MBA 611 STATISTICS AND QUANTITATIVE METHODS


 Constance Casey
 3 years ago
 Views:
Transcription
1 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 events. We use statistical methods and statistical analysis to make decisions in uncertain environment. Population: Sample: A population is the complete set of all items in which an investigator is interested. A sample is a subset of population values. & Eample: Population  High school students  Households in the U.S. Sample  A sample of 30 students  A Gallup poll of 1,000 consumers  Nielson Survey of TV rating Random Sample: A random sample of n data values is one selected from the population in such a way that every different sample of size n has an equal chance of selection. & Eample: Random Selection  Lotto numbers  Random numbers Random Variable: A variable takes different possible values for a given subject of study. Numerical Variable: A numerical variable takes some countable finite numbers or infinite numbers. Categorical Variable: A categorical variable takes values that belong to groups or categories. Data: Data are measured values of the variable. There are two types of data: quantitative data and qualitative data. 1
2 Quantitative Data: Qualitative Data: Quantitative data are data measured on a numerical scale. Qualitative data are nonnumerical data that can only be classified into one of a group of categories. & Eample: 1. Temperature. Height 3. Age in years 3. Income 4. Prices 5. Occupations 6. Race 7. Sales and Advertising 8. Consumption and Income Statistics: Statistics is the science of data. This involves collecting, classifying, summarizing, analyzing data, and then making inferences and decisions based on the data collected. Population Parameters: The numerical measures of a population are called parameters. & Eample: Population average. Sample Statistics: The numerical measures of a sample are called sample statistics. & Eample: Sample average. Descriptive Statistics: Descriptive statistics involves collecting, classifying, and summarizing data. Inferential Statistics: Inferential statistics makes statistical inference about the population parameters based on sample information. Business Decisions: From time to time, we use quantitative analysis to make business decisions. & Eample: Economics: Price of a Good, Interest Rate, Mortgage Rate Finance: Returns, Stock Prices Marketing: Advertising, Sales Management: Quality Control
3 B. Descriptive Statistics (Chapters and 3) B.1 Describing Data Sets Graphically (Chapter ) The simplest way to describe data is to use graphs. The following shows two types of graphs: frequency histogram and line graph. B.1.1 Relative Frequency Histogram The relative frequency histogram shows the proportions of the total set of data values that fall in various numerical intervals. & Eample: Sale Prices The following data represent sale prices (in thousands of dollars) for a random sample of 5 residential properties sold Sort the data Organize the data and construct the following relative frequency distribution table. Class i Class Limits Freq. ( f i ) Relative Frequency 1 (30, 49) /5 =0.08 (50, 69) 7 7/5 = (70, 89) 8 8/5 = (90, 109) 5 5/5 = (110, 19) /5 = (130, 149) 1 1/5 = 0.04 Sum 5 1 3
4 The relative frequency histogram is Relative Frequency Relative Frequency Sale Price In this graph, 1. The data are classified into 6 classes.. Each class has the same width. The width is equal to The graph shows the midpoints of these classes on the horizontal ais. 4. The vertical bar shows the relative frequency of sale prices falling in each class interval. How to decide the class width: the largest number  the smallest number Width =. the number of classes & Eample: Sale Prices Width = = O Eercise: The following data are yeartoday (YTD) returns for a sample of 30 mutual funds ( ) Then Width = =
5 Sort the data as the following: Organize the data and construct the following relative frequency distribution table. Class i Class Limits Freq. ( f i ) Relative Frequency 1 (5.00, .51) (.50, 0.01) Sum Draw a relative frequency histogram. Tetbook Eercises:.5,.6,.8,.9, pages 3. Ecel: Create a Histogram 1. Click on Tools.. Click on Data Analysis. (If Data Analysis is not on the list, click and Check AAnalysis to install the addin from Microsoft Office CD.) 3. Select Histogram; click OK. 4. Complete dialog bo: Input range contains data; Bin range contains upper boundary of interval; click OK. 5. Delete (using Edit) last row called More. 5
6 B.1. Line Graph (Time Plot) A line graph is graphic representation for a time series. Time series are data collected at different time period. & Eample: The following data are daily high temperatures from Monday through Friday: The line graph for the temperatures is 80 Temperature Temperature Monday Tuesday Wedn. Thursday Friday Date & Eample: The line graph of IBM stock price is IBM Stock Price Price Date Tetbook Eercises:..9, pages 3; , pages
7 Ecel: Create a Line Graph 1. Click on Insert.. Click on Chart. 3. In ChartWizard Step 1: Select Line and the topleft line chart; click Net. 4. In ChartWizard Step : Click Series tab, Values contains data, Category (X) ais labels contains the values of date or time. Click Net and complete the rest steps. B. Measures of Central Tendency (Section 3.1) To describe data sets numerically, we use mean, median, range, and standard deviation. B..1 Mean (Average) The mean of a collection of n data values is the sum of the data values divided by n. & Eample: Calculate the mean of the following daily high temperatures: The mean is = Notation: Sum and Mean Suppose there is a collection of n data values. These values are represented by 1,, K,,. The n sum of these values is denoted as n i i= 1 The mean is equal to. n i=1 n i. Sample Mean, X The mean of a sample of n data values, 1,, K n is denoted as X. And n i i= X = 1. n 7
8 O Eercise: Prices of product A Suppose the prices of product A in the past five months are Calculate the mean. Answer: Population Mean, μ The mean of a population is denoted as μ. If the data values of are represented by then the population variance is defined as N i i= μ = 1. N, 1,, K N, B.. Median The median of a collection of data values is the data value in the middle position for sorted data. & Eample: Calculate the median of the following daily high temperatures: The sorted data are The median is 74. Tetbook Eercises: , pages
9 B.3 Measures of Variability (Section 3.) B.3.1 Range The range of a collection of data values is the difference between the largest and the smallest values. & Eample: Calculate the range of the following daily high temperatures: The range is = 8. & Eample: Sale Prices for Residential Properties Calculate the range. The range is = 11. O Eercise: YTD Returns Calculate the range. The range is B.3. Variance and Standard Deviation The variance is used to measure the variation of the data values from its mean. The variance of a collection of data values is defined to be the average of the squares of the deviations of the data values about their mean. s Sample Variance, The variance of a sample of n data values 1,, K, n is defined as s = n ( i X ) i= 1 n 1. & Eample: Prices of product A Suppose the prices of product A in the past five months are Calculate the mean and the variance. 9
10 i i deviation i X (deviation) ( X ) i = = = = = 1 1 Sum The sample mean is X = = The sample variance is s = = Alternative Formula: A shortcut formula to compute s is ( ) n ( X ) s = n 1 i. & Eample: Prices of product A Suppose the prices of product A in the past five months are Use a shortcut formula to compute the sample variance. 10
11 i i i Sum The sample mean is X = = 4. 5 ( ) n ( X ) The sample variance is s = n = =.5. 4 O Eercise: Prices of product B Suppose the prices for product B in the past five months are Calculate the sample mean and the sample variance. i Sum 0 The sample mean is i i i The sample variance is 11
12 Standard Deviation The standard deviation of a collection of data values is equal to the square root of their variance. Sample Standard Deviation, s s = s. & Eample: Prices of Product A The sample standard deviation is s =.5 = O Eercise: Prices of Product B Calculate the sample standard deviation. The sample standard deviation is Population Variance σ and Population Standard Deviation σ The population variance is denoted as σ. For a population with the data values of and the mean μ, population variance is defined as σ = n i= 1 (i  μ ). N The population standard deviation is σ = σ.,,, 1 K Note: Sample mean X, variance s, and standard deviation s are sample statistics. Population mean μ, variance σ, and standard deviation σ are population parameters. Tetbook Eercises: , , pages N 1
13 B.4 Skewness and Kurtosis We use skewness and kurtosis to show the shape of distribution. B.4.1 Skewness The skewness measures the amount of asymmetry in a distribution or in a relative frequency histogram. If a distribution is symmetric, skewness equals zero; the larger the absolute size of the skewness statistic, the more asymmetric is the distribution. The measure of sample skewness is defined as ( X ) 1 3 i skewness = n. 3 s When skewness has a large positive value indicates a long right tail. When skewness has a large negative value indicates a long left tail. & Eample: Sale Prices The data set has a positive skewness. Hence, the distribution has a long right tail. Column1 Mean 81 Standard Error Median 76 Mode #N/A Standard Deviation Sample Variance Kurtosis Skewness Range 11 Minimum 36 Maimum 148 Sum 05 Count 5 B.4. Kurtosis The kurtosis is a measure of the thickness of the tails of its distribution (or relative frequency histogram) relative to those of a normal distribution. A normal distribution has a kurtosis of three. A kurtosis above three indicates Afat The measure of sample kurtosis is defined as ( X ) 1 4 i Kurtosis = n. 4 s 13
14 & Eercise: YTD Returns Column1 Mean 1.1 Standard Error Median 0.85 Mode 0.6 Standard Deviation Sample Variance Kurtosis Skewness Range 13.9 Minimum 4.3 Maimum 9.6 Sum 33.6 Count 30 Tetbook Eercises: 3.4, 3.6, , pages 50, 51. Ecel: Descriptive Statistics (See Appendi) 1. Click on Tools.. Click on Data Analysis. (If Data Analysis is not on the list, click and Check AAnalysis to install the addin from Microsoft Office CD.) 3. Select Descriptive Statistics; click OK. 4. Complete dialog bo: Input range contains data; Output range contains the starting cell with descriptive statistics; select Summary statistics. Click OK. 14
15 C. Random Variables and Normal Distribution (Sections , 6.1, 6.3) C.1 Random Variables (Section 5.1) Part I (Chapters 1 11) Random Eperiment: A random eperiment is a process leading to two or more possible outcomes with uncertainty as to which outcome will occur. Random Variable: A random variable is a variable that takes on numerical values determined by the outcome of a random eperiment. Usually, there are two usages of random variables. Random Variables for a Population: We can use a random variable to represent different possible data values for a population. This random variable has a probability distribution. & Eample: The sale price can be represented by a variable X. Then different data values of sale price can also be represented by ( 1,, K, n ). The population mean is denoted as μ X and the population standard deviation isσ X. Random Variables for Statistical Analysis: Some random variables have interesting probability distributions. These probability distributions are useful in statistical inference. & Eample: The random variable Z has a standard normal distribution. There are two types of random variables. One is discrete random variable and the other is continuous variable. Discrete Random Variable: Continuous Random Variable: A discrete random variable takes some countable number of values. A continuous random variable is a random variable taking values on a line interval. & Eample: Age in years  Discrete random variable Income  Discrete Prices  Discrete Temperature  Continuous Height  Continuous Growth rates  Continuous 15
16 C. Discrete Random Variable (Sections 5., 5.3) The probability distribution of a random variable X is denoted as P(). The properties of P() are a. ( ) 0 b. ( ) P. P = 1. & Eample: New Products Suppose the number of new products introduced each year is a random variable X. The values and the probabilities of Χ are P ( ) Mean and Standard Deviation The mean of a discrete random variable X is ( ) μ = P. The mean of is also called the epected value of X, ( ) = ( ) E Χ P. The variance of a discrete random variable X is ( ) P( ) σ =. μ 16
17 & Eample: New Products Calculate the mean and standard deviation. P ( ) P( ) μ ( ) ( μ ) P( ) μ Sum The mean is μ = The variance is σ = The standard deviation is σ = 0.84 = O Eercise: Returned Checks Suppose the number of returned checks in a day for a department store is a random variable X. The values and the probabilities of X are P ( ) Calculate the mean, variance, and standard deviation. 17
18 P ( ) P( ) μ ( μ ) ( μ ) P( ) Sum The mean is The variance is The standard deviation is Alternative Formula for Calculating Variance: A shortcut formula to compute σ is ( P( ) ) μ σ =. & Eample: New Products The variance is P ( ) P( ) P( ) Sum ( P( ) ) μ = σ = =. 18
19 O Eercise: Returned Checks P ( ) P( ) P( ) Sum The variance is σ X = Tetbook Eercises: , pages 136, 137; , , pages C.3 Continuous Random Variable (Sections 6.1, 6.3, 8.3) The probability distribution of a random variable X can be denoted as f ( ) probability distribution of X has the following properties: a. f ( ) 0. b. Total area under f ( ) is one. c. The probability of falling within an interval ( a, b) is denoted as P ( a < < b). It is the area under the curve ( ) f between a and b. One of the most commonly used continuous random variable is normal random variable. C.3.1 Normal Distribution (Section 6.3). The Normal Random Variable and Normal Probability Distribution A normal random variable with a normal probability distribution has the following properties: a. The probability distribution has a bellshaped. b. The distribution is symmetric about its mean μ. c. The spread of the distribution is determined by the standard deviation σ. d. Any normal random variable X with mean μ and standard deviation σ can be standardized as a standard normal random variable. X μ Z =. σ 19
20 Standard Normal Random Variable A standard normal random variable is a normal random variable with mean zero and standard deviation one. The probability table for standard normal random variable shows the probability of ( < Z a) P 0 <. Using Standard Normal Probability Distribution Table Case 1. Find P ( < Z < a) & Eample: 0. ( 0 < Z < 1.) = ( 0 < Z < 1.76) = P. P. O Eercise: P ( 0 < Z < 1. 64)= P ( 0 < Z < 1. 96)= Case. Find ( a < Z < 0) P. & Eample: P ( 1. < Z < 0) = P ( 1.76 < Z < 0) = P ( Z < 0 ) = P Z > 0 = 0.. ( ) 5 O Eercise: P ( 1.8 < Z < 0)= P (.33 < Z < 0)= Case 3. Find ( Z a) & Eample: P <. ( Z < 1.) = = ( Z < 1.76) = = P. P. 0
21 Note: We denote the cumulative probability as F ( a), such that F ( a) P( Z < a) O Eercise: P ( Z < 1. 64)= P ( Z < 1. 96)= Case 4. Find ( Z a) & Eample: P >. ( Z > 1.) = = ( Z > 1.76) = = P. P. O Eercise: P ( Z > 1. 64)= P ( Z. > 1. 96)= P ( Z > 1. 8)= P ( Z >. 33)= Case 5. The probability P ( < Z < a) & Eample: P( 0 < Z < a) = 30%. What is a? From the table, a = O Eercise: P 0 < Z < a = 40. What is a? ( ) % 0 is given. Find the value of a. Part I (Chapters 1 11) =. Case 6. The probability ( Z a) P > is given. Find the value of a. & Eample: P ( Z > a) = 5%, find a. The point a locates on the righthand side of origin and P ( 0 < Z < a) = = With the given probability 0.45, we find a = from the table. 1
22 O Eercise: P ( Z > a) = 0. 10, find a. Answer: Tetbook Eercises:6.17, 6.18, page 07. Probabilities for Normal Random Variables Let X be a normal random variable with mean μ and variance σ. Then random variable X μ Z = is a standard normal random variable. Also, σ a μ b μ P ( a < X < b) = P < Z <. σ σ & Eample: A company produces light bulbs whose life follows a normal distribution with mean 1,00 hours and standard deviation 50 hours. If we choose a light bulb at random, what is the probability that its lifetime will be between 900 and 1,300 hours? Answers: P ( 900 < X < 1300) X = P < < = P 1. < Z < 0.4 = = 0.. ( ) 5403 O Eercise: Anticipated consumer demand for a product net month can be represented by a normal random variable with mean 1,00 units and standard deviation 100 units. a. What is the probability that sales will be between 1,000 and 1,300 units? b. What is the probability that sales will eceed 1,100 units? Answers: Tetbook Eercises: 6.19 abc, 6.0 abc, 6.1 abc, 6. abd, 6.3 ab, 6.4 abc, 6.5, 6.6, 6.7 a, 6.31 ab, 6.35 ab, 6.36a, 6.37 ab, pages
23 C.3. Student=s t Distribution (Section 8.3) Student's t Distribution (t distribution) Let t be a random variable with t distribution. Properties of t distribution: 1. Bellshaped.. Symmetrical about t = The probability distribution has tails that are more spread out than the standard normal distribution. 4. The shape of probability distribution depends on a constant, the degrees of freedom (v). 5. When v is large, t distribution is close to the standard normal distribution. t Statistical Table The table shows the value of t α, such that ( t > t α ) = α P. For α = 0. 01, = α, and α = 0. 05, the values of t α for different v are v t. 05 t. 05 t
24 & Eample: Find the value a such that, a. P ( t > a) = when v = 5. b. P ( t < a) = when v = 10. c. P ( t > a) = when v = 0. Answer: a: a =. 015 ; b: a =. 8; c: a =.58. O Eercise: Find the value a such that, a. P ( t > a) = when v = 5. b. P ( t < a) = when v = 10. c. P ( t > a) = when v = 15. Answer: 4
Foundation 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 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 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 Tools. Tools for Summarizing Data
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
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 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 informationSECTION 21: OVERVIEW SECTION 22: FREQUENCY DISTRIBUTIONS
SECTION 21: OVERVIEW Chapter 2 Describing, Exploring and Comparing Data 19 In this chapter, we will use the capabilities of Excel to help us look more carefully at sets of data. We can do this by reorganizing
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 informationAppendix 2.1 Tabular and Graphical Methods Using Excel
Appendix 2.1 Tabular and Graphical Methods Using Excel 1 Appendix 2.1 Tabular and Graphical Methods Using Excel The instructions in this section begin by describing the entry of data into an Excel spreadsheet.
More informationDrawing a histogram using Excel
Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries 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 informationBelow is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information.
Excel Tutorial Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information. Working with Data Entering and Formatting Data Before entering data
More informationProbability Distributions
CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution
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 informationThe Big Picture. Describing Data: Categorical and Quantitative Variables Population. Descriptive Statistics. Community Coalitions (n = 175)
Describing Data: Categorical and Quantitative Variables Population The Big Picture Sampling Statistical Inference Sample Exploratory Data Analysis Descriptive Statistics In order to make sense of data,
More 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 informationMathematics. Probability and Statistics Curriculum Guide. Revised 2010
Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction
More informationTo create a histogram, you must organize the data in two columns on the worksheet. These columns must contain the following data:
You can analyze your data and display it in a histogram (a column chart that displays frequency data) by using the Histogram tool of the Analysis ToolPak. This data analysis addin is available when you
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 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 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 informationSAMPLING DISTRIBUTIONS
0009T_c07_308352.qd 06/03/03 20:44 Page 308 7Chapter SAMPLING DISTRIBUTIONS 7.1 Population and Sampling Distributions 7.2 Sampling and Nonsampling Errors 7.3 Mean and Standard Deviation of 7.4 Shape of
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 informationChapter 5 Discrete Probability Distribution. Learning objectives
Chapter 5 Discrete Probability Distribution Slide 1 Learning objectives 1. Understand random variables and probability distributions. 1.1. Distinguish discrete and continuous random variables. 2. Able
More informationData exploration with Microsoft Excel: univariate analysis
Data exploration with Microsoft Excel: univariate analysis Contents 1 Introduction... 1 2 Exploring a variable s frequency distribution... 2 3 Calculating measures of central tendency... 16 4 Calculating
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 informationHow to Use a Data Spreadsheet: Excel
How to Use a Data Spreadsheet: Excel One does not necessarily have special statistical software to perform statistical analyses. Microsoft Office Excel can be used to run statistical procedures. Although
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 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 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 informationBill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1
Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce
More informationDescribing, Exploring, and Comparing Data
24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter
More 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 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 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 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 informationbusiness statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar
business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel
More informationTable of Contents TASK 1: DATA ANALYSIS TOOLPAK... 2 TASK 2: HISTOGRAMS... 5 TASK 3: ENTER MIDPOINT FORMULAS... 11
Table of Contents TASK 1: DATA ANALYSIS TOOLPAK... 2 TASK 2: HISTOGRAMS... 5 TASK 3: ENTER MIDPOINT FORMULAS... 11 TASK 4: ADD TOTAL LABEL AND FORMULA FOR FREQUENCY... 12 TASK 5: MODIFICATIONS TO THE HISTOGRAM...
More informationUsing SPSS, Chapter 2: Descriptive Statistics
1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,
More 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 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 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) 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 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 informationAn introduction to using Microsoft Excel for quantitative data analysis
Contents An introduction to using Microsoft Excel for quantitative data analysis 1 Introduction... 1 2 Why use Excel?... 2 3 Quantitative data analysis tools in Excel... 3 4 Entering your data... 6 5 Preparing
More informationData Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools
Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Occam s razor.......................................................... 2 A look at data I.........................................................
More informationLAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
More informationAdvanced Excel for Institutional Researchers
Advanced Excel for Institutional Researchers Presented by: Sandra Archer Helen Fu University Analysis and Planning Support University of Central Florida September 2225, 2012 Agenda Sunday, September 23,
More informationActivity 3.7 Statistical Analysis with Excel
Activity 3.7 Statistical Analysis with Excel Introduction Engineers use various tools to make their jobs easier. Spreadsheets can greatly improve the accuracy and efficiency of repetitive and common calculations;
More informationt Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon
ttests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly
More informationData Analysis. Using Excel. Jeffrey L. Rummel. BBA Seminar. Data in Excel. Excel Calculations of Descriptive Statistics. Single Variable Graphs
Using Excel Jeffrey L. Rummel Emory University Goizueta Business School BBA Seminar Jeffrey L. Rummel BBA Seminar 1 / 54 Excel Calculations of Descriptive Statistics Single Variable Graphs Relationships
More informationCoins, Presidents, and Justices: Normal Distributions and zscores
activity 17.1 Coins, Presidents, and Justices: Normal Distributions and zscores In the first part of this activity, you will generate some data that should have an approximately normal (or bellshaped)
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 informationseven Statistical Analysis with Excel chapter OVERVIEW CHAPTER
seven Statistical Analysis with Excel CHAPTER chapter OVERVIEW 7.1 Introduction 7.2 Understanding Data 7.3 Relationships in Data 7.4 Distributions 7.5 Summary 7.6 Exercises 147 148 CHAPTER 7 Statistical
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 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 informationLecture Notes Module 1
Lecture Notes Module 1 Study Populations A study population is a clearly defined collection of people, animals, plants, or objects. In psychological research, a study population usually consists of a specific
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 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 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 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 informationChapter 4. Probability and Probability Distributions
Chapter 4. robability and robability Distributions Importance of Knowing robability To know whether a sample is not identical to the population from which it was selected, it is necessary to assess the
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 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 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 informationSPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)
Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer
More 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 informationRandom variables P(X = 3) = P(X = 3) = 1 8, P(X = 1) = P(X = 1) = 3 8.
Random variables Remark on Notations 1. When X is a number chosen uniformly from a data set, What I call P(X = k) is called Freq[k, X] in the courseware. 2. When X is a random variable, what I call F ()
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 informationStatistical Data analysis With Excel For HSMG.632 students
1 Statistical Data analysis With Excel For HSMG.632 students Dialog Boxes Descriptive Statistics with Excel To find a single descriptive value of a data set such as mean, median, mode or the standard deviation,
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 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 informationNormality Testing in Excel
Normality Testing in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com
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 information1. Go to your programs menu and click on Microsoft Excel.
Elementary Statistics Computer Assignment 1 Using Microsoft EXCEL 2003, follow the steps below. For Microsoft EXCEL 2007 instructions, go to the next page. For Microsoft 2010 and 2007 instructions with
More information1 SAMPLE SIGN TEST. NonParametric Univariate Tests: 1 Sample Sign Test 1. A nonparametric equivalent of the 1 SAMPLE TTEST.
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 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 informationADDINS: ENHANCING EXCEL
CHAPTER 9 ADDINS: ENHANCING EXCEL This chapter discusses the following topics: WHAT CAN AN ADDIN DO? WHY USE AN ADDIN (AND NOT JUST EXCEL MACROS/PROGRAMS)? ADD INS INSTALLED WITH EXCEL OTHER ADDINS
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 informationMICROSOFT EXCEL 2010 ANALYZE DATA
MICROSOFT EXCEL 2010 ANALYZE DATA Microsoft Excel 2010 Essential Analyze data Last Edited: 20120709 1 Basic analyze data... 4 Use diagram to audit formulas... 4 Use Error Checking feature... 4 Use Evaluate
More informationScatter Plots with Error Bars
Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each
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 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 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 information6 3 The Standard Normal Distribution
290 Chapter 6 The Normal Distribution Figure 6 5 Areas Under a Normal Distribution Curve 34.13% 34.13% 2.28% 13.59% 13.59% 2.28% 3 2 1 + 1 + 2 + 3 About 68% About 95% About 99.7% 6 3 The Distribution Since
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 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 informationDescriptive Statistics
Descriptive Statistics Descriptive statistics consist of methods for organizing and summarizing data. It includes the construction of graphs, charts and tables, as well various descriptive measures such
More informationIBM SPSS Direct Marketing 23
IBM SPSS Direct Marketing 23 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 23, release
More informationChapter 3 RANDOM VARIATE GENERATION
Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of random variables having known distributions.
More informationData exploration with Microsoft Excel: analysing more than one variable
Data exploration with Microsoft Excel: analysing more than one variable Contents 1 Introduction... 1 2 Comparing different groups or different variables... 2 3 Exploring the association between categorical
More informationClass 19: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationChapter 4 Lecture Notes
Chapter 4 Lecture Notes Random Variables October 27, 2015 1 Section 4.1 Random Variables A random variable is typically a realvalued function defined on the sample space of some experiment. For instance,
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 informationDescribing Populations Statistically: The Mean, Variance, and Standard Deviation
Describing Populations Statistically: The Mean, Variance, and Standard Deviation BIOLOGICAL VARIATION One aspect of biology that holds true for almost all species is that not every individual is exactly
More informationFinite Mathematics Using Microsoft Excel
Overview and examples from Finite Mathematics Using Microsoft Excel Revathi Narasimhan Saint Peter's College An electronic supplement to Finite Mathematics and Its Applications, 6th Ed., by Goldstein,
More informationMicrosoft Excel. Qi Wei
Microsoft Excel Qi Wei Excel (Microsoft Office Excel) is a spreadsheet application written and distributed by Microsoft for Microsoft Windows and Mac OS X. It features calculation, graphing tools, pivot
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 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 information