) Age group
9 Describing most typical value in data set  measures of central tendency Mean is often referred to as average though average can be any of these measures of central tendency: Mean (arithmetic average) Median Mode
10 Mean Most popular statistic for summarizing data Can be used for interval or ratio data Based on all observations of the data set Arithmetic average of a set of observations Example: mean of 5, 10, and 30 is 15, since 45 3 = 15 Mean of a set of numbers can be a number not in set Example: mean of 1, 2, 3, and 4 is 3.5, since 10 4 = 2.5
11 ple size σ population stdev jth quartile Samplep standard population deviation: General N population addition rule: size Probab P(A proportion ple mean x 2 ( x) d 2 paired /n difference population s CHAPTER size µ population mean n 1 O observed (x x) frequency s 2 Mean of a discrete x random ple stdev ˆp sample proportion or s 2 ( x population mean E expected n 1frequency Probab nwhere 1 (n uartile + 1)/2, 3(n + p1)/4 population proportion Standard Descriptive Statistics Quartile positions: N den CHAPTER (n + 1)/4, 3 (n deviation of a disc lation size O observed frequencyσ Descriptive (x + 1)/2, µ) 2 3(n P(X Measu + 1)/ x Q Descriptive 1 Measures lation Formula mean of mean Sample mean: x x Specia mean: x x Interquartile E expected range: frequency IQR Factorial: Q 3 Q 1 k! k(k where 1) Upper limit Q IQR Sample mean: = mean of sample n P n Lower limit Q IQR, Upper limit N( Q deno ) 3 n + 1 (A, B, able): = mean of population Range: Range Max Min Range µ x Binomial coefficient: criptive Measures MaxN Min Population mean (mean Population of a variable): mean: µ x Specia x = sigma, sum of values N Comp standard deviation: of a variable): Sample Binomial standard probability deviation: formu x x P X n= set of observations Population STAstandard 570 deviation (standard Formula deviation Sheet (x x) 2 Gener of a v (x x) 2 x 2 x X i = specific observations or s 2 ( x) 2 /n (A, B, P(X x) or Maxσ Min Sample Mean = X s = X 1+X X o n n 1 (x n µ) 1 = Mean σ 2 x N µ2 or nσ 1 2 Compl n n or N = number of N where n denotes the numbe N rd deviation: positions: µ (n + 1)/4, (n + 1)/2, 3(n observations Quartile + 1)/4 Standa probability. positions: (n + 1)/4, Gary Sample Geisler Simmons Variance College LIS 403 Spring, = 2004 rtile range: IQR Standardized Q s 2 = (X 1 X) 2 +(X 2 X) 2 3 Q variable: z x µ Genera (x x) 2 x 2 ( x) 2 /n 1 +. or s Interquartile Mean σ of arange: binomial IQRrandom Q n i=1 X σ
12 Median Value that is above the lower onehalf and below the upper onehalf of the values  middle value of set of observations when they have been arranged in order Can be used for ordinal, interval or ratio data Most central measure of a distribution Every data set has a median that is unique Difference in sets with odd numbers of observations than for even numbers of observations Example: median of the five observations 1, 3, 15, 16, and 17 = 15 Example: median of the six observations 1, 2, 3, 5, 8, and 9 = 4
13 Mode Can be used for any type of data Most frequently occuring value among a set of observations Examples: Mode of the observations 1, 2, 2, 3, 4, 5 = 2 Set of observations 1, 2, 3, 4, 5 has no mode Set of observations 1, 2, 3, 3, 4, 5, 5 has no single mode, but can be considered to have two modes, or is bimodal
14 Advantages of mean Always exists Is unique Can always be calculated by a simple formula Disadvantages of mean Mean value for a data set is not necessarily one of the values of the data set Sensitive to extreme scores, either high or low Easily distorted by extremely large or extremely small values among the set of observations, Example: mean of 1, 2, and 1,000,000 is 333,334.33
15 Advantages of median Not affected by extreme scores Useful way of describing sets of observations that are skewed by including extremely large or small values Disadvantages of median Median is not necessarily one of the values of the data set Defined differently for odd and even numbers of observations
16 Advantages of mode Can be used with any scale of measurement If set of observations has a mode, mode usefully characterizing the set For example, set of observations noting result of rolling two dice will have a mode of 7 Disadvantages of mode Many sets of observations lack a mode because no observed value occurs more than once Other sets of observations may have several different most frequent values Doesn t characterize set beyond most frequently occuring value
17 Calculating mean Age Frequency
18 Calculating mean Age Frequency 13 x 3 = x 4 = x 6 = x 8 = x 4 = x 3 = x 3 = 57 N = 31 Sum of X = /31 = Mean = 15.87
19 Calculating Age mode Frequency Mode =
20 Calculating median Age 13 Frequency 13 Nongrouped data N = 31 so midpoint is 16th value Median = 16
21 Calculating median Age Frequency Grouped data: Each value is somewhere within each age range Values are assumed to be equally distributed within range N = 31 so midpoint is 16th value Median =
22 Mean = Mode = 16 Median = 16.31
23 Normal distribution Normal curve, bellshaped curve, Gaussian distribution Many types of data are normally distributed in a population Histogram of data approximates a bellshaped, symmetrical curve Concentration of scores in the middle, with fewer and fewer scores as you approach extremes Example: heights of people in a population are normally distributed
24 Skewness Not all sets of data will exhibit properties of a normal distribution Some data sets are asymmetrical around a central point Majority of scores are closer to one extreme or the other: skewed distribution In a skewed distribution, the mean does not equal the median
25 Positively skewed distribution, tail goes to the right  median is less than the mean Example: Annual income of population Negatively skewed distribution tail goes to the left  mean is less than the median
26 Special case of skewness: JCurve Extreme skewness Proposed by Allport to describe conforming behavior in groups of people Large majority of scores fall at end representing socially acceptable behavior, small minority represent deviation from norm Example: amount of time drivers who park in No Parking zone stay there < 5 5 to to to to 25 >25
27 Determining when a distribution is skewed too much to be considered normal General rule of thumb: values beyond 2 standard errors of skewness (ses) are probably significantly skewed ses = 6/N or use ses statistic from software (SPSS, for example) output Example: if sample size = 30 and skewness statistic is.9814: ses = 6/30 =.20 = ses =.4472 x 2 =.8944 skewness statistic of.9814 is beyond 2 ses, so is significantly skewed Other factors (histograms, normal probability plots, type of test to be used) should influence decision, depending on exact circumstances of analysis
28 Kurtosis  amount of peakedness or flatness of the distribution Mesokurtic  normal Leptokurtic  peaked, many scores around middle Platykurtic  flat, many scores dispersed from middle Nonnormal kurtosis determined by similar process to skewness Nonnormal kurtosis only a concern with some statistical tests
29 Selecting appropriate measure of central tendency Interactive selection at Selecting Statistics by William M.K. Trochim: Rules below can be bent, depending on situation Unimodal, Ratio or interval data, skewed Unimodal, Ratio or interval data, not skewed Unimodal, ordinal Unimodal, Nominal Bimodal or multimodal distribution median mean median mode mode
30 Measures of Dispersion Variability is a fundamental characteristic of most data sets, but is not addressed by measures of central tendency Measures of central tendency are not enough to accurately describe a data set Also need to be able to describe the variability or dispersion of the data Dispersion: scatteredness or flucuation of scores around average score Several types of measures of dispersion Range Standard deviation Variance
31 Measures of Dispersion Range Distance between the smallest and largest observations in a set of data Examples: Range of the set of observations 2, 4, 7 is 5 Range of the set 10, 3, 4 is 14
32 Measures of Dispersion Interquartile range Simplified version: ignore the top and bottom 25% after sorting Difference between the remaining largest and smallest numbers is interquartile range Addresses the problem of outliers Other methods of calculating interquartile range are slightly more complicated but take into account more data
33 Measures of Dispersion Standard deviation Measures the variability or the degree of dispersion of the data set Square root of the average squared deviations from the mean Roughly speaking, standard deviation is the average distance between the individual observations and the center of the set of observations
34 Range: Range Max Min Measures of Dispersion Calculating standard deviation 1. Subtract each each observation from sample/population mean and square 2. Add squared distances 3. Divide sum by n  1 or N (adjusted mean of squared distances) 4. Take square root of mean squared distances Sample CHAPTER standard 3 Descriptive deviation: Meas (x x) Sample s mean: x 2 x or n 1 n Quartile Range: positions: Range (n Max + 1)/4, Mi Interquartile Sample standard deviation: range: IQR Q 3 (x x) SD of sample: Lower limit s Q IQR, n 1 Population Quartile mean positions: (mean (n of + a 1)/ va Population Interquartile standard range: deviation IQR ( Q Lower limit (x Q 1 µ) SD of population: 1.5 IQ σ 2 N Population mean (mean of a Standardized variable: z x Population standard deviatio CHAPTER 4 Descriptive (x Method µ) σ 2 S xx, S xy, and S yy : N
35 Measures of Dispersion Variance Square of standard deviation Not used for descriptive statistics, but is important for specific inferential statistics tests Variance of sample Variance of population
36 Measures of Dispersion Advantages of range as measure of dispersion Very simple to calculate Provides a meaningful characteristic of a set of observations (total spread of the observations) Disadvantages of range as measure of dispersion Extreme values distort range Only measures the total spread; tells us nothing about the pattern of data distribution Examples: Data set 1, 2, 3, 4, 5, 6, 7, 8, 9 has a range of 8 Data set 1, 9, 9, 9, 9, 9, 9, 9, 9 also has range of 8, though clearly less scattered
37 Measures of Dispersion Advantages of standard deviation as measure of dispersion Can always be calculated Meaningful characteristic of a set of observations; takes every observation into account to express the scatteredness of observations Examples: Set of observations 1, 2, 3, 4, 5, 6, 7, 8, 9 has a standard deviation s = 2.74 Set of observations 1, 9, 9, 9, 9, 9, 9, 9, 9 has a standard deviation s = 2.67 Range doesn t distinguish difference in scatteredness of sets, but standard deviation does Disadvantage of standard deviation as measure of dispersion is that it is more complicated to calculate  though not for computers
Descriptive Statistics
Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web
More informationDESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
More informationStatistics. Measurement. Scales of Measurement 7/18/2012
Statistics Measurement Measurement is defined as a set of rules for assigning numbers to represent objects, traits, attributes, or behaviors A variableis something that varies (eye color), a constant does
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 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 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 informationMBA 611 STATISTICS AND QUANTITATIVE METHODS
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 111) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
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 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 informationHow To Write A Data Analysis
Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction
More 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 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 informationFoundation of Quantitative Data Analysis
Foundation of Quantitative Data Analysis Part 1: Data manipulation and descriptive statistics with SPSS/Excel HSRS #10  October 17, 2013 Reference : A. Aczel, Complete Business Statistics. Chapters 1
More informationCA200 Quantitative Analysis for Business Decisions. File name: CA200_Section_04A_StatisticsIntroduction
CA200 Quantitative Analysis for Business Decisions File name: CA200_Section_04A_StatisticsIntroduction Table of Contents 4. Introduction to Statistics... 1 4.1 Overview... 3 4.2 Discrete or continuous
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 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 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 informationIntroduction; Descriptive & Univariate Statistics
Introduction; Descriptive & Univariate Statistics I. KEY COCEPTS A. Population. Definitions:. The entire set of members in a group. EXAMPLES: All U.S. citizens; all otre Dame Students. 2. All values of
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 informationNorthumberland Knowledge
Northumberland Knowledge Know Guide How to Analyse Data  November 2012  This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about
More 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 informationDescriptive Statistics and Measurement Scales
Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample
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 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 informationSummarizing and Displaying Categorical Data
Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency
More 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 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 informationSKEWNESS. Measure of Dispersion tells us about the variation of the data set. Skewness tells us about the direction of variation of the data set.
SKEWNESS All about Skewness: Aim Definition Types of Skewness Measure of Skewness Example A fundamental task in many statistical analyses is to characterize the location and variability of a data set.
More informationCALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 15 scale to 0100 scores When you look at your report, you will notice that the scores are reported on a 0100 scale, even though respondents
More information2. Filling Data Gaps, Data validation & Descriptive Statistics
2. Filling Data Gaps, Data validation & Descriptive Statistics Dr. Prasad Modak Background Data collected from field may suffer from these problems Data may contain gaps ( = no readings during this period)
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 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 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 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 informationTHE BINOMIAL DISTRIBUTION & PROBABILITY
REVISION SHEET STATISTICS 1 (MEI) THE BINOMIAL DISTRIBUTION & PROBABILITY The main ideas in this chapter are Probabilities based on selecting or arranging objects Probabilities based on the binomial distribution
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 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) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x  x) B. x 3 x C. 3x  x D. x  3x 2) Write the following as an algebraic expression
More 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 informationWithout data, all you are is just another person with an opinion.
OCR Statistics Module Revision Sheet The S exam is hour 30 minutes long. You are allowed a graphics calculator. Before you go into the exam make sureyou are fully aware of the contents of theformula booklet
More informationCHAPTER THREE COMMON DESCRIPTIVE STATISTICS COMMON DESCRIPTIVE STATISTICS / 13
COMMON DESCRIPTIVE STATISTICS / 13 CHAPTER THREE COMMON DESCRIPTIVE STATISTICS The analysis of data begins with descriptive statistics such as the mean, median, mode, range, standard deviation, variance,
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 Review PSY379
Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses
More informationFrequency Distributions
Descriptive Statistics Dr. Tom Pierce Department of Psychology Radford University Descriptive statistics comprise a collection of techniques for better understanding what the people in a group look like
More information5/31/2013. 6.1 Normal Distributions. Normal Distributions. Chapter 6. Distribution. The Normal Distribution. Outline. Objectives.
The Normal Distribution C H 6A P T E R The Normal Distribution Outline 6 1 6 2 Applications of the Normal Distribution 6 3 The Central Limit Theorem 6 4 The Normal Approximation to the Binomial Distribution
More information4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"
Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses
More 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 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 informationII. DISTRIBUTIONS distribution normal distribution. standard scores
Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More information6.4 Normal Distribution
Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under
More informationMEASURES OF VARIATION
NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are
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 informationEXAM #1 (Example) Instructor: Ela Jackiewicz. Relax and good luck!
STP 231 EXAM #1 (Example) Instructor: Ela Jackiewicz Honor Statement: I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.
More information4. Continuous Random Variables, the Pareto and Normal Distributions
4. Continuous Random Variables, the Pareto and Normal Distributions A continuous random variable X can take any value in a given range (e.g. height, weight, age). The distribution of a continuous random
More informationDATA INTERPRETATION AND STATISTICS
PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE
More information3.2 Measures of Spread
3.2 Measures of Spread In some data sets the observations are close together, while in others they are more spread out. In addition to measures of the center, it's often important to measure the spread
More informationStandard Deviation Estimator
CSS.com Chapter 905 Standard Deviation Estimator Introduction Even though it is not of primary interest, an estimate of the standard deviation (SD) is needed when calculating the power or sample size of
More informationDiagrams and Graphs of Statistical Data
Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in
More informationDensity Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties:
Density Curve A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: 1. The total area under the curve must equal 1. 2. Every point on the curve
More informationCHAPTER THREE. Key Concepts
CHAPTER THREE Key Concepts interval, ordinal, and nominal scale quantitative, qualitative continuous data, categorical or discrete data table, frequency distribution histogram, bar graph, frequency polygon,
More informationSTT315 Chapter 4 Random Variables & Probability Distributions KM. Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables
Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables Discrete vs. continuous random variables Examples of continuous distributions o Uniform o Exponential o Normal Recall: A random
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 informationLecture 2. Summarizing the Sample
Lecture 2 Summarizing the Sample WARNING: Today s lecture may bore some of you It s (sort of) not my fault I m required to teach you about what we re going to cover today. I ll try to make it as exciting
More informationBasics of Statistics
Basics of Statistics Jarkko Isotalo 30 20 10 Std. Dev = 486.32 Mean = 3553.8 0 N = 120.00 2400.0 2800.0 3200.0 3600.0 4000.0 4400.0 4800.0 2600.0 3000.0 3400.0 3800.0 4200.0 4600.0 5000.0 Birthweights
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationIntroduction to Environmental Statistics. The Big Picture. Populations and Samples. Sample Data. Examples of sample data
A Few Sources for Data Examples Used Introduction to Environmental Statistics Professor Jessica Utts University of California, Irvine jutts@uci.edu 1. Statistical Methods in Water Resources by D.R. Helsel
More informationMeasurement & Data Analysis. On the importance of math & measurement. Steps Involved in Doing Scientific Research. Measurement
Measurement & Data Analysis Overview of Measurement. Variability & Measurement Error.. Descriptive vs. Inferential Statistics. Descriptive Statistics. Distributions. Standardized Scores. Graphing Data.
More informationA Picture Really Is Worth a Thousand Words
4 A Picture Really Is Worth a Thousand Words Difficulty Scale (pretty easy, but not a cinch) What you ll learn about in this chapter Why a picture is really worth a thousand words How to create a histogram
More informationWeek 3&4: Z tables and the Sampling Distribution of X
Week 3&4: Z tables and the Sampling Distribution of X 2 / 36 The Standard Normal Distribution, or Z Distribution, is the distribution of a random variable, Z N(0, 1 2 ). The distribution of any other normal
More informationStatistics Revision Sheet Question 6 of Paper 2
Statistics Revision Sheet Question 6 of Paper The Statistics question is concerned mainly with the following terms. The Mean and the Median and are two ways of measuring the average. sumof values no. of
More informationHow To Test For Significance On A Data Set
NonParametric Univariate Tests: 1 Sample Sign Test 1 1 SAMPLE SIGN TEST A nonparametric equivalent of the 1 SAMPLE TTEST. ASSUMPTIONS: Data is nonnormally distributed, even after log transforming.
More informationEngineering Problem Solving and Excel. EGN 1006 Introduction to Engineering
Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques
More informationDongfeng Li. Autumn 2010
Autumn 2010 Chapter Contents Some statistics background; ; Comparing means and proportions; variance. Students should master the basic concepts, descriptive statistics measures and graphs, basic hypothesis
More informationStatistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013
Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.11.6) Objectives
More informationDescribing Data: Measures of Central Tendency and Dispersion
100 Part 2 / Basic Tools of Research: Sampling, Measurement, Distributions, and Descriptive Statistics Chapter 8 Describing Data: Measures of Central Tendency and Dispersion In the previous chapter we
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 informationAnalysing Questionnaires using Minitab (for SPSS queries contact ) Graham.Currell@uwe.ac.uk
Analysing Questionnaires using Minitab (for SPSS queries contact ) Graham.Currell@uwe.ac.uk Structure As a starting point it is useful to consider a basic questionnaire as containing three main sections:
More informationModule 3: Correlation and Covariance
Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis
More informationBowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition
Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology StepbyStep  Excel Microsoft Excel is a spreadsheet software application
More informationHISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS
Mathematics Revision Guides Histograms, Cumulative Frequency and Box Plots Page 1 of 25 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS
More informationFirst Midterm Exam (MATH1070 Spring 2012)
First Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notecard. Calculators are allowed, but other electronics are prohibited. 1. [40pts] Multiple Choice Problems
More informationPie Charts. proportion of icecream flavors sold annually by a given brand. AMS5: Statistics. Cherry. Cherry. Blueberry. Blueberry. Apple.
Graphical Representations of Data, Mean, Median and Standard Deviation In this class we will consider graphical representations of the distribution of a set of data. The goal is to identify the range of
More informationDescription. Textbook. Grading. Objective
EC151.02 Statistics for Business and Economics (MWF 8:008:50) Instructor: Chiu Yu Ko Office: 462D, 21 Campenalla Way Phone: 26093 Email: kocb@bc.edu Office Hours: by appointment Description This course
More informationSTA201TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance
Principles of Statistics STA201TE This TECEP is an introduction to descriptive and inferential statistics. Topics include: measures of central tendency, variability, correlation, regression, hypothesis
More informationMean = (sum of the values / the number of the value) if probabilities are equal
Population Mean Mean = (sum of the values / the number of the value) if probabilities are equal Compute the population mean Population/Sample mean: 1. Collect the data 2. sum all the values in the population/sample.
More informationChapter 2 Statistical Foundations: Descriptive Statistics
Chapter 2 Statistical Foundations: Descriptive Statistics 20 Chapter 2 Statistical Foundations: Descriptive Statistics Presented in this chapter is a discussion of the types of data and the use of frequency
More informationProbability and Statistics Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur
Probability and Statistics Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur Module No. #01 Lecture No. #15 Special DistributionsVI Today, I am going to introduce
More informationIntroduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
More informationAP STATISTICS REVIEW (YMS Chapters 18)
AP STATISTICS REVIEW (YMS Chapters 18) Exploring Data (Chapter 1) Categorical Data nominal scale, names e.g. male/female or eye color or breeds of dogs Quantitative Data rational scale (can +,,, with
More information1 Descriptive statistics: mode, mean and median
1 Descriptive statistics: mode, mean and median Statistics and Linguistic Applications Hale February 5, 2008 It s hard to understand data if you have to look at it all. Descriptive statistics are things
More informationExpression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds
Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative
More informationDESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS
DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi  110 012 seema@iasri.res.in 1. Descriptive Statistics Statistics
More informationSampling and Descriptive Statistics
Sampling and Descriptive Statistics Berlin Chen Department of Computer Science & Information Engineering National Taiwan Normal University Reference: 1. W. Navidi. Statistics for Engineering and Scientists.
More informationELEMENTARY STATISTICS
ELEMENTARY STATISTICS Study Guide Dr. Shinemin Lin Table of Contents 1. Introduction to Statistics. Descriptive Statistics 3. Probabilities and Standard Normal Distribution 4. Estimates and Sample Sizes
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 informationThe Dummy s Guide to Data Analysis Using SPSS
The Dummy s Guide to Data Analysis Using SPSS Mathematics 57 Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved TABLE OF CONTENTS PAGE Helpful Hints for All Tests...1 Tests
More informationDESCRIPTIVE STATISTICS  CHAPTERS 1 & 2 1
DESCRIPTIVE STATISTICS  CHAPTERS 1 & 2 1 OVERVIEW STATISTICS PANIK...THE THEORY AND METHODS OF COLLECTING, ORGANIZING, PRESENTING, ANALYZING, AND INTERPRETING DATA SETS SO AS TO DETERMINE THEIR ESSENTIAL
More informationTEACHER NOTES MATH NSPIRED
Math Objectives Students will understand that normal distributions can be used to approximate binomial distributions whenever both np and n(1 p) are sufficiently large. Students will understand that when
More information