The Normal Distribution & z-scores
|
|
- Juniper Baldwin
- 6 years ago
- Views:
Transcription
1 & z-scores
2 Distributions: Who needs them? Why are we interested in distributions? Important link between distributions and probabilities of events If we know the distribution of a set of events, then we know something about the probability that one of those events is likely to occur
3 Distributions and Probabilities Whose course would you rather take? Professor A Professor B C/C+ 30% D 8% F 5% A 19% B/B+ 38% D 4% C/C+ 22% F 7% B/B+ 35% A 32%
4 Distributions and Probabilities Whose course would you rather take? Professor A Professor B D 4% F 5% D 8% C 30% B 38% A 19% F 7% C 22% B 35% A 32%
5 A Note on Continuous Versus Discrete Distributions Y-axis represents density Probability density function Probability of any exact value is zero Y-axis represents probability Probability mass function Probability of exact values can be positive
6 The Normal Distribution Okay, distributions can be useful. But why should we care about this particular distribution? Most prominent distribution in statistics Normally distributed data Computational convenience Normality of sample means
7 Normally Distributed Data Many of the dependent variables that we deal with are approximately normally distributed in the population Originally used to describe errors in astronomical measurements Examples of normally distributed data Height Weight Normalized test scores Speed of cars on Route 18 Anything averaged across a large number of observations
8 Normally Distributed Data
9 Computational Convenience Many statistics related to the normal distribution, along with their sampling distributions are analytically tractable If we can assume that a variable is at least approximately normally distributed, then we can use standard techniques (i.e., those that make up most of this book) to make inferences about values of that variable
10 Normality of Sample Means Regardless of the distribution of the underlying variable (with limited exceptions), the distribution of sample means approaches normality as the sample size n grows. We will discuss this in greater detail later in the course when we cover the central limit theorem. Generally, this means that the sampling distribution of the mean can be approximated by a normal distribution
11 The Standard Normal Distribution The Normal Distribution σ 2.1% 13.6% 34.1% 34.1% 13.6% 2.1%
12 Standardizing Normal Variables By itself, a raw score or x value provides very little information about how that particular score compares with other values in the distribution. A score of x = 53, for example, may be a relatively low score, or an average score, or an extremely high score depending on the mean and standard deviation for the distribution from which the score was obtained. If the raw score is transformed into a z-score, however, the value of the z-score tells you where the score is located relative to all the other scores in the distribution.
13 Standardizing Normal Variables To transform an x value into a z-score: z x µ = σ To transform a z-score into an x value: x = µ + zσ
14 Standardizing Normal Variables In addition to knowing the basic definition of a z-score and the formula for a z-score, it is useful to be able to visualize z- scores as locations in a distribution. Remember, z = 0 is in the center (at the mean), and the extreme tails correspond to z-scores of approximately 2.00 on the left and on the right. 95.4% of the distribution is contained between z = -2 and z = % of the distribution is contained between z = -3 and z = 3
15 Standardizing Normal Distributions The Normal Distribution z = ( x µ ) : ( x µ ) : σ
16 Standard Normal Tables (z-tables) Another important advantage of standardizing distributions is that it allows us to compute and use a single probability table for all normal distributions The Normal Distribution
17 Standard Normal Tables (z-tables) Upper-Tail Probabilities The Normal Distribution z
18 Standard Normal Tables: Meaning The Normal Distribution
19 Standard Normal Tables: Meaning The Normal Distribution
20 Standard Normal Tables: Meaning The Normal Distribution
21 Standard Normal Tables: Meaning The Normal Distribution
22 Standard Normal Tables: Meaning The Normal Distribution
23 Using z-tables Area under curve sums to 1 The normal distribution is symmetrical E.g., P(Z < -z) = P(Z > +z) (non-overlapping) areas sum E.g., P(0.0 < Z < 1.0) = P(Z > 0.0) P(Z > 1.0) Note: In this slide and in the rest of this lecture, I m using Z (capital) to indicate a randomly selected value of a standard normal variable, and z (lower-case) to indicate a particular value of that variable.
24 What is the probability that a randomly selected woman is taller than 5 6 (66 inches)?
25 Using z-tables to Compute Interval Probabilities Step 1: standardize value (i.e., compute z-score) 66 µ z(66) = = σ Step 2: Look up upper-tail area P( Z > z(66) ) =
26 Standard Normal Tables (z-tables) Upper-Tail Probabilities The Normal Distribution z
27 What is the probability that a randomly selected woman is between 64 and 68 inches tall?
28 Using z-tables to Compute Interval Probabilities Step 1: standardize values (i.e., compute z-scores) 64 µ z(64) = = σ 68 µ z(68) = = σ Step 2: Look up upper-tail area ( z(64) ) ( z(68) ) P Z P Z > = > = Step 3: Compute difference ( ) ( (64)) ( (68)) P < Z < = P Z > z P Z > z =
29 Standard Normal Tables (z-tables) Upper-Tail Probabilities The Normal Distribution z
30 What is the probability that a randomly selected woman is between 62 and 66 inches tall?
31 Standard Normal Tables (z-tables) Upper-Tail Probabilities The Normal Distribution z
32 Computing Probable Intervals 95% 2.5% 2.5%
33 Standard Normal Tables (z-tables) Upper-Tail Probabilities The Normal Distribution z
34 Using z-tables to Compute Probable Intervals Step 1: look up z-score corresponding to 2.5% (0.0250) ( > z) = P Z z z + = 1.96 = z = Step 2: transform z-scores to heights x x = z σ + µ = = = z σ + µ = = 58.61
The Normal Distribution & z-scores
& z-scores Distributions: Who needs them? Why are we interested in distributions? Important link between distributions and probabilities of events If we know the distribution of a set of events, then we
More informationThe Normal Distribution & z-scores
& z-scores Distributions: Who needs them? Why are we interested in distributions? Important link between distributions and probabilities of events If we know the distribution of a set of events, then we
More informationNormal Distribution. 6.4 Applications of Normal Distribution
Normal Distribution 6.4 Applications of Normal Distribution 1 /20 Homework Read Sec 6-4. Discussion question p316 Do p316 probs 1-10, 16-22, 31, 32, 34-37, 39 2 /20 3 /20 Objective Find the probabilities
More informationLecture Slides. Elementary Statistics Twelfth Edition. by Mario F. Triola. and the Triola Statistics Series. Section 6.2-1
Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series by Mario F. Triola Section 6.2-1 Chapter 6 Normal Probability Distributions 6-1 Review and Preview 6-2 The Standard
More informationExample 1. Find the x value that has a left tail area of.1131 P ( x <??? ) =. 1131
Section 6 4D: Finding a Value of x with a Given tail arae Label the shaded area for both graphs. Find the value for z and label the z axis. Find the value for x for the given area under the normal curve
More informationFrequency Distributions
Displaying Data Frequency Distributions After collecting data, the first task for a researcher is to organize and summarize the data so that it is possible to get a general overview of the results. Remember,
More informationChapter 6: Continuous Random Variables & the Normal Distribution. 6.1 Continuous Probability Distribution
Chapter 6: Continuous Random Variables & the Normal Distribution 6.1 Continuous Probability Distribution and the Normal Probability Distribution 6.2 Standardizing a Normal Distribution 6.3 Applications
More information2) In the formula for the Confidence Interval for the Mean, if the Confidence Coefficient, z(α/2) = 1.65, what is the Confidence Level?
Pg.431 1)The mean of the sampling distribution of means is equal to the mean of the population. T-F, and why or why not? True. If you were to take every possible sample from the population, and calculate
More informationCh6: The Normal Distribution
Ch6: The Normal Distribution Introduction Review: A continuous random variable can assume any value between two endpoints. Many continuous random variables have an approximately normal distribution, which
More informationMath 14 Lecture Notes Ch. 6.1
6.1 Normal Distribution What is normal? a 10-year old boy that is 4' tall? 5' tall? 6' tall? a 25-year old woman with a shoe size of 5? 7? 9? an adult alligator that weighs 200 pounds? 500 pounds? 800
More informationDensity Curve (p52) Density curve is a curve that - is always on or above the horizontal axis.
1.3 Density curves p50 Some times the overall pattern of a large number of observations is so regular that we can describe it by a smooth curve. It is easier to work with a smooth curve, because the histogram
More informationPrepare a stem-and-leaf graph for the following data. In your final display, you should arrange the leaves for each stem in increasing order.
Chapter 2 2.1 Descriptive Statistics A stem-and-leaf graph, also called a stemplot, allows for a nice overview of quantitative data without losing information on individual observations. It can be a good
More informationProbability and Statistics. Copyright Cengage Learning. All rights reserved.
Probability and Statistics Copyright Cengage Learning. All rights reserved. 14.6 Descriptive Statistics (Graphical) Copyright Cengage Learning. All rights reserved. Objectives Data in Categories Histograms
More informationIntroduction to the Practice of Statistics Fifth Edition Moore, McCabe
Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 1.3 Homework Answers Assignment 5 1.80 If you ask a computer to generate "random numbers between 0 and 1, you uniform will
More information6-1 THE STANDARD NORMAL DISTRIBUTION
6-1 THE STANDARD NORMAL DISTRIBUTION The major focus of this chapter is the concept of a normal probability distribution, but we begin with a uniform distribution so that we can see the following two very
More informationChapter 2: The Normal Distribution
Chapter 2: The Normal Distribution 2.1 Density Curves and the Normal Distributions 2.2 Standard Normal Calculations 1 2 Histogram for Strength of Yarn Bobbins 15.60 16.10 16.60 17.10 17.60 18.10 18.60
More informationZ-TEST / Z-STATISTIC: used to test hypotheses about. µ when the population standard deviation is unknown
Z-TEST / Z-STATISTIC: used to test hypotheses about µ when the population standard deviation is known and population distribution is normal or sample size is large T-TEST / T-STATISTIC: used to test hypotheses
More informationChapter 6 Normal Probability Distributions
Chapter 6 Normal Probability Distributions 6-1 Review and Preview 6-2 The Standard Normal Distribution 6-3 Applications of Normal Distributions 6-4 Sampling Distributions and Estimators 6-5 The Central
More informationUnit 5: Estimating with Confidence
Unit 5: Estimating with Confidence Section 8.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Unit 5 Estimating with Confidence 8.1 8.2 8.3 Confidence Intervals: The Basics Estimating
More informationIT 403 Practice Problems (1-2) Answers
IT 403 Practice Problems (1-2) Answers #1. Using Tukey's Hinges method ('Inclusionary'), what is Q3 for this dataset? 2 3 5 7 11 13 17 a. 7 b. 11 c. 12 d. 15 c (12) #2. How do quartiles and percentiles
More information23.2 Normal Distributions
1_ Locker LESSON 23.2 Normal Distributions Common Core Math Standards The student is expected to: S-ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate
More informationMAT 142 College Mathematics. Module ST. Statistics. Terri Miller revised July 14, 2015
MAT 142 College Mathematics Statistics Module ST Terri Miller revised July 14, 2015 2 Statistics Data Organization and Visualization Basic Terms. A population is the set of all objects under study, a sample
More informationSampling Distribution Examples Sections 15.4, 15.5
Sampling Distribution Examples Sections 15.4, 15.5 Lecture 27 Robb T. Koether Hampden-Sydney College Wed, Mar 2, 2016 Robb T. Koether (Hampden-Sydney College)Sampling Distribution ExamplesSections 15.4,
More informationData Analysis & Probability
Unit 5 Probability Distributions Name: Date: Hour: Section 7.2: The Standard Normal Distribution (Area under the curve) Notes By the end of this lesson, you will be able to Find the area under the standard
More informationSec 6.3. Bluman, Chapter 6 1
Sec 6.3 Bluman, Chapter 6 1 Bluman, Chapter 6 2 Review: Find the z values; the graph is symmetrical. z = ±1. 96 z 0 z the total area of the shaded regions=5% Bluman, Chapter 6 3 Review: Find the z values;
More informationChapter 2 Modeling Distributions of Data
Chapter 2 Modeling Distributions of Data Section 2.1 Describing Location in a Distribution Describing Location in a Distribution Learning Objectives After this section, you should be able to: FIND and
More informationUnit 8: Normal Calculations
Unit 8: Normal Calculations Prerequisites This unit requires familiarity with basic facts about normal distributions, which are covered in Unit 7, Normal Curves. In addition, students need some background
More informationDistributions of random variables
Chapter 3 Distributions of random variables 31 Normal distribution Among all the distributions we see in practice, one is overwhelmingly the most common The symmetric, unimodal, bell curve is ubiquitous
More informationSections 4.3 and 4.4
Sections 4.3 and 4.4 Timothy Hanson Department of Statistics, University of South Carolina Stat 205: Elementary Statistics for the Biological and Life Sciences 1 / 32 4.3 Areas under normal densities Every
More informationConfidence Intervals: Estimators
Confidence Intervals: Estimators Point Estimate: a specific value at estimates a parameter e.g., best estimator of e population mean ( ) is a sample mean problem is at ere is no way to determine how close
More informationMAT 110 WORKSHOP. Updated Fall 2018
MAT 110 WORKSHOP Updated Fall 2018 UNIT 3: STATISTICS Introduction Choosing a Sample Simple Random Sample: a set of individuals from the population chosen in a way that every individual has an equal chance
More information1. The Normal Distribution, continued
Math 1125-Introductory Statistics Lecture 16 10/9/06 1. The Normal Distribution, continued Recall that the standard normal distribution is symmetric about z = 0, so the area to the right of zero is 0.5000.
More informationCHAPTER 2 Modeling Distributions of Data
CHAPTER 2 Modeling Distributions of Data 2.2 Density Curves and Normal Distributions The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers HW 34. Sketch
More informationMATH 1070 Introductory Statistics Lecture notes Descriptive Statistics and Graphical Representation
MATH 1070 Introductory Statistics Lecture notes Descriptive Statistics and Graphical Representation Objectives: 1. Learn the meaning of descriptive versus inferential statistics 2. Identify bar graphs,
More informationappstats6.notebook September 27, 2016
Chapter 6 The Standard Deviation as a Ruler and the Normal Model Objectives: 1.Students will calculate and interpret z scores. 2.Students will compare/contrast values from different distributions using
More informationMs Nurazrin Jupri. Frequency Distributions
Frequency Distributions Frequency Distributions After collecting data, the first task for a researcher is to organize and simplify the data so that it is possible to get a general overview of the results.
More informationThe Normal Distribution
Chapter 6 The Normal Distribution Continuous random variables are used to approximate probabilities where there are many possibilities or an infinite number of possibilities on a given trial. One of the
More informationCHAPTER 2 Modeling Distributions of Data
CHAPTER 2 Modeling Distributions of Data 2.2 Density Curves and Normal Distributions The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Density Curves
More informationChapter 5snow year.notebook March 15, 2018
Chapter 5: Statistical Reasoning Section 5.1 Exploring Data Measures of central tendency (Mean, Median and Mode) attempt to describe a set of data by identifying the central position within a set of data
More informationThe Normal Distribution
The Normal Distribution Lecture 20 Section 6.3.1 Robb T. Koether Hampden-Sydney College Wed, Sep 28, 2011 Robb T. Koether (Hampden-Sydney College) The Normal Distribution Wed, Sep 28, 2011 1 / 41 Outline
More informationChapter 2: The Normal Distributions
Chapter 2: The Normal Distributions Measures of Relative Standing & Density Curves Z-scores (Measures of Relative Standing) Suppose there is one spot left in the University of Michigan class of 2014 and
More informationChapter 5: The standard deviation as a ruler and the normal model p131
Chapter 5: The standard deviation as a ruler and the normal model p131 Which is the better exam score? 67 on an exam with mean 50 and SD 10 62 on an exam with mean 40 and SD 12? Is it fair to say: 67 is
More information7.2. The Standard Normal Distribution
7.2 The Standard Normal Distribution Standard Normal The standard normal curve is the one with mean μ = 0 and standard deviation σ = 1 We have related the general normal random variable to the standard
More informationLecture 21 Section Fri, Oct 3, 2008
Lecture 21 Section 6.3.1 Hampden-Sydney College Fri, Oct 3, 2008 Outline 1 2 3 4 5 6 Exercise 6.15, page 378. A young woman needs a 15-ampere fuse for the electrical system in her apartment and has decided
More informationThe Normal Curve. June 20, Bryan T. Karazsia, M.A.
The Normal Curve June 20, 2006 Bryan T. Karazsia, M.A. Overview Hand-in Homework Why are distributions so important (particularly the normal distribution)? What is the normal distribution? Z-scores Using
More informationStudent Learning Objectives
Student Learning Objectives A. Understand that the overall shape of a distribution of a large number of observations can be summarized by a smooth curve called a density curve. B. Know that an area under
More informationCHAPTER 2 DESCRIPTIVE STATISTICS
CHAPTER 2 DESCRIPTIVE STATISTICS 1. Stem-and-Leaf Graphs, Line Graphs, and Bar Graphs The distribution of data is how the data is spread or distributed over the range of the data values. This is one of
More informationCHAPTER 2 Modeling Distributions of Data
CHAPTER 2 Modeling Distributions of Data 2.2 Density Curves and Normal Distributions The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Density Curves
More informationEcon 3790: Business and Economics Statistics. Instructor: Yogesh Uppal
Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal Email: yuppal@ysu.edu Chapter 8: Interval Estimation Population Mean: Known Population Mean: Unknown Margin of Error and the Interval
More informationCHAPTER 2: DESCRIPTIVE STATISTICS Lecture Notes for Introductory Statistics 1. Daphne Skipper, Augusta University (2016)
CHAPTER 2: DESCRIPTIVE STATISTICS Lecture Notes for Introductory Statistics 1 Daphne Skipper, Augusta University (2016) 1. Stem-and-Leaf Graphs, Line Graphs, and Bar Graphs The distribution of data is
More informationThe first few questions on this worksheet will deal with measures of central tendency. These data types tell us where the center of the data set lies.
Instructions: You are given the following data below these instructions. Your client (Courtney) wants you to statistically analyze the data to help her reach conclusions about how well she is teaching.
More informationSTA Module 4 The Normal Distribution
STA 2023 Module 4 The Normal Distribution Learning Objectives Upon completing this module, you should be able to 1. Explain what it means for a variable to be normally distributed or approximately normally
More informationSTA /25/12. Module 4 The Normal Distribution. Learning Objectives. Let s Look at Some Examples of Normal Curves
STA 2023 Module 4 The Normal Distribution Learning Objectives Upon completing this module, you should be able to 1. Explain what it means for a variable to be normally distributed or approximately normally
More informationBIOL Gradation of a histogram (a) into the normal curve (b)
(التوزيع الطبيعي ( Distribution Normal (Gaussian) One of the most important distributions in statistics is a continuous distribution called the normal distribution or Gaussian distribution. Consider the
More informationCHAPTER 2: Describing Location in a Distribution
CHAPTER 2: Describing Location in a Distribution 2.1 Goals: 1. Compute and use z-scores given the mean and sd 2. Compute and use the p th percentile of an observation 3. Intro to density curves 4. More
More informationContinuous Improvement Toolkit. Normal Distribution. Continuous Improvement Toolkit.
Continuous Improvement Toolkit Normal Distribution The Continuous Improvement Map Managing Risk FMEA Understanding Performance** Check Sheets Data Collection PDPC RAID Log* Risk Analysis* Benchmarking***
More informationDescriptive Statistics, Standard Deviation and Standard Error
AP Biology Calculations: Descriptive Statistics, Standard Deviation and Standard Error SBI4UP The Scientific Method & Experimental Design Scientific method is used to explore observations and answer questions.
More informationLearning Objectives. Continuous Random Variables & The Normal Probability Distribution. Continuous Random Variable
Learning Objectives Continuous Random Variables & The Normal Probability Distribution 1. Understand characteristics about continuous random variables and probability distributions 2. Understand the uniform
More informationNormal Curves and Sampling Distributions
Normal Curves and Sampling Distributions 6 Copyright Cengage Learning. All rights reserved. Section 6.2 Standard Units and Areas Under the Standard Normal Distribution Copyright Cengage Learning. All rights
More informationMAT 102 Introduction to Statistics Chapter 6. Chapter 6 Continuous Probability Distributions and the Normal Distribution
MAT 102 Introduction to Statistics Chapter 6 Chapter 6 Continuous Probability Distributions and the Normal Distribution 6.2 Continuous Probability Distributions Characteristics of a Continuous Probability
More informationCHAPTER 6. The Normal Probability Distribution
The Normal Probability Distribution CHAPTER 6 The normal probability distribution is the most widely used distribution in statistics as many statistical procedures are built around it. The central limit
More informationToday s Topics. Percentile ranks and percentiles. Standardized scores. Using standardized scores to estimate percentiles
Today s Topics Percentile ranks and percentiles Standardized scores Using standardized scores to estimate percentiles Using µ and σ x to learn about percentiles Percentiles, standardized scores, and the
More informationadjacent angles Two angles in a plane which share a common vertex and a common side, but do not overlap. Angles 1 and 2 are adjacent angles.
Angle 1 Angle 2 Angles 1 and 2 are adjacent angles. Two angles in a plane which share a common vertex and a common side, but do not overlap. adjacent angles 2 5 8 11 This arithmetic sequence has a constant
More informationChapter 6. THE NORMAL DISTRIBUTION
Chapter 6. THE NORMAL DISTRIBUTION Introducing Normally Distributed Variables The distributions of some variables like thickness of the eggshell, serum cholesterol concentration in blood, white blood cells
More informationNormal Data ID1050 Quantitative & Qualitative Reasoning
Normal Data ID1050 Quantitative & Qualitative Reasoning Histogram for Different Sample Sizes For a small sample, the choice of class (group) size dramatically affects how the histogram appears. Say we
More informationMath 120 Introduction to Statistics Mr. Toner s Lecture Notes 3.1 Measures of Central Tendency
Math 1 Introduction to Statistics Mr. Toner s Lecture Notes 3.1 Measures of Central Tendency lowest value + highest value midrange The word average: is very ambiguous and can actually refer to the mean,
More informationThe Normal Distribution. John McGready, PhD Johns Hopkins University
The Normal Distribution John McGready, PhD Johns Hopkins University General Properties of The Normal Distribution The material in this video is subject to the copyright of the owners of the material and
More informationMeasures of Position
Measures of Position In this section, we will learn to use fractiles. Fractiles are numbers that partition, or divide, an ordered data set into equal parts (each part has the same number of data entries).
More informationLecture 3 Questions that we should be able to answer by the end of this lecture:
Lecture 3 Questions that we should be able to answer by the end of this lecture: Which is the better exam score? 67 on an exam with mean 50 and SD 10 or 62 on an exam with mean 40 and SD 12 Is it fair
More informationChapter 1. Looking at Data-Distribution
Chapter 1. Looking at Data-Distribution Statistics is the scientific discipline that provides methods to draw right conclusions: 1)Collecting the data 2)Describing the data 3)Drawing the conclusions Raw
More informationLecture 3 Questions that we should be able to answer by the end of this lecture:
Lecture 3 Questions that we should be able to answer by the end of this lecture: Which is the better exam score? 67 on an exam with mean 50 and SD 10 or 62 on an exam with mean 40 and SD 12 Is it fair
More informationIQR = number. summary: largest. = 2. Upper half: Q3 =
Step by step box plot Height in centimeters of players on the 003 Women s Worldd Cup soccer team. 157 1611 163 163 164 165 165 165 168 168 168 170 170 170 171 173 173 175 180 180 Determine the 5 number
More informationCHAPTER 8: INTEGRALS 8.1 REVIEW: APPROXIMATING INTEGRALS WITH RIEMANN SUMS IN 2-D
CHAPTER 8: INTEGRALS 8.1 REVIEW: APPROXIMATING INTEGRALS WITH RIEMANN SUMS IN 2-D In two dimensions we have previously used Riemann sums to approximate ( ) following steps: with the 1. Divide the region
More informationSection 10.4 Normal Distributions
Section 10.4 Normal Distributions Random Variables Suppose a bank is interested in improving its services to customers. The manager decides to begin by finding the amount of time tellers spend on each
More informationTopic 5 - Joint distributions and the CLT
Topic 5 - Joint distributions and the CLT Joint distributions Calculation of probabilities, mean and variance Expectations of functions based on joint distributions Central Limit Theorem Sampling distributions
More informationChapter 3 - Displaying and Summarizing Quantitative Data
Chapter 3 - Displaying and Summarizing Quantitative Data 3.1 Graphs for Quantitative Data (LABEL GRAPHS) August 25, 2014 Histogram (p. 44) - Graph that uses bars to represent different frequencies or relative
More informationDeveloping Effect Sizes for Non-Normal Data in Two-Sample Comparison Studies
Developing Effect Sizes for Non-Normal Data in Two-Sample Comparison Studies with an Application in E-commerce Durham University Apr 13, 2010 Outline 1 Introduction Effect Size, Complementory for Hypothesis
More informationChapter 2 Describing, Exploring, and Comparing Data
Slide 1 Chapter 2 Describing, Exploring, and Comparing Data Slide 2 2-1 Overview 2-2 Frequency Distributions 2-3 Visualizing Data 2-4 Measures of Center 2-5 Measures of Variation 2-6 Measures of Relative
More informationSo..to be able to make comparisons possible, we need to compare them with their respective distributions.
Unit 3 ~ Modeling Distributions of Data 1 ***Section 2.1*** Measures of Relative Standing and Density Curves (ex) Suppose that a professional soccer team has the money to sign one additional player and
More informationLearner Expectations UNIT 1: GRAPICAL AND NUMERIC REPRESENTATIONS OF DATA. Sept. Fathom Lab: Distributions and Best Methods of Display
CURRICULUM MAP TEMPLATE Priority Standards = Approximately 70% Supporting Standards = Approximately 20% Additional Standards = Approximately 10% HONORS PROBABILITY AND STATISTICS Essential Questions &
More informationDownloaded from
UNIT 2 WHAT IS STATISTICS? Researchers deal with a large amount of data and have to draw dependable conclusions on the basis of data collected for the purpose. Statistics help the researchers in making
More information6.2 Areas under the curve 2018.notebook January 18, 2018
More details about z scores * A z score is the number of standard deviations between a measurement and its mean. * Use z scores to make comparisons of measurements from different distributions (if the
More informationGoals. The Normal Probability Distribution. A distribution. A Discrete Probability Distribution. Results of Tossing Two Dice. Probabilities involve
Goals The Normal Probability Distribution Chapter 7 Dr. Richard Jerz Understand the difference between discrete and continuous distributions. Compute the mean, standard deviation, and probabilities for
More informationStat 528 (Autumn 2008) Density Curves and the Normal Distribution. Measures of center and spread. Features of the normal distribution
Stat 528 (Autumn 2008) Density Curves and the Normal Distribution Reading: Section 1.3 Density curves An example: GRE scores Measures of center and spread The normal distribution Features of the normal
More information1 Overview of Statistics; Essential Vocabulary
1 Overview of Statistics; Essential Vocabulary Statistics: the science of collecting, organizing, analyzing, and interpreting data in order to make decisions Population and sample Population: the entire
More informationAP Statistics. Study Guide
Measuring Relative Standing Standardized Values and z-scores AP Statistics Percentiles Rank the data lowest to highest. Counting up from the lowest value to the select data point we discover the percentile
More informationData can be in the form of numbers, words, measurements, observations or even just descriptions of things.
+ What is Data? Data is a collection of facts. Data can be in the form of numbers, words, measurements, observations or even just descriptions of things. In most cases, data needs to be interpreted and
More informationThe Normal Probability Distribution. Goals. A distribution 2/27/16. Chapter 7 Dr. Richard Jerz
The Normal Probability Distribution Chapter 7 Dr. Richard Jerz 1 2016 rjerz.com Goals Understand the difference between discrete and continuous distributions. Compute the mean, standard deviation, and
More informationCHAPTER 1. Introduction. Statistics: Statistics is the science of collecting, organizing, analyzing, presenting and interpreting data.
1 CHAPTER 1 Introduction Statistics: Statistics is the science of collecting, organizing, analyzing, presenting and interpreting data. Variable: Any characteristic of a person or thing that can be expressed
More informationa. divided by the. 1) Always round!! a) Even if class width comes out to a, go up one.
Probability and Statistics Chapter 2 Notes I Section 2-1 A Steps to Constructing Frequency Distributions 1 Determine number of (may be given to you) a Should be between and classes 2 Find the Range a The
More informationChapter 6. The Normal Distribution. McGraw-Hill, Bluman, 7 th ed., Chapter 6 1
Chapter 6 The Normal Distribution McGraw-Hill, Bluman, 7 th ed., Chapter 6 1 Bluman, Chapter 6 2 Chapter 6 Overview Introduction 6-1 Normal Distributions 6-2 Applications of the Normal Distribution 6-3
More informationChapter 2 - Graphical Summaries of Data
Chapter 2 - Graphical Summaries of Data Data recorded in the sequence in which they are collected and before they are processed or ranked are called raw data. Raw data is often difficult to make sense
More informationApplications of Integration. Copyright Cengage Learning. All rights reserved.
Applications of Integration Copyright Cengage Learning. All rights reserved. Area of a Region Between Two Curves Copyright Cengage Learning. All rights reserved. Objectives Find the area of a region between
More informationCondence Intervals about a Single Parameter:
Chapter 9 Condence Intervals about a Single Parameter: 9.1 About a Population Mean, known Denition 9.1.1 A point estimate of a parameter is the value of a statistic that estimates the value of the parameter.
More informationChapter 2: Modeling Distributions of Data
Chapter 2: Modeling Distributions of Data Section 2.2 The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE Chapter 2 Modeling Distributions of Data 2.1 Describing Location in a Distribution
More informationMEASURES OF CENTRAL TENDENCY
11.1 Find Measures of Central Tendency and Dispersion STATISTICS Numerical values used to summarize and compare sets of data MEASURE OF CENTRAL TENDENCY A number used to represent the center or middle
More informationLab 4: Distributions of random variables
Lab 4: Distributions of random variables In this lab we ll investigate the probability distribution that is most central to statistics: the normal distribution If we are confident that our data are nearly
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I. 4 th Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I 4 th Nine Weeks, 2016-2017 1 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource for
More informationSTA Rev. F Learning Objectives. Learning Objectives (Cont.) Module 3 Descriptive Measures
STA 2023 Module 3 Descriptive Measures Learning Objectives Upon completing this module, you should be able to: 1. Explain the purpose of a measure of center. 2. Obtain and interpret the mean, median, and
More informationHow individual data points are positioned within a data set.
Section 3.4 Measures of Position Percentiles How individual data points are positioned within a data set. P k is the value such that k% of a data set is less than or equal to P k. For example if we said
More information