Lectures 1 to 3 (for students).pptx
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Western University**We aren't endorsed by this school
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ECONOMIC 2222A
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Statistics
Date
Dec 16, 2024
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80
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GROUP ASSIGNMENTS © 1 will announce groups of 77?7 students in alphabetical order from the list. © If any student decides to change their group and join another group, he or she needs to get into an agreement with a student in the other group. Then, both students should inform me about their intention and willingness to change their group. © Any changes in group membership can be done only up to 77?7 at 4 pm. © Each group will solve the assignment and o give me only one copy owhich is typed (not hand-written) - stapled, o Includes the official name of all group members con the due date of the assignment C oright in the beginning of the class. Fa T P R L Ll | [ R DR .
GROUP ASSIGNMENTS © If a student in a group does not participate, it is the duty of the rest of the group to inform the instructor. How? © A student who feels a groupmate is shirking should send an email to that student, cc me ( prof.mahdiveh@gmail.com) in that email, and explain the problem to that student at least a week before the due date of the assignment. © | will also contact that student and if | am convinced that the suggested student is indeed shirking, | will give that student zero on that assignment. © | do not accept any complaint from < E groupmates after the assignment is submitted. =
HOW ABOUT YOU? O Attend lectures on time=>You do not miss a pop-quiz and its bonus mark © Read chapters of the textbook before attending lectures. © Be focused and attentive during lectures and ask your questions if you have any. Remember that | also hold office hours for your questions. © Solve practice questions © Participate in solving your group assignments and hand it in on time (\ © Take midterm and final exams
SOME OF THE FORMULAS IN THE LECTURES © You are not supposed to memorize some of the formulas. As | lecture, | specify them on slides. © 1 will give you these formulas in exam without any explanation. You should know what they are and how to use them. © However, there are other formulas that you have to memorize them. This is standard for an econometrics course. © This is an econometrics course filled with formulas and equations. Some of you might not understand formulas. Please let me know if you cannot follow me or please come to my office C\ hours before you get into real trouble. o
IMPORTANT NOTE © In this course, | base my lectures on the posted lecture notes, but of course | elaborate on them in the class, and | solve problems on the board. These notes are useful for review, but they are not meant to take the place of lectures. Students who rely on notes only, they traditionally do not do well on their exams in this course. © Whatever is on slides, board, and explained in words by me are in your exams. ( =
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© Examples solved during lectures (the Most important source) © Sets of practice questions and their answers posted by the instructor on Owl. © Group Assignments in the course. © Bonus Pop-quizzes. © Student solutions manual which is a separate book bundled by your textbook. This book contains detailed solutions to all even numbered exercises and applications in the textbook. © MyStatLab which is bundled by your textbook and contains tutorial exercises which are algorithmically generated for unlimited practice. The student access code for MyStatLab is inside the student access kit. Inside the kit, you can find the web address for registration on-line as well as a step-by-step guidance. The Course ID is already posted on Owl.
w INTRODUCTION: ® DESCRIBING DATA Based on chapter 1 of your textbook ®
Lecture Goals for Students After completing the first few lectures of the course, you should be able to: © Explain key definitions: + Population vs. Sample ¢ Parameter vs. Statistic + Descriptive vs. Inferential Statistics © Describe random sampling © Explain the difference between Descriptive and Inferential statistics © |ldentify types of variables and levels of measurement &
Lecture Goals for Students © Create and interpret graphs to describe categorical variables: ¢ frequency distribution, bar chart, pie chart, Pareto diagram © Create a line graph to describe time-series data © Create and interpret graphs to describe numerical variables: ¢ frequency distribution, histogram, ogive © Construct and interpret graphs to describe relationships between variables: ¢ Scatter plot, cross table
Data *Data values or observations are information collected regarding some subject * Data are often organized into a data table such as the one below Purchase Order Ship to Area | PreviousCD Purchase Gift? Name ‘ Province ASIN ‘ Artist Number Price | Code 10675489 Katherine H. | Alberta 1099 | 403 | Nashville N | B00000I5Y6 | Kansas 10783489 Samuel P. Nova Scotia 1699 | 902 | Classical Y | B000002BK9 | Boston 12837593 Chris G. Quebec 1598 | 819 | Hip Hop N | B000068ZVQ | Chicago 15783947 Monique D. | Ontario 1199 | 905 | Reggae N | BOO000IOAA | Garbage &
Variable The characteristics recorded about each individual, case, or subject are called variables Variables are usually shown as the columns of a data table and identify What has been measyred g Yamables ppooooom Purchase Order Ship to Area | PreviousCD Number Name Province | Price | Code Purchase | Gift? ASIN Artist 10675489 Katherine H. | Alberta 1099 | 403 | Nashville N | B00000I5Y6 | Kansas 10783489 Samuel P. Nova Scotia 1699 | 902 | Classical Y | B000002BK9 | Boston 12837593 Chris G. Quebec 1598 | 819 | Hip Hop N | B000068ZVQ | Chicago N 15783947 Monique D. | Ontario 1199 | 905 | Reggae B00000IOAA | Garbage
Variable Types: Categorical and Numerical When a variable names categories and answers questions about how cases fall into those categories, it is called a categorical variable When a variable has measured numerical values with units and the variable tells us about the quantity of what is measured, it is called a quantitative or numerical variable &
Categorical variables Example Categorical variables ... * arise from descriptive responses to questions such as “What kind of advertising do you use?” * may only have two possible values (like “Yes” or “No”) * may be a number like a telephone area Question Categories or Responses Do you invest in the stock market? _ Yes__No What kind of advertising do you use? | __ Newspapers ___Internet ___ Direct mailings What is your class at school? __ Freshman___ Sophomore ___Junior __Senior I would recommend this course to __ Strongly Disagree __ Slightly Disagree __ Slightly Agree _ Strongly Agree another student. How satisfied are you with this __ Very Unsatisfied ___ Unsatisfied __Satisfied __ Very Satisfied product?
Numerical Variables Numerical or quantitative variables have units. The units indicate * how each value has been measured * the corresponding scale of measurement * how much of something we have * how far apart two values are &
FURTHER CLASSIFICATIONS OF VARIABLES Variables r Categorical Numerical (quantitative) Discrete Continuous Examples: Examples: " Number of =« Weight Children " Voltage " Defects per (Measured hour characteristics® (Counted ) o items)
MEASUREMENT LEVELS OF CATEGORICAL VARIABLES: ORDINAL AND NOMINAL Nominal Data Ordinal Data *In nominal data, the numbers are used only for the purpose of convenience, and they do not mean any ordering (Example: If female it is 1 and if male it is zero. The responses are words that describe the categories) *Ordinal data shows rank ordering of items, and similar to nominal data the values are words that describe responses (Example: C\ product quality rating: 1:poor, 2: average, - 3:good).
EXAMPLE 1 Upon visiting a newly opened Starbucks store, customers were given a brief survey. Is the answer to each of the following questions categorical or numerical? If categorical, give the level of measurement. If numerical, is it discreet or continuous? a) Is this your first visit to this Starbucks store? b)On a scale from 1 (very dissatisfied) to 5 (very satisfied), rate your level of satisfaction with today’s purchase? ¢) What was the actual cost of your purchase today? &
DECISION MAKING IN AN UNCERTAIN ENVIRONMENT © Everyday decisions are based on uncertainty or incomplete information Examples: Will the job market be strong when | graduate? © Data are used to assist decision making. How? © Statistics and Econometrics are tools to help process, summarize, analyze, and interpret data @
SOME KEY DEFINITIONS © A population is the collection of all items of interest or under investigation ° N represents the population size ©A sample is an observed subset of the population °n represents the sample size © A parameter is a specific characteristic of a population © A statistic is a specific characteristic of a sample
POPULATION VS. SAMPLE Population Sample “ .f‘fl" |I'I||flH I Hfi“fll Values calculated Values computed using population from sample data data are called are called C\ parameters statistic
EXAMPLE 2 Suppose we are interested in examining the household income in Canada. © Population: All households in Canada © Sample: A group of households participated in the LFS survey (Labour Force Survey by statistics Canada)
WHY DO WE NEED SAMPLES? © Getting access to the population is not always feasible, and it is very costly. ©Thus, we select a sample from the population to make a statement about that population. ©How valid is this statement? It is valid if the sample is a representative of the population. ©How can we achieve a representative sample? One important principal is selecting a random sample.
RANDOM SAMPLING Simple random sampling is a procedure in which ©each member of the sample is chosen strictly by chance, ©each member of the population is equally likely to be chosen, ©and every possible sample of n objects is equally likely to be chosen. The resulting sample is called a random sample. C
©Now when we collect a random sample, we are looking for ways to illustrate the information in the data before calculating statistic and using it in making a decision under uncertainty. ©Therefore, we can use descriptive statistics
DESCRIPTIVE AND INFERENTIAL STATISTICS Two branches of statistics: © Descriptive statistics ¢ Graphical and numerical procedures to summarize and process data ¢ It includes tables, graphs, mean, etc. O |Inferential statistics ¢ Using data to make predictions, forecasts, and estimates to assist decision making ¢ Inference is the process of drawing conclusions or making decisions about a population based < E on sample results -
DESCRIPTIVE STATISTICS: GRAPHICAL PRESENTATION OF DATA © Data in raw form are usually not easy to use for decision making © Some type of organization is needed °Table ©Graph © The type of the organization to use depends on whether the variable is C-\ categorical or numerical. J
DESCRIPTIVE STATISTICS: GRAPHICAL PRESENTATION OF DATA CTD. Categorical Numerical Variables Variables * Frequency * Line chart distribution * Frequency * Cross table distribution * Bar chart * Histogram and * Pie chart ogive * Pareto diagram * Scatter plot
DESCRIPTIVE STATISTICS: TABLES AND GRAPHS FOR CATEGORICAL VARIABLES Categorical Data Tabulating Data -Frequency Graphing Data -Bar Chart Distribution Table -Cross Table 1 -Stacked or Component bar chart Pie Chart Pareto Diagra m -
DESCRIPTIVE STATISTICS: FREQUENCY DISTRIBUTION FOR TABULATING CATEGORICAL VARIABLE © A frequency distribution table is a table used to organize data. ©The left column (called classes or groups) includes all possible responses on a variable being studied. ©The right column is a list of frequencies, or number of observations, for each class. C
DESCRIPTIVE STATISTICS: THE FREQUENCY DISTRIBUTION TABLE FOR CATEGORICAL VARIABLE Example 3: Hospital Patients by Unit JL?%EFP' Unit Number of Patients (rounded) Cardiac Care 1,052 11.93 Emergency 2,245 25.46 Intensive Care 340 3.86 Maternity 552 6.26 Surgery 4,630 52.50 Total: 8,819 100.0 (Variables are Frequencies </ categorical)
A NOTE O Frequency is the number of observations in each category. O Relative frequency is obtained by dividing each frequency by the number of observations. O Percent is obtained from dividing each frequency by the number of observations and multiplying the resulting proportion by 100%.
DESCRIPTIVE STATISTICS: BAR CHART FOR CATEGORICAL VARIABLE - When we want to draw attention to the frequency of each category (in the frequency distribution table) in the categorical variable, we will use bar chart. * The height of a rectangle for a category is the frequency of each category or the number of observations in each category. - There is no need for the bars to touch each other. C
EXAMPLE 3 CTD. Bar chart for patient data ng@_'ltal Frequencies -pat|39$ of Cardiac Care 1,052 / Emergency 2,245 Hospital Patients by Unit Intensive Cane 340 5000 Maternity 552 c 4000 Surgery 4,630 s & 58 3000 % E2 28 2000 g 1000 0 1 Cardiac Care Emergency Intensive Care Maternity Surgery
DE FO oIf Y SCRIPTIVE STATISTICS: PIE CHARTS R CATEGORICAL VARIABLE the goal is drawing attention to the roportion of frequencies in each category of the frequency table, pie C oT hart is proper. he circle or pie represents the total. oT he pieces of pie display shares of the total, frequencies, or percentage for each category of the categorical variable. @
EXAMPLE 3 CTD. Pie chart for patient data c,#—Iospital Number % fl’otall"njt——o'f—ea'flej‘ts— Hospital Patients by Unit Cardiac Care 1,052 11.93 Cardiac Care Emergency 2,245 25.46 12% Intensive Care 340 3.86 Maternity 552 6.26 Critr ey A 2N =A% 1] ycl y =, UJVU Emergency Surgery 250% 53% <__Intensive Care (Percentages are ! 4% rounded to the Mat(irnlty nearest percent) 6%
DESCRIPTIVE STATISTICS: CROSS TABLES FOR CATEGORICAL VARIABLES © Cross Tables (or contingency tables) list the number of observations for every combination of values for two categorical variables ©1If there are r categories for the first variable (rows) and ¢ categories for the second variable (columns), the table is called an r x ¢ cross table. ©When you want to display two categorical variables together, you describe them by (‘\ cross tables and you picture them by w component bar charts.
EXAMPLE 4 © 3 x 3 Cross Table for Investment Choices by Investor (values in $1000’s) Investment| Investor A Investor|B Investor C Total Catannrvu A J ] Stocks 46 55 27 128 Borgis 32 44 19 Cegh 15 20 33 Total 93 119 79 291 -
EXAMPLE 4 CTD ©To display the cross table, we use the stacked or component bar chart 140 120 100 80 60 40 20 Investment Choices Investor A Investor B Investor C M Stocks i( | wsens M Cash
EXAMPLE 5 (Q 1.12 ON PAGE 14) The supervisor of a plant obtained a random sample of employee experience {in months) and times to com- plete a task (in minutes). Graph the data with a com- ponent bar chart. Less 5 Minutes to 10 Minutes to Experience/ Than Less Than Less Than Time 5Minutes 10 Minutes 15 Minutes Less than 10 13 25 3 months 3 < 6 months 10 13 12 6 << 9 months 9 22 8 9 < 12 months 5 18 19 gLy
ANSWER TO EXAMPLE 5 Number of Employees 60 50 40 30 20 10 Employee Performance 010 to <15 min m5to <10 min m<5min N N Less than 3 months 3 to 6 months 6 to 9 months Experience 9 to 12 months
At Home for extra practice: ORead example 1.2 on page 10 (Cross table and component bar chart). ORead example 1.3 on page 11 (Pie chart).
DESCRIPTIVE STATISTICS: PARETO DIAGRAM FOR CATEGORICAL VARIABLE ©Many managers who need to identify major causes of problems and attempt to correct them quickly with a minimum cost use a special bar chart known as Pareto diagram. ©The underlying idea is that in most cases a small number of factors (vital few) are responsible for most of the problems (trivial many). ©This graph is used to separate the “vital ('\ few” from the “trivial many” o
DESCRIPTIVE STATISTICS: PARETO DIAGRAM CTD. © Pareto diagram is used to portray categorical variables © Pareto diagram is a bar chart, where categories are shown in descending order of frequency
EXAMPLE 6 400 defective items are examined for cause of defect. Display the Pareto Diagram. Source of Manufacturing Error Number of defects Bad Weld 34 Poor Alignment 223 Missing Part 25 Paint Flaw 78 Electrical Short 19 Cracked case 21 Total 400
ANSWER TO EXAMPLE © Step 1: Sort by defect cause, in descending order _Ctoanrn D DNAataAarvnina 0/ in A~ ~atrAanArv Source of Manufacturing Error | Number of defects | % of Total Defects Poor Alignment 223 55.75 Paint Flaw 78 19.50 Bad Weld 34 8.50 Missing Part 25 6.25 Cracked case 21 5.25 Electrical Short 19 4.75 Total 400 100% @
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DESCRIPTIVE STATISTICS: GRAPHS TO DESCRIBE TIME-SERIES VARIABLES ©A line chart (time-series plot) is used to show the values of a variable over time O9Time is measured on the horizontal axis ©9The variable of interest is measured on the vertical axis Note: Time series data is a numerical data
: LINE CHART EXAMPLE 7 Number of Park Visitors by Year 350 300 250 200 150 SIOJISIA JO spuesnoyL 100 50 1 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996
REMINDER: CLASSIFICATION OF VARIABLES Data Categorical Numerical Discrete Continuous
REMINDER: TABLES AND GRAPHS FOR CATEGORICAL VARIABLES Categorical variables Tabulating Data Graphing Data -Frequency Distribution Table -Cross table -Bar Chart -Component Bar Chart Pie Chart Pareto Diagra m -
DESCRIPTIVE STATISTICS: GRAPHS TO DESCRIBE NUMERICAL VARIABLES Numerical Data Frequency Distributions and OB Y Ss Histogram Ogive Graph Graph
DESCRIPTIVE STATISTICS: FREQUENCY DISTRIBUTION TABLE FOR NUMERICAL VARIABLES ©Similar to categorical variables, we also have the frequency distribution table for numerical variables to organize data. ©This table contains class groupings (categories or ranges within which the data fall) and the corresponding frequencies (number of observations) with which data fall within each class or category. ©In contrast to the case of categorical variables, groups in the frequency distribution table for numerical variables are defined by numbers. w
DESCRIPTIVE STATISTICS: FREQUENCY DISTRIBUTION TABLE FOR NUMERICAL VARIABLE CTD. ©Therefore, we need to know: 1-How many classes or groups do we have? 2-How wide should each class be? ©We should also know that classes should have the same width. This makes comparison of groups easier. ©We should also know that classes should never overlap and must be inclusive. Wh)(?\ 4
DESCRIPTIVE STATISTICS: FREQUENCY DISTRIBUTION TABLE FOR NUMERICAL VARIABLE CTD ©No overlap because we do not want to count the same observation in two different groups. Inclusive because of including all information that we have. The above points imply that we need to know more information than the case of categorical variable to plot the frequency distribution table.
CLASS INTERVALS AND CLASS BOUNDARIES FOR FREQUENCY DISTRIBUTION TABLE OF NUMERICAL VARIABLES ©Each class grouping has the same width © Determine the width of each interval by largest number - smallest number number of desiredintervals w =interval width = " Use at least 5 but no more than 15-20 intervals * Intervals never overlap ® Round up the interval width to get desirable interval endpoints C\
EXAMPLE 8 A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature data: 24, 35,17, 21, 24, 37, 26, 46, 58, 30, 32,13,12, 38, 41, 43, 44, 27, 58, 27 Find the frequency distribution table for this variable. C\
ANSWER TO EXAMPLE 8 ©Sort raw data in ascending order: 12,13,17,21,24,24,26,27,27,30,3fi, 35, 37, 38, 41, 43, 44, 46, 53, 58 ©Find range: 58 - 12 = 46 ©Select number of classes: 5 (usually between 5 and 15) © Compute interval width: 10 (46/5 then round up) © Determine interval boundaries: 10 but less than 20, 20 but less than 30, ..., 50 but less than 60 (J' O Count observations & assian to classes
ANSWER TO EXAMPLE 8 CTD. Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Interval Frequency Ffei:zg\rlliy Percentage 10 but less than 20 3 15 15 20 but less than 30 6 .30 30 30 but less than 40 5 .25 25 40 but less than 50 4 .20 20 50 but less than 60 2 .10 10 Total 20 1.00 100
DESCRIPTIVE STATISTICS: HISTOGRAM FOR NUMERICAL VARIABLE © A histogram is a graph that consists of vertical bars constructed on a horizontal line that is marked off with intervals for the variable (in the frequency distribution table) being displayed. © The interval endpoints are shown on the horizontal axis © the vertical axis is either frequency, relative frequency, or percentage for each interval. © Histogram displays the distribution of the variable. O
EXAMPLE 8 CTD.: PLOT THE HISTOGRAM FOR THE MANUFACTURER OF INSULIN Interval 10 but less than 20 3 20 but less than 30 6 30 but less than 40 5 40 but less than 50 4 50 but less than 60 2 > o c o = o < w (No gaps between bars) Histogram: Daily High Tem perature 7 6 [&)] - N W b | o o 70 10 20 Degrees 30 40 50 60
QUESTIONS FOR GROUPING DATA INTO INTERVALS FOR FREQUENCY DISTIRBUTION ©1. How wide should each interval be? (How many classes should be used?) largest number - smallest number number of desired intervals w =interval width = © 2. How should the endpoints of the intervals be determined? ©0Often answered by trial and error, subject to user judgment °The goal is to create a distribution that is neither too "jagged" nor too "blocky” ©Goal is to appropriately show the pattern of variation in the data =
HOW MANY CLASS INTERVALS? © Many (Narrow class intervals) °may yield a very jagged distribution with gaps from empty classes 2, 5 15 ©Can give a poor indication * 05 0 +——————————— thOWfrequencyvanes TN eRIRNEIIINSSE across classes 12 © Few (Wide class intervals) °may compress variation . ~ too much and yield a : blocky distribution (X axis labels are upper clagsms | ©can obscure important endpoints)
SHAPE OF A DISTRIBUTION © Histogram helps us in deciding the shape of the data distribution. © We can visually determine whether data are evenly spread from its middle or center. © A distribution is said to be symmetric if the observations are balanced or evenly distributed around its center. © If you fold the histogram along a vertical line through the middle and have the edges match pretty close, you have a symmetric distribution. Frequency 9 8 7 6 5 4- 3 2 1 0
SHAPE OF A DISTRIBUTION CTD. ©The usually thinner ends of a distribution are called tails. © A distribution is skewed, or asymmetric, if the observations are not symmetrically distributed on either side of the center . O1f one tail stretches out farther than the other, the distribution is skewed to the side of the longer tail.
SHAPE OF A DISTRIBUTION CTD. © A skewed-right distribution (sometimes called positively skewed) has a tail that extends farther to the right. © A skewed-left distribution (sometimes called negatively skewed) has a tail that extends farther to the left. 24 0 ; : ‘ 5§ 6 7 8 9 R Skewed-left Distribution 1.2 3 4 5 6 7 8 9 Skewed-right Distribution
A REMINDER O Frequency is the number of observations in each category. O Relative frequency is obtained by dividing each frequency by the number of observations. O Percent is obtained from dividing each frequency by the number of observations and multiplying the resulting proportion by 100%.
THE CUMULATIVE FREQUENCY DISTRIBUTION © A cumulative frequency distribution contains the total number of observations whose values are less than the upper limit for each class in the frequency distribution table of numerical variables. or © Cumulative distribution is frequency distribution of each group plus the frequency distribution of previous group.
EXAMPLE o CID.: MANUFACTURER OF INSULIN 12,13, 17, 21, Data in ordered array: 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Class Frequency|Percentage ?:l:;ztl:::; g:m:rllatggg 10 but less than 20 3 15 3 15 20 but less than 30 6 30 9 45 30 but less than 40 5 25 14 70 40 but less than 50 4 20 18 90 50 but less than 60 2 10 20 100 Total 20 100
At Home for extra practice: ©Read example 1.9 on page 22 (frequency and cumulative frequency for numerical variables).
DESCRIPTIVE S ATISTICS: OGIVE GRAPH FOR NUMERICAL VARIABLES ©An ogive, sometimes called a cumulative line graph, is a line that connects points that are the cumulative percent of observations below the upper limit of each interval in @ cumulative frequency distribution.
EXAMPLE 8 CTD.: Plot the Ogive graph. NSULIN MANUFACTURER Upper Cumulative interval Interval endpoint Percentage (Less than 10 10 ] 10 butTess than 20 20 15 20 but less than 30 30 45 30 but less than 40 40 70 40 but less than 50 50 20 50 but less than 60 60 100 Class Frequency|Percentage (;l:::ll:::::; g::?g:::‘g’: Lessthan16 e 6 6 10 but less than 20 3 15 3 15 20 but less than 30 [ 30 9 45 30 but less than 40 5 25 14 70 40 but less than 50 4 20 18 90 50 but less than 60 2 10 20 100 Total 20 100 100 Ogive: Daily High Temperature (o] o D o Cumulative Percentage N o ‘LthperS?nter?/%l
EXAMPLE 9 Suppose we have the following data: 17 62 15 65 28 51 24 65 39 41 35 15 39 32 36 37 40 21 44 37 59 13 44 56 12 54 64 59 Construct a frequency distribution table. Construct a histogram.
So far ©we used bar chart, pie chart, and Pareto diagram to describe a single categorical variable. ©we used component bar chart to describe two categorical variables. ©we used histograms and ogives to describe a single numerical variable. Now we use scatter plot to describe two numerical variables.
Descriptive statistics: Scatter Diagrams or Plots for numerical variables © Scatter Diagrams are used for paired observations taken from two numerical variables ©The Scatter Diagram: ® one variable is measured on the vertical axis and the other variable is measured on the horizontal axis
EXAMPLE 12: PLOT THE SCATTER DIAGRAM FOR THE TABLE. Average SAT scores by state: 1998 Verbal Alabama 562 Alaska 521 Arizona 525 Arkansas 568 California 497 Colorado 581 Connecticut 510 Delaware 501 D.C. 488 Florida 500 Georgia 486 Hawaii 483 W.Va. 525 Wis. 581 Wyo. 548 Math 558 520 528 555 516 542 509 493 476 501 482 513 13 594 546 SAT Math Score g g S g Average SAT Math vs. Verbal Scores by State » 9% é’*’ MR < 4 o 450 500 550 600 650 SAT Verbal Score
LECTURE SUMMARY FOR STUDENTS ©Introduced key definitions: ® Population vs. Sample ® Parameter vs. Statistic ¢ Descriptive vs. Inferential statistics ©Described random sampling ©Examined the decision making process @
STUDENTS © Reviewed types of data and measurement evels © Data in raw form are usually not easy to use for decision making -- Some type of organization is needed: + Table + Graph © Techniques reviewed in this ghaRterart ® Cross tables distribution ¢ Bar chart = Histogram and ® Pie chart ogive ¢ Pareto diagram " Scatter plot C