MEASURING THE SPREAD OF DATA: 6F
|
|
- Mildred Griffith
- 6 years ago
- Views:
Transcription
1 CONTINUING WITH DESCRIPTIVE STATS 6E,6F,6G,6H,6I MEASURING THE SPREAD OF DATA: 6F othink about this example: Suppose you are at a high school football game and you sample 40 people from the student section about their age. othen you head to a professional game and you sample 40 random people there. You find that you have the same mean as the high school game. owhat is different about the two scenarios? oare they a good representation of the data collected? 1
2 DISPERSION osometimes mean, median and mode don t give you an accurate description of the distribution. To do that, we need to measure both the centre and its dispersion. owe can identify the centre, but the spread of the data can be analyzed 3 different ways: orange, ointerquartile range, ostandard deviation. RANGE The range of the data, or the max minus the min is not a particularly reliable measure of spread. Why do you think that would be true? 2
3 THE QUARTILES AND THE INTERQUARTILE RANGE The median divides the data into two even halves. If we look at the middle of the lower half, we have found the 1 st quartile, or the lower quartile. If we look at the middle of the upper half, we have found the 3 rd quartile, or the upper quartile. The distance between the two quartiles is called the Interquartile range. The tells us the range of the middle 50% of the data. = EXAMPLE 1) Reorder the set 2) Find the median 3) Find the lower quartile and upper quartile. If there is a middle term, disregard it when finding the quartiles. If there are 2 terms for the median, use the lower one for and the upper on for. 4) Calculate the 3
4 CALCULATOR EXAMPLE Use a GDC to calculate the Range, &, and IQR. 6G BOX AND WHISKER PLOT Hopefully you have seen these before. Lets break it down Quickly. Make sure that you use a number line that is in increments. Why would that need to be true? 4
5 WHAT WOULD A B&W LOOK LIKE IF DRAW AN EXAMPLE! Where on the number line is the outlier? Toward the positive side = positively skewed Toward the negative side = negatively skewed The data was a symmetrical distribution? The data was positively skewed? The data was negatively skewed? OYO: TRY IT Create a box and whisker plot (boxplot) from the data: 13, 24, 14, 11, 9, 31, 33, 33, 33, 18, 29, 28 Use of a calculator can be helpful but it doesn t label the important values for you, so 5
6 PARALLEL BOXPLOTS Simply put, two sets of data are compared on the same number line with two boxplots. Example: A hospital is trialing a new anesthetic drug and has collected data on how long the new and old drugs take before the patient becomes unconscious. They wish to know which drug acts faster and which is more reliable. Old drug times (s): 8, 12, 9, 8, 16, 10, 14, 7, 5, 21, 13, 10, 8, 10, 11, 8, 11, 9, 11, 14 New drug times (s): 8, 12, 7, 8, 12, 11, 9, 8, 10, 8, 10, 9, 12, 8, 8, 7, 10, 7, 9, 9 Lets put these on the same number line and compare the data. Use a 5-number summary! PARALLEL BOXPLOTS Old drug times (s): 8, 12, 9, 8, 16, 10, 14, 7, 5, 21, 13, 10, 8, 10, 11, 8, 11, 9, 11, 14 New drug times (s): 8, 12, 7, 8, 12, 11, 9, 8, 10, 8, 10, 9, 12, 8, 8, 7, 10, 7, 9, 9 Faster? Reliable? 6
7 INTERESTING TO NOTE Old drug times (s): 8, 12, 9, 8, 16, 10, 14, 7, 5, 21, 13, 10, 8, 10, 11, 8, 11, 9, 11, 14 Are any of these outliers? CUMULATIVE FREQUENCY GRAPHS Before we get started: Cumulative Frequency: The frequency of an event is the accumulation of the frequencies up to and including the event. Cumulative Relative Frequency of an event is the sum of the relative frequencies up to and including that event divided by the total number n. (the percent of data used thus far) 7
8 EXAMPLE BY HAND Lengths Tally Frequency Relative frequency Total Length of steel Rod to 3 decimal places. Cumulative frequency Cumu. Relative Frequency PERCENTILES (EXACT PERCENTILES ARE NOT ON IB EXAM) A percentile is the score below which a certain percentage of the data lies. For example: The 85th percentile is the score below which 85% of the data lies. If your score in a test is the 95th percentile, then 95% of the class have scored less than you. Notice that: the lower quartile (Q1) is the 25th percentile the median (Q2) is the 50th percentile the upper quartile (Q3) is the 75th percentile. 8
9 CUMULATIVE FREQUENCY GRAPH: Represents only cumulative frequency. It starts at 0 and ends at the total (these are the boundaries). CONTINUED 9
10 LETS CREATE OUR OWN From the table on slide 18. Length of steel Rod. OYO FROM YOUR BOOK 10
11 9/27/2017 THE LIMITATIONS Range and IQR are limited in the amount information. We talked about the limitations of range. What would the limitations of IQR be? We need a better way of describing the dispersion of the data!! STANDARD DEVIATION DEF: The measures of deviation between scores and the mean; the measure of dispersal of the data. The larger the standard deviation, then more widely spread the data would be. The smaller the standard deviation, the less spread (less dispersed). How deviated each score is from the mean We calculate it by considering a data set of n values:,,,,.,, with mean. = ( ) 11
12 9/27/2017 LETS BREAK IT DOWN First thing first. We are talking about individual ungrouped data. = total frequency = individual Score = mean = is the Standard Deviation = SD. ( ) We are looking at the measure of how far an individual score is from the mean. We then sum up all of those distances after we have made them all positive, by squaring them. If this number is smaller, then we know that most of the data values are close to. Dividing by n averages out each data value and square rooting it corrects the units. STANDARD DEVIATION BY HAND This will be an expectation of mine, so learn how to do it. I will be testing you on this, but the IB papers, and IA will not require you to do it by hand. The best way to find standard deviation by hand is to use a table. Lets look at an example and fill in the table by hand. We do it by hand to understand the mechanisms of how the GDC computes the. 12
13 9/27/2017 EXAMPLE: IA MATH SCORES FOR WILLAMETTE HS. Calculate the SD, or for the data below. We will need to know some information before we can calculate it. What info do we need? Math IA Scores TOTAL = ( ) NOW, USING A CALCULATOR For larger sets up data, it would only make sense to use a GDC. Therefore, lets do an example. Calculate the standard deviation of the data set: 2, 5, 4, 6, 7, 5, 6, 8, 5, 8, 3, 9, 6, 8, 1, 1, 2, 2, 2, 5 As before, we would enter this into a list and use 1- variable stats to calculate the Make sure you always use the standard deviation of the population (this is a new development!). 13
14 9/27/2017 FREQUENCY TABLES. For frequency tables, we can still find the SD by hand or by use of GDC. By hand, we use the formula. This simply adds one more column to our table. Lets calculate this by hand. = ( ) Math IA Scores Frequency GROUPED DATA FREQUENCY TABLES Same thing here, but we use as the midpoint of the class intervals. Lets use technology to calculate this one! Steps for grouped Data: 1. Create 2. Enter into 3. Enter freq. into 4. Press List 6. Freq. 7. Press calculate and find 14
15 COMPARING THE SPREAD OF TWO DATA SETS The following exam results were recorded by two classes of students studying Spanish: Class A: Class B: Compare the results of the two classes including their spread. Lets use the GDC to 1) Compare mean, 2) compare SD for dispersion. CORRECT, in a galaxy far far away 15
16 THAT PUTS US AT THE END OF THE POWER STANDARD! We will have one day of a review/activity, then take the PS2 assessment! Your homework is 6G.1 #2,4 6G.2 #2,4 (use GDC!!) 6H #1,4, 5 6I.1 #1, 3, 5 6I.2 #1,2, 6,7 6I.3 #1, 3 16
Objective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode.
Chapter 3 Numerically Summarizing Data Chapter 3.1 Measures of Central Tendency Objective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode. A1. Mean The
More informationCHAPTER 2: Describing Distributions with Numbers
CHAPTER 2: Describing Distributions with Numbers The Basic Practice of Statistics 6 th Edition Moore / Notz / Fligner Lecture PowerPoint Slides Chapter 2 Concepts 2 Measuring Center: Mean and Median Measuring
More informationDescribing Distributions
Describing Distributions With Numbers April 18, 2012 Summary Statistics. Measures of Center. Percentiles. Measures of Spread. A Summary Statement. Choosing Numerical Summaries. 1.0 What Are Summary Statistics?
More informationQUANTITATIVE DATA. UNIVARIATE DATA data for one variable
QUANTITATIVE DATA Recall that quantitative (numeric) data values are numbers where data take numerical values for which it is sensible to find averages, such as height, hourly pay, and pulse rates. UNIVARIATE
More informationIn this investigation you will use the statistics skills that you learned the to display and analyze a cup of peanut M&Ms.
M&M Madness In this investigation you will use the statistics skills that you learned the to display and analyze a cup of peanut M&Ms. Part I: Categorical Analysis: M&M Color Distribution 1. Record the
More information2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 2 Methods for Describing Sets of Data Summary of Central Tendency Measures Measure Formula Description Mean x i / n Balance Point Median ( n +1) Middle Value
More information3.1 Measure of Center
3.1 Measure of Center Calculate the mean for a given data set Find the median, and describe why the median is sometimes preferable to the mean Find the mode of a data set Describe how skewness affects
More informationReview for Exam #1. Chapter 1. The Nature of Data. Definitions. Population. Sample. Quantitative data. Qualitative (attribute) data
Review for Exam #1 1 Chapter 1 Population the complete collection of elements (scores, people, measurements, etc.) to be studied Sample a subcollection of elements drawn from a population 11 The Nature
More informationMath 140 Introductory Statistics
Math 140 Introductory Statistics Professor Silvia Fernández Chapter 2 Based on the book Statistics in Action by A. Watkins, R. Scheaffer, and G. Cobb. Visualizing Distributions Recall the definition: The
More informationMath 140 Introductory Statistics
Visualizing Distributions Math 140 Introductory Statistics Professor Silvia Fernández Chapter Based on the book Statistics in Action by A. Watkins, R. Scheaffer, and G. Cobb. Recall the definition: The
More informationMATH 117 Statistical Methods for Management I Chapter Three
Jubail University College MATH 117 Statistical Methods for Management I Chapter Three This chapter covers the following topics: I. Measures of Center Tendency. 1. Mean for Ungrouped Data (Raw Data) 2.
More informationWhat is statistics? Statistics is the science of: Collecting information. Organizing and summarizing the information collected
What is statistics? Statistics is the science of: Collecting information Organizing and summarizing the information collected Analyzing the information collected in order to draw conclusions Two types
More informationChapter 1: Exploring Data
Chapter 1: Exploring Data Section 1.3 with Numbers The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE Chapter 1 Exploring Data Introduction: Data Analysis: Making Sense of Data 1.1
More informationChapter 2: Tools for Exploring Univariate Data
Stats 11 (Fall 2004) Lecture Note Introduction to Statistical Methods for Business and Economics Instructor: Hongquan Xu Chapter 2: Tools for Exploring Univariate Data Section 2.1: Introduction What is
More informationDescribing distributions with numbers
Describing distributions with numbers A large number or numerical methods are available for describing quantitative data sets. Most of these methods measure one of two data characteristics: The central
More informationChapter 6 Group Activity - SOLUTIONS
Chapter 6 Group Activity - SOLUTIONS Group Activity Summarizing a Distribution 1. The following data are the number of credit hours taken by Math 105 students during a summer term. You will be analyzing
More informationExample 2. Given the data below, complete the chart:
Statistics 2035 Quiz 1 Solutions Example 1. 2 64 150 150 2 128 150 2 256 150 8 8 Example 2. Given the data below, complete the chart: 52.4, 68.1, 66.5, 75.0, 60.5, 78.8, 63.5, 48.9, 81.3 n=9 The data is
More informationFurther Mathematics 2018 CORE: Data analysis Chapter 2 Summarising numerical data
Chapter 2: Summarising numerical data Further Mathematics 2018 CORE: Data analysis Chapter 2 Summarising numerical data Extract from Study Design Key knowledge Types of data: categorical (nominal and ordinal)
More informationDescribing distributions with numbers
Describing distributions with numbers A large number or numerical methods are available for describing quantitative data sets. Most of these methods measure one of two data characteristics: The central
More informationMath 14 Lecture Notes Ch Percentile
.3 Measures of the Location of the Data Percentile g A measure of position, the percentile, p, is an integer (1 p 99) such that the p th percentile is the position of a data value where p% of the data
More informationSection 2.3: One Quantitative Variable: Measures of Spread
Section 2.3: One Quantitative Variable: Measures of Spread Objectives: 1) Measures of spread, variability a. Range b. Standard deviation i. Formula ii. Notation for samples and population 2) The 95% rule
More informationSection 3. Measures of Variation
Section 3 Measures of Variation Range Range = (maximum value) (minimum value) It is very sensitive to extreme values; therefore not as useful as other measures of variation. Sample Standard Deviation The
More informationChapter 5. Understanding and Comparing. Distributions
STAT 141 Introduction to Statistics Chapter 5 Understanding and Comparing Distributions Bin Zou (bzou@ualberta.ca) STAT 141 University of Alberta Winter 2015 1 / 27 Boxplots How to create a boxplot? Assume
More information1.3: Describing Quantitative Data with Numbers
1.3: Describing Quantitative Data with Numbers Section 1.3 Describing Quantitative Data with Numbers After this section, you should be able to MEASURE center with the mean and median MEASURE spread with
More informationDescribing Distributions With Numbers
Describing Distributions With Numbers October 24, 2012 What Do We Usually Summarize? Measures of Center. Percentiles. Measures of Spread. A Summary Statement. Choosing Numerical Summaries. 1.0 What Do
More informationUnit Two Descriptive Biostatistics. Dr Mahmoud Alhussami
Unit Two Descriptive Biostatistics Dr Mahmoud Alhussami Descriptive Biostatistics The best way to work with data is to summarize and organize them. Numbers that have not been summarized and organized are
More informationCHAPTER 5: EXPLORING DATA DISTRIBUTIONS. Individuals are the objects described by a set of data. These individuals may be people, animals or things.
(c) Epstein 2013 Chapter 5: Exploring Data Distributions Page 1 CHAPTER 5: EXPLORING DATA DISTRIBUTIONS 5.1 Creating Histograms Individuals are the objects described by a set of data. These individuals
More informationSTP 420 INTRODUCTION TO APPLIED STATISTICS NOTES
INTRODUCTION TO APPLIED STATISTICS NOTES PART - DATA CHAPTER LOOKING AT DATA - DISTRIBUTIONS Individuals objects described by a set of data (people, animals, things) - all the data for one individual make
More informationCHAPTER 1. Introduction
CHAPTER 1 Introduction Engineers and scientists are constantly exposed to collections of facts, or data. The discipline of statistics provides methods for organizing and summarizing data, and for drawing
More informationLecture 2. Quantitative variables. There are three main graphical methods for describing, summarizing, and detecting patterns in quantitative data:
Lecture 2 Quantitative variables There are three main graphical methods for describing, summarizing, and detecting patterns in quantitative data: Stemplot (stem-and-leaf plot) Histogram Dot plot Stemplots
More informationMeasures of center. The mean The mean of a distribution is the arithmetic average of the observations:
Measures of center The mean The mean of a distribution is the arithmetic average of the observations: x = x 1 + + x n n n = 1 x i n i=1 The median The median is the midpoint of a distribution: the number
More informationUnit 2. Describing Data: Numerical
Unit 2 Describing Data: Numerical Describing Data Numerically Describing Data Numerically Central Tendency Arithmetic Mean Median Mode Variation Range Interquartile Range Variance Standard Deviation Coefficient
More informationDetermining the Spread of a Distribution
Determining the Spread of a Distribution 1.3-1.5 Cathy Poliak, Ph.D. cathy@math.uh.edu Department of Mathematics University of Houston Lecture 3-2311 Lecture 3-2311 1 / 58 Outline 1 Describing Quantitative
More informationDetermining the Spread of a Distribution
Determining the Spread of a Distribution 1.3-1.5 Cathy Poliak, Ph.D. cathy@math.uh.edu Department of Mathematics University of Houston Lecture 3-2311 Lecture 3-2311 1 / 58 Outline 1 Describing Quantitative
More informationStatistics Add Ins.notebook. November 22, Add ins
Add ins We have LOADS of things we need to know for the IGCSE that you haven't learnt as part of the Bavarian Curriculum. We are now going to shoehorn in some of those topics and ideas. Nov 12 11:50 Main
More informationThe Normal Distribution. Chapter 6
+ The Normal Distribution Chapter 6 + Applications of the Normal Distribution Section 6-2 + The Standard Normal Distribution and Practical Applications! We can convert any variable that in normally distributed
More informationChapter 1. Looking at Data
Chapter 1 Looking at Data Types of variables Looking at Data Be sure that each variable really does measure what you want it to. A poor choice of variables can lead to misleading conclusions!! For example,
More informationDescriptive Statistics-I. Dr Mahmoud Alhussami
Descriptive Statistics-I Dr Mahmoud Alhussami Biostatistics What is the biostatistics? A branch of applied math. that deals with collecting, organizing and interpreting data using well-defined procedures.
More informationLecture 6: Chapter 4, Section 2 Quantitative Variables (Displays, Begin Summaries)
Lecture 6: Chapter 4, Section 2 Quantitative Variables (Displays, Begin Summaries) Summarize with Shape, Center, Spread Displays: Stemplots, Histograms Five Number Summary, Outliers, Boxplots Cengage Learning
More informationResistant Measure - A statistic that is not affected very much by extreme observations.
Chapter 1.3 Lecture Notes & Examples Section 1.3 Describing Quantitative Data with Numbers (pp. 50-74) 1.3.1 Measuring Center: The Mean Mean - The arithmetic average. To find the mean (pronounced x bar)
More informationSTRAND E: STATISTICS. UNIT E4 Measures of Variation: Text * * Contents. Section. E4.1 Cumulative Frequency. E4.2 Box and Whisker Plots
STRAND E: STATISTICS E4 Measures of Variation Text Contents * * Section E4.1 E4.2 Box and Whisker Plots E4 Measures of Variation E4.1 * frequencies are useful if more detailed information is required about
More informationLast Lecture. Distinguish Populations from Samples. Knowing different Sampling Techniques. Distinguish Parameters from Statistics
Last Lecture Distinguish Populations from Samples Importance of identifying a population and well chosen sample Knowing different Sampling Techniques Distinguish Parameters from Statistics Knowing different
More informationChapter 6 The Standard Deviation as a Ruler and the Normal Model
Chapter 6 The Standard Deviation as a Ruler and the Normal Model Overview Key Concepts Understand how adding (subtracting) a constant or multiplying (dividing) by a constant changes the center and/or spread
More informationUnit 2: Numerical Descriptive Measures
Unit 2: Numerical Descriptive Measures Summation Notation Measures of Central Tendency Measures of Dispersion Chebyshev's Rule Empirical Rule Measures of Relative Standing Box Plots z scores Jan 28 10:48
More informationAlgebra 2. Outliers. Measures of Central Tendency (Mean, Median, Mode) Standard Deviation Normal Distribution (Bell Curves)
Algebra 2 Outliers Measures of Central Tendency (Mean, Median, Mode) Standard Deviation Normal Distribution (Bell Curves) Algebra 2 Notes #1 Chp 12 Outliers In a set of numbers, sometimes there will be
More informationADMS2320.com. We Make Stats Easy. Chapter 4. ADMS2320.com Tutorials Past Tests. Tutorial Length 1 Hour 45 Minutes
We Make Stats Easy. Chapter 4 Tutorial Length 1 Hour 45 Minutes Tutorials Past Tests Chapter 4 Page 1 Chapter 4 Note The following topics will be covered in this chapter: Measures of central location Measures
More informationExercises from Chapter 3, Section 1
Exercises from Chapter 3, Section 1 1. Consider the following sample consisting of 20 numbers. (a) Find the mode of the data 21 23 24 24 25 26 29 30 32 34 39 41 41 41 42 43 48 51 53 53 (b) Find the median
More informationChapter 3. Data Description
Chapter 3. Data Description Graphical Methods Pie chart It is used to display the percentage of the total number of measurements falling into each of the categories of the variable by partition a circle.
More informationST Presenting & Summarising Data Descriptive Statistics. Frequency Distribution, Histogram & Bar Chart
ST2001 2. Presenting & Summarising Data Descriptive Statistics Frequency Distribution, Histogram & Bar Chart Summary of Previous Lecture u A study often involves taking a sample from a population that
More information1-1. Chapter 1. Sampling and Descriptive Statistics by The McGraw-Hill Companies, Inc. All rights reserved.
1-1 Chapter 1 Sampling and Descriptive Statistics 1-2 Why Statistics? Deal with uncertainty in repeated scientific measurements Draw conclusions from data Design valid experiments and draw reliable conclusions
More information6 THE NORMAL DISTRIBUTION
CHAPTER 6 THE NORMAL DISTRIBUTION 341 6 THE NORMAL DISTRIBUTION Figure 6.1 If you ask enough people about their shoe size, you will find that your graphed data is shaped like a bell curve and can be described
More informationRevision Topic 13: Statistics 1
Revision Topic 13: Statistics 1 Averages There are three common types of average: the mean, median and mode. The mode (or modal value) is the data value (or values) that occurs the most often. The median
More informationIB Questionbank Mathematical Studies 3rd edition. Grouped discrete. 184 min 183 marks
IB Questionbank Mathematical Studies 3rd edition Grouped discrete 184 min 183 marks 1. The weights in kg, of 80 adult males, were collected and are summarized in the box and whisker plot shown below. Write
More informationLesson Plan. Answer Questions. Summary Statistics. Histograms. The Normal Distribution. Using the Standard Normal Table
Lesson Plan Answer Questions Summary Statistics Histograms The Normal Distribution Using the Standard Normal Table 1 2. Summary Statistics Given a collection of data, one needs to find representations
More informationF78SC2 Notes 2 RJRC. If the interest rate is 5%, we substitute x = 0.05 in the formula. This gives
F78SC2 Notes 2 RJRC Algebra It is useful to use letters to represent numbers. We can use the rules of arithmetic to manipulate the formula and just substitute in the numbers at the end. Example: 100 invested
More informationDetermining the Spread of a Distribution Variance & Standard Deviation
Determining the Spread of a Distribution Variance & Standard Deviation 1.3 Cathy Poliak, Ph.D. cathy@math.uh.edu Department of Mathematics University of Houston Lecture 3 Lecture 3 1 / 32 Outline 1 Describing
More informationPercentile: Formula: To find the percentile rank of a score, x, out of a set of n scores, where x is included:
AP Statistics Chapter 2 Notes 2.1 Describing Location in a Distribution Percentile: The pth percentile of a distribution is the value with p percent of the observations (If your test score places you in
More information2.1 Measures of Location (P.9-11)
MATH1015 Biostatistics Week.1 Measures of Location (P.9-11).1.1 Summation Notation Suppose that we observe n values from an experiment. This collection (or set) of n values is called a sample. Let x 1
More informationLecture 11. Data Description Estimation
Lecture 11 Data Description Estimation Measures of Central Tendency (continued, see last lecture) Sample mean, population mean Sample mean for frequency distributions The median The mode The midrange 3-22
More informationCHAPTER 2 Modeling Distributions of Data
CHAPTER 2 Modeling Distributions of Data 2.1 Describing Location in a Distribution The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Describing Location
More informationDescribing Distributions with Numbers
Describing Distributions with Numbers Using graphs, we could determine the center, spread, and shape of the distribution of a quantitative variable. We can also use numbers (called summary statistics)
More informationLecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series. Slide 1
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 3 Statistics for Describing, Exploring, and Comparing Data 3-1 Overview 3-2 Measures
More informationSlide 1. Slide 2. Slide 3. Pick a Brick. Daphne. 400 pts 200 pts 300 pts 500 pts 100 pts. 300 pts. 300 pts 400 pts 100 pts 400 pts.
Slide 1 Slide 2 Daphne Phillip Kathy Slide 3 Pick a Brick 100 pts 200 pts 500 pts 300 pts 400 pts 200 pts 300 pts 500 pts 100 pts 300 pts 400 pts 100 pts 400 pts 100 pts 200 pts 500 pts 100 pts 400 pts
More informationGRACEY/STATISTICS CH. 3. CHAPTER PROBLEM Do women really talk more than men? Science, Vol. 317, No. 5834). The study
CHAPTER PROBLEM Do women really talk more than men? A common belief is that women talk more than men. Is that belief founded in fact, or is it a myth? Do men actually talk more than women? Or do men and
More informationare the objects described by a set of data. They may be people, animals or things.
( c ) E p s t e i n, C a r t e r a n d B o l l i n g e r 2016 C h a p t e r 5 : E x p l o r i n g D a t a : D i s t r i b u t i o n s P a g e 1 CHAPTER 5: EXPLORING DATA DISTRIBUTIONS 5.1 Creating Histograms
More informationChapter 3. Measuring data
Chapter 3 Measuring data 1 Measuring data versus presenting data We present data to help us draw meaning from it But pictures of data are subjective They re also not susceptible to rigorous inference Measuring
More informationLecture 2. Descriptive Statistics: Measures of Center
Lecture 2. Descriptive Statistics: Measures of Center Descriptive Statistics summarize or describe the important characteristics of a known set of data Inferential Statistics use sample data to make inferences
More informationPS2.1 & 2.2: Linear Correlations PS2: Bivariate Statistics
PS2.1 & 2.2: Linear Correlations PS2: Bivariate Statistics LT1: Basics of Correlation LT2: Measuring Correlation and Line of best fit by eye Univariate (one variable) Displays Frequency tables Bar graphs
More informationTopic 2 Part 1 [195 marks]
Topic 2 Part 1 [195 marks] The distribution of rainfall in a town over 80 days is displayed on the following box-and-whisker diagram. 1a. Write down the median rainfall. 1b. Write down the minimum rainfall.
More information1.3.1 Measuring Center: The Mean
1.3.1 Measuring Center: The Mean Mean - The arithmetic average. To find the mean (pronounced x bar) of a set of observations, add their values and divide by the number of observations. If the n observations
More informationRecap: Ø Distribution Shape Ø Mean, Median, Mode Ø Standard Deviations
DAY 4 16 Jan 2014 Recap: Ø Distribution Shape Ø Mean, Median, Mode Ø Standard Deviations Two Important Three-Standard-Deviation Rules 1. Chebychev s Rule : Implies that at least 89% of the observations
More informationMATH 1150 Chapter 2 Notation and Terminology
MATH 1150 Chapter 2 Notation and Terminology Categorical Data The following is a dataset for 30 randomly selected adults in the U.S., showing the values of two categorical variables: whether or not the
More informationDescribing Distributions With Numbers Chapter 12
Describing Distributions With Numbers Chapter 12 May 1, 2013 What Do We Usually Summarize? Measures of Center. Percentiles. Measures of Spread. A Summary. 1.0 What Do We Usually Summarize? source: Prof.
More informationLecture 3B: Chapter 4, Section 2 Quantitative Variables (Displays, Begin Summaries)
Lecture 3B: Chapter 4, Section 2 Quantitative Variables (Displays, Begin Summaries) Summarize with Shape, Center, Spread Displays: Stemplots, Histograms Five Number Summary, Outliers, Boxplots Mean vs.
More informationSTAT 200 Chapter 1 Looking at Data - Distributions
STAT 200 Chapter 1 Looking at Data - Distributions What is Statistics? Statistics is a science that involves the design of studies, data collection, summarizing and analyzing the data, interpreting the
More informationSection 3.2 Measures of Central Tendency
Section 3.2 Measures of Central Tendency 1 of 149 Section 3.2 Objectives Determine the mean, median, and mode of a population and of a sample Determine the weighted mean of a data set and the mean of a
More informationWhat are the mean, median, and mode for the data set below? Step 1
Unit 11 Review Analyzing Data Name Per The mean is the average of the values. The median is the middle value(s) when the values are listed in order. The mode is the most common value(s). What are the mean,
More informationLecture 2 and Lecture 3
Lecture 2 and Lecture 3 1 Lecture 2 and Lecture 3 We can describe distributions using 3 characteristics: shape, center and spread. These characteristics have been discussed since the foundation of statistics.
More informationElementary Statistics
Elementary Statistics Q: What is data? Q: What does the data look like? Q: What conclusions can we draw from the data? Q: Where is the middle of the data? Q: Why is the spread of the data important? Q:
More informationMeasures of disease spread
Measures of disease spread Marco De Nardi Milk Safety Project 1 Objectives 1. Describe the following measures of spread: range, interquartile range, variance, and standard deviation 2. Discuss examples
More informationReview: Central Measures
Review: Central Measures Mean, Median and Mode When do we use mean or median? If there is (are) outliers, use Median If there is no outlier, use Mean. Example: For a data 1, 1.2, 1.5, 1.7, 1.8, 1.9, 2.3,
More informationChapter 3 Data Description
Chapter 3 Data Description Section 3.1: Measures of Central Tendency Section 3.2: Measures of Variation Section 3.3: Measures of Position Section 3.1: Measures of Central Tendency Definition of Average
More informationadditionalmathematicsstatisticsadditi onalmathematicsstatisticsadditionalm athematicsstatisticsadditionalmathem aticsstatisticsadditionalmathematicsst
additionalmathematicsstatisticsadditi onalmathematicsstatisticsadditionalm athematicsstatisticsadditionalmathem aticsstatisticsadditionalmathematicsst STATISTICS atisticsadditionalmathematicsstatistic
More informationPS2: Two Variable Statistics
PS2: Two Variable Statistics LT2: Measuring Correlation and Line of best fit by eye. LT3: Linear regression LT4: The χ 2 test of independence. 1 Pearson's Correlation Coefficient In examinations you are
More informationStat 101 Exam 1 Important Formulas and Concepts 1
1 Chapter 1 1.1 Definitions Stat 101 Exam 1 Important Formulas and Concepts 1 1. Data Any collection of numbers, characters, images, or other items that provide information about something. 2. Categorical/Qualitative
More informationMgtOp 215 Chapter 3 Dr. Ahn
MgtOp 215 Chapter 3 Dr. Ahn Measures of central tendency (center, location): measures the middle point of a distribution or data; these include mean and median. Measures of dispersion (variability, spread):
More informationStats Review Chapter 3. Mary Stangler Center for Academic Success Revised 8/16
Stats Review Chapter Revised 8/16 Note: This review is composed of questions similar to those found in the chapter review and/or chapter test. This review is meant to highlight basic concepts from the
More informationMATH 10 INTRODUCTORY STATISTICS
MATH 10 INTRODUCTORY STATISTICS Tommy Khoo Your friendly neighbourhood graduate student. Week 1 Chapter 1 Introduction What is Statistics? Why do you need to know Statistics? Technical lingo and concepts:
More informationUNIVERSITY OF MASSACHUSETTS Department of Biostatistics and Epidemiology BioEpi 540W - Introduction to Biostatistics Fall 2004
UNIVERSITY OF MASSACHUSETTS Department of Biostatistics and Epidemiology BioEpi 50W - Introduction to Biostatistics Fall 00 Exercises with Solutions Topic Summarizing Data Due: Monday September 7, 00 READINGS.
More informationUnivariate data. topic 12. Why learn this? What do you know? Learning sequence
topic 12 Univariate data 12.1 Overview Why learn this? According to the novelist Mark Twain, There are three kinds of lies: lies, damned lies and statistics. There is so much information in our lives,
More informationMeasures of Location. Measures of position are used to describe the relative location of an observation
Measures of Location Measures of position are used to describe the relative location of an observation 1 Measures of Position Quartiles and percentiles are two of the most popular measures of position
More informationTOPIC: Descriptive Statistics Single Variable
TOPIC: Descriptive Statistics Single Variable I. Numerical data summary measurements A. Measures of Location. Measures of central tendency Mean; Median; Mode. Quantiles - measures of noncentral tendency
More informationA is one of the categories into which qualitative data can be classified.
Chapter 2 Methods for Describing Sets of Data 2.1 Describing qualitative data Recall qualitative data: non-numerical or categorical data Basic definitions: A is one of the categories into which qualitative
More informationChapters 1 & 2 Exam Review
Problems 1-3 refer to the following five boxplots. 1.) To which of the above boxplots does the following histogram correspond? (A) A (B) B (C) C (D) D (E) E 2.) To which of the above boxplots does the
More informationLecture Slides. Elementary Statistics Twelfth Edition. by Mario F. Triola. and the Triola Statistics Series. Section 3.1- #
Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series by Mario F. Triola Chapter 3 Statistics for Describing, Exploring, and Comparing Data 3-1 Review and Preview 3-2 Measures
More information3.3. Section. Measures of Central Tendency and Dispersion from Grouped Data. Copyright 2013, 2010 and 2007 Pearson Education, Inc.
Section 3.3 Measures of Central Tendency and Dispersion from Grouped Data Objectives 1. Approximate the mean of a variable from grouped data 2. Compute the weighted mean 3. Approximate the standard deviation
More informationChapter 6. The Standard Deviation as a Ruler and the Normal Model 1 /67
Chapter 6 The Standard Deviation as a Ruler and the Normal Model 1 /67 Homework Read Chpt 6 Complete Reading Notes Do P129 1, 3, 5, 7, 15, 17, 23, 27, 29, 31, 37, 39, 43 2 /67 Objective Students calculate
More informationMath 140 Introductory Statistics
Box Plots Math 140 Introductory Statistics Professor B. Ábrego Lecture 6 Sections 2.3, 2.4, and 2.5 11,12,20,25,30,30,30,32,35, 39,40,40,40,42,45,48,50,70. = 11 Q 1 = 30 Median = 37 Q 3 = 42 = 70. = 70
More informationWhat is Statistics? Statistics is the science of understanding data and of making decisions in the face of variability and uncertainty.
What is Statistics? Statistics is the science of understanding data and of making decisions in the face of variability and uncertainty. Statistics is a field of study concerned with the data collection,
More informationDescribing Data: Two Variables
STAT 250 Dr. Kari Lock Morgan Describing Data: Two Variables SECTIONS 2.4, 2.5 One quantitative variable (2.4) One quantitative and one categorical (2.4) Two quantitative (2.5) z- score Which is better,
More information