Mini-Lecture 3.1 Measures of Central Tendency
|
|
- Johnathan Farmer
- 6 years ago
- Views:
Transcription
1 Mini-Lecture 3.1 Measures of Central Tendency Objectives 1. Determine the arithmetic mean of a variable from raw data 2. Determine the median of a variable from raw data 3. Explain what it means for a statistic to be resistant 4. Determine the mode of a variable from raw data Examples 1. Every six months, the United States Federal Reserve Board conducts a survey of credit card plans in the U.S. The following data are the interest rates charged by 10 credit card issuers randomly selected for the January 2008 survey. (Source: Institution Rate Pulaski Bank and Trust Company 6.5% Rainier Pacific Savings Bank 12.0% Wells Fargo Bank NA 14.4% Firstbank of Colorado 14.4% Lafayette Ambassador Bank 14.3% Infibank 13.0% United Bank, Inc. 13.3% First National Bank of The Mid-Cities 13.9% Bank of Louisiana 9.9% Bar Harbor Bank and Trust Company 14.5% a. Compute the mean, median, and mode of this sample of interest rates. (12.62%, 13.6%, 14.4%) b. Create a histogram of this data using a class width of 1% (See section 2.2.)
2 c. What proportion of the interest rates is less than the mean? (0.3) d. What proportion of the interest rates is less than the median? (0.5) e. Which statistic is least influenced by extreme observations, the mean or the median? (Median)
3 2. A group of Brigham Young University Idaho students (Matthew Herring, Nathan Spencer, Mark Walker, and Mark Steiner) collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted (construction) speed limit was 25 mph. The recorded speeds for 14 randomly selected vehicles are given below: 20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40 a. Compute the mean, median, and mode of the observed speeds. (32.1; 32.5; 40) b. Make a histogram of this data using a class width of 5 mph.
4 Mini-Lecture 3.2 Measures of Dispersion Objectives 1. Compute the range of a variable from raw data 2. Compute the variance of a variable from raw data 3. Compute the standard deviation of a variable from raw data 4. Use the Empirical Rule to describe data that are bell shaped 5. Use Chebyshev s inequality to describe any set of data Examples 1. Every six months, the United States Federal Reserve Board conducts a survey of credit card plans in the U.S. The following data are the interest rates charged by 10 credit card issuers randomly selected for the January 2008 survey. (Source: Institution Rate Pulaski Bank and Trust Company 6.5% Rainier Pacific Savings Bank 12.0% Wells Fargo Bank NA 14.4% Firstbank of Colorado 14.4% Lafayette Ambassador Bank 14.3% Infibank 13.0% United Bank, Inc. 13.3% First National Bank of The Mid-Cities 13.9% Bank of Louisiana 9.9% Bar Harbor Bank and Trust Company 14.5% a. Compute the range, sample variance, and sample standard deviation for the interest rates. Express your answers rounded to the nearest tenth of a percent. (Range = 8.0%, s 2 = 6.7, s = 2.6%) b. On the basis of the histogram drawn in Section 3.1, comment on the appropriateness of using the Empirical Rule to make any general statements about interest rates. (The data do not appear to follow a symmetric or bell-shaped distribution. They appear to be skewed left, so it is not appropriate to use the Empirical Rule to make any general statements about interest rates in the U.S.) c. Does the interest rate for Pulaski Bank and Trust Company appear to be unusual? (Yes)
5 2. A group of Brigham Young University Idaho students (Matthew Herring, Nathan Spencer, Mark Walker, and Mark Steiner) collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted (construction) speed limit was 25 mph. The recorded speeds for 14 randomly selected vehicles are given below: 20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40 a. Determine the sample standard deviation of the speeds. Express your answer rounded to the nearest mile per hour. (s = 6 mph) b. On the basis of the histogram drawn in Section 3.1, comment on the appropriateness of using the Empirical Rule to make any general statements about drivers speeds. (The data appear to roughly follow a symmetric, bell-shaped distribution. It is appropriate to apply the Empirical Rule.) c. Use the Empirical Rule to estimate the percentage of speeds that are between 26 and 38 mph. (Hint: the sample mean is approximately 32 mph.) (68%) d. Determine the actual percentage of drivers whose speeds were between 26 and 38 mph. (64%) e. Use the Empirical Rule to determine the percentage of drivers whose speeds are 26 mph or higher, so they exceed the posted speed limit. (84%) f. Determine the actual percentage of drivers whose speeds are 26 mph or higher, so they exceed the posted speed limit. (86%)
6 Mini-Lecture 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 variance and standard deviation of a variable from grouped data Examples 1. The National Survey of Student Engagement is a survey that (among other things) asked first year students at liberal arts colleges how much time they spend preparing for class each week. The results from the 2007 survey are summarized below. (Source: NSSE_2007_Annual_Report.pdf ) Hours Percentage 13% 25% 23% 18% 10% 6% 5% a. Approximate the mean and standard deviation for the number of hours students spend preparing for class each week. (14.75 hours; 8.1 hours) b. Draw a relative frequency histogram of the data. What is the shape of the distribution? (Right-skewed) Relative Frequency Hours Spent Studying
7 c. Can the Empirical Rule be used with this data? (No, the data are not symmetric) 2. A simple random sample of 89 two-year old Toyota Prius cars that are listed for sale was collected from The advertised prices of the cars are summarized in the table below. Price 15,000-17,500-20,000-22,500-25,000-27,500-30,000-32,500- (in dollars) 17,499 19,999 22,499 24,999 27,499 29,999 32,499 34,999 Frequency a. Find the approximate mean and standard deviation for the advertised prices of the cars. ($25,575.84; $2,711.61) b. Draw a relative frequency histogram of the data. What is the shape of the distribution? (Left skewed, although one could argue the data are symmetric) c. Can the Empirical Rule be used with this data? (No, if the data are deemed to be left skewed; if deemed symmetric, it is appropriate to use the empirical rule)
8 Mini-Lecture 3.4 Measures of Position Objectives 1. Determine and interpret z-scores 2. Interpret percentiles 3. Determine and interpret quartiles 4. Determine and interpret the interquartile range 5. Check a set of data for outliers Examples 1. The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. The University of Pittsburgh Graduate School of Public Health requires a GRE score no less than the 70 th percentile for admission into their Human Genetics MPH or MS program. (Source: Interpret this admissions requirement. (In order to be admitted to this program, an applicant must score as high or higher than 70% of the people who take the GRE.) 2. Every six months, the United States Federal Reserve Board conducts a survey of credit card plans in the U.S. The following data are the interest rates charged by 10 credit card issuers randomly selected for the January 2008 survey. The population mean credit card interest rate in January 2008 was 13.5%, and the population standard deviation was 3.2%. (Source: Institution Rate Pulaski Bank and Trust Company 6.5% Rainier Pacific Savings Bank 12.0% Wells Fargo Bank NA 14.4% Firstbank of Colorado 14.4% Lafayette Ambassador Bank 14.3% Infibank 13.0% United Bank, Inc. 13.3% First National Bank of The Mid-Cities 13.9% Bank of Louisiana 9.9% Bar Harbor Bank and Trust Company 14.5% a. Use the population mean and standard deviation to find the z-score corresponding to 6.5%, the rate offered by the Pulaski Bank and Trust Company. (z = 2.19)
9 b. Use the population mean and standard deviation to find the z-score corresponding to 14.5%, the rate offered by the Bar Harbor Bank and Trust Company. (z = 0.31) c. Find the first quartile of the interest rates. (12.0%) d. Find the interquartile range of the interest rates. (2.4%) 3. A group of Brigham Young University Idaho students (Matthew Herring, Nathan Spencer, Mark Walker, and Mark Steiner) collected data in November 2005 on the speed of vehicles traveling through a construction zone on a state highway, where the posted speed was 25 mph. The recorded speed of 14 randomly selected vehicles is given below: 20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40. The sample mean and standard deviation for these vehicle speeds are 32.1 and 6.2, respectively. a. Find the z-score for a car driving 20 mph in this construction zone. ( 1.95) b. Find the z-score for a car driving 40 mph in this construction zone. (1.27) c. Determine the quartiles. (Q1 = 28 mph; Q2 = 32.5 mph; Q3 = 38 mph) d. Compute the interquartile range, IQR. (IQR = 10) e. Determine the lower and upper fences. Are there any outliers, according to this criterion? (Lower fence = 13 mph, Upper fence = 53 mph; there are no outliers according to this criterion)
10 Mini-Lecture 3.5 The Five-Number Summary and Boxplots Objectives 1. Compute the five-number summary 2. Draw and interpret boxplots Examples 1. Every six months, the United States Federal Reserve Board conducts a survey of credit card plans in the U.S. The following data are the interest rates charged by 10 credit card issuers randomly selected for the January 2008 survey. Based on this survey, the mean credit card interest rate in January 2008 was 13.5%, and the standard deviation of the national interest rates was 3.3% (Source: Institution Rate Pulaski Bank and Trust Company 6.5% Rainier Pacific Savings Bank 12.0% Wells Fargo Bank NA 14.4% Firstbank of Colorado 14.4% Lafayette Ambassador Bank 14.3% Infibank 13.0% United Bank, Inc. 13.3% First National Bank of The Mid-Cities 13.9% Bank of Louisiana 9.9% Bar Harbor Bank and Trust Company 14.5% a. Find the five-number summary for the observed credit card rates. (Min = 6.5%; Q1 = 12.0%; Median = 13.6%; Q3 = 14.4%; Max = 14.5%) b. Draw a boxplot for the observed credit card rates. c. Determine the shape of the distribution from the boxplot. Refer to the histogram drawn in Section 2.2 to test your answer. (Left-skewed) 2. A group of Brigham Young University Idaho students (Matthew Herring, Nathan Spencer, Mark Walker, and Mark Steiner) collected data in November
11 2005 on the speed of vehicles traveling through a construction zone on a state highway, where the posted speed was 25 mph. The recorded speed of 14 randomly selected vehicles is given below: 20, 24, 27, 28, 29, 30, 32, 33, 34, 36, 38, 39, 40, 40 a. Find the five-number summary for the observed speeds. (20, 27.5, 32, 38.5, 40) b. Construct a boxplot for the observed speeds. c. Determine the shape of the distribution from the boxplot. Refer to the histogram drawn in Section 2.2 to test your answer. (Symmetric or leftskewed)
Mini-Lecture 7.1 Properties of the Normal Distribution
Mini-Lecture 7.1 Properties of the Normal Distribution Objectives 1. Understand the uniform probability distribution 2. Graph a normal curve 3. State the properties of the normal curve 4. Understand the
More informationSection3-2: Measures of Center
Chapter 3 Section3-: Measures of Center Notation Suppose we are making a series of observations, n of them, to be exact. Then we write x 1, x, x 3,K, x n as the values we observe. Thus n is the total number
More informationChapter 2: Descriptive Statistics. Mean (Arithmetic Mean): Found by adding the data values and dividing the total by the number of data.
-3: Measure of Central Tendency Chapter : Descriptive Statistics The value at the center or middle of a data set. It is a tool for analyzing data. Part 1: Basic concepts of Measures of Center Ex. Data
More information1 Describing Distributions with numbers
1 Describing Distributions with numbers Only for quantitative variables!! 1.1 Describing the center of a data set The mean of a set of numerical observation is the familiar arithmetic average. To write
More informationChapter 3. Descriptive Measures. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 3, Slide 1
Chapter 3 Descriptive Measures Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 3, Slide 1 Chapter 3 Descriptive Measures Mean, Median and Mode Copyright 2016, 2012, 2008 Pearson Education, Inc.
More informationCHAPTER 2 Describing Data: Numerical
CHAPTER Multiple-Choice Questions 1. A scatter plot can illustrate all of the following except: A) the median of each of the two variables B) the range of each of the two variables C) an indication of
More informationNumerical Descriptions of Data
Numerical Descriptions of Data Measures of Center Mean x = x i n Excel: = average ( ) Weighted mean x = (x i w i ) w i x = data values x i = i th data value w i = weight of the i th data value Median =
More informationMeasures of Center. Mean. 1. Mean 2. Median 3. Mode 4. Midrange (rarely used) Measure of Center. Notation. Mean
Measure of Center Measures of Center The value at the center or middle of a data set 1. Mean 2. Median 3. Mode 4. Midrange (rarely used) 1 2 Mean Notation The measure of center obtained by adding the values
More informationappstats5.notebook September 07, 2016 Chapter 5
Chapter 5 Describing Distributions Numerically Chapter 5 Objective: Students will be able to use statistics appropriate to the shape of the data distribution to compare of two or more different data sets.
More informationChapter 3. Numerical Descriptive Measures. Copyright 2016 Pearson Education, Ltd. Chapter 3, Slide 1
Chapter 3 Numerical Descriptive Measures Copyright 2016 Pearson Education, Ltd. Chapter 3, Slide 1 Objectives In this chapter, you learn to: Describe the properties of central tendency, variation, and
More informationNOTES TO CONSIDER BEFORE ATTEMPTING EX 2C BOX PLOTS
NOTES TO CONSIDER BEFORE ATTEMPTING EX 2C BOX PLOTS A box plot is a pictorial representation of the data and can be used to get a good idea and a clear picture about the distribution of the data. It shows
More informationDescriptive Statistics
Petra Petrovics Descriptive Statistics 2 nd seminar DESCRIPTIVE STATISTICS Definition: Descriptive statistics is concerned only with collecting and describing data Methods: - statistical tables and graphs
More informationSome estimates of the height of the podium
Some estimates of the height of the podium 24 36 40 40 40 41 42 44 46 48 50 53 65 98 1 5 number summary Inter quartile range (IQR) range = max min 2 1.5 IQR outlier rule 3 make a boxplot 24 36 40 40 40
More informationDescribing Data: One Quantitative Variable
STAT 250 Dr. Kari Lock Morgan The Big Picture Describing Data: One Quantitative Variable Population Sampling SECTIONS 2.2, 2.3 One quantitative variable (2.2, 2.3) Statistical Inference Sample Descriptive
More informationPercentiles, STATA, Box Plots, Standardizing, and Other Transformations
Percentiles, STATA, Box Plots, Standardizing, and Other Transformations Lecture 3 Reading: Sections 5.7 54 Remember, when you finish a chapter make sure not to miss the last couple of boxes: What Can Go
More informationSource: Fall 2015 Biostats 540 Exam I. BIOSTATS 540 Fall 2016 Practice Test for Unit 1 Summarizing Data Page 1 of 6
BIOSTATS 540 Fall 2016 Practice Test for Unit 1 Summarizing Data Page 1 of 6 Source: Fall 2015 Biostats 540 Exam I. 1. 1a. The U.S. Census Bureau reports the median family income in its summary of census
More informationPutting Things Together Part 1
Putting Things Together Part 1 These exercise blend ideas from various graphs (histograms and boxplots), differing shapes of distributions, and values summarizing the data. Data for 1, 5, and 6 are in
More information3.1 Measures of Central Tendency
3.1 Measures of Central Tendency n Summation Notation x i or x Sum observation on the variable that appears to the right of the summation symbol. Example 1 Suppose the variable x i is used to represent
More informationPutting Things Together Part 2
Frequency Putting Things Together Part These exercise blend ideas from various graphs (histograms and boxplots), differing shapes of distributions, and values summarizing the data. Data for, and are in
More informationApplications of Data Dispersions
1 Applications of Data Dispersions Key Definitions Standard Deviation: The standard deviation shows how far away each value is from the mean on average. Z-Scores: The distance between the mean and a given
More information2 Exploring Univariate Data
2 Exploring Univariate Data A good picture is worth more than a thousand words! Having the data collected we examine them to get a feel for they main messages and any surprising features, before attempting
More informationHandout 4 numerical descriptive measures part 2. Example 1. Variance and Standard Deviation for Grouped Data. mf N 535 = = 25
Handout 4 numerical descriptive measures part Calculating Mean for Grouped Data mf Mean for population data: µ mf Mean for sample data: x n where m is the midpoint and f is the frequency of a class. Example
More informationSTAT 113 Variability
STAT 113 Variability Colin Reimer Dawson Oberlin College September 14, 2017 1 / 48 Outline Last Time: Shape and Center Variability Boxplots and the IQR Variance and Standard Deviaton Transformations 2
More informationTest Bank Elementary Statistics 2nd Edition William Navidi
Test Bank Elementary Statistics 2nd Edition William Navidi Completed downloadable package TEST BANK for Elementary Statistics 2nd Edition by William Navidi, Barry Monk: https://testbankreal.com/download/elementary-statistics-2nd-edition-test-banknavidi-monk/
More informationLecture Week 4 Inspecting Data: Distributions
Lecture Week 4 Inspecting Data: Distributions Introduction to Research Methods & Statistics 2013 2014 Hemmo Smit So next week No lecture & workgroups But Practice Test on-line (BB) Enter data for your
More information3) Marital status of each member of a randomly selected group of adults is an example of what type of variable?
MATH112 STATISTICS; REVIEW1 CH1,2,&3 Name CH1 Vocabulary 1) A statistics student wants to find some information about all college students who ride a bike. She collected data from other students in her
More informationLecture 1: Review and Exploratory Data Analysis (EDA)
Lecture 1: Review and Exploratory Data Analysis (EDA) Ani Manichaikul amanicha@jhsph.edu 16 April 2007 1 / 40 Course Information I Office hours For questions and help When? I ll announce this tomorrow
More informationDescription of Data I
Description of Data I (Summary and Variability measures) Objectives: Able to understand how to summarize the data Able to understand how to measure the variability of the data Able to use and interpret
More informationEmpirical Rule (P148)
Interpreting the Standard Deviation Numerical Descriptive Measures for Quantitative data III Dr. Tom Ilvento FREC 408 We can use the standard deviation to express the proportion of cases that might fall
More informationNOTES: Chapter 4 Describing Data
NOTES: Chapter 4 Describing Data Intro to Statistics COLYER Spring 2017 Student Name: Page 2 Section 4.1 ~ What is Average? Objective: In this section you will understand the difference between the three
More informationStandardized Data Percentiles, Quartiles and Box Plots Grouped Data Skewness and Kurtosis
Descriptive Statistics (Part 2) 4 Chapter Percentiles, Quartiles and Box Plots Grouped Data Skewness and Kurtosis McGraw-Hill/Irwin Copyright 2009 by The McGraw-Hill Companies, Inc. Chebyshev s Theorem
More informationMath 2311 Bekki George Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment
Math 2311 Bekki George bekki@math.uh.edu Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment Class webpage: http://www.math.uh.edu/~bekki/math2311.html Math 2311 Class
More informationData that can be any numerical value are called continuous. These are usually things that are measured, such as height, length, time, speed, etc.
Chapter 8 Measures of Center Data that can be any numerical value are called continuous. These are usually things that are measured, such as height, length, time, speed, etc. Data that can only be integer
More informationEdexcel past paper questions
Edexcel past paper questions Statistics 1 Chapters 2-4 (Continuous) S1 Chapters 2-4 Page 1 S1 Chapters 2-4 Page 2 S1 Chapters 2-4 Page 3 S1 Chapters 2-4 Page 4 Histograms When you are asked to draw a histogram
More informationSOLUTIONS TO THE LAB 1 ASSIGNMENT
SOLUTIONS TO THE LAB 1 ASSIGNMENT Question 1 Excel produces the following histogram of pull strengths for the 100 resistors: 2 20 Histogram of Pull Strengths (lb) Frequency 1 10 0 9 61 63 6 67 69 71 73
More informationKING FAHD UNIVERSITY OF PETROLEUM & MINERALS DEPARTMENT OF MATHEMATICAL SCIENCES DHAHRAN, SAUDI ARABIA. Name: ID# Section
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DEPARTMENT OF MATHEMATICAL SCIENCES DHAHRAN, SAUDI ARABIA STAT 11: BUSINESS STATISTICS I Semester 04 Major Exam #1 Sunday March 7, 005 Please circle your instructor
More information4. DESCRIPTIVE STATISTICS
4. DESCRIPTIVE STATISTICS Descriptive Statistics is a body of techniques for summarizing and presenting the essential information in a data set. Eg: Here are daily high temperatures for Jan 16, 2009 in
More informationSimple Descriptive Statistics
Simple Descriptive Statistics These are ways to summarize a data set quickly and accurately The most common way of describing a variable distribution is in terms of two of its properties: Central tendency
More informationLecture 2 Describing Data
Lecture 2 Describing Data Thais Paiva STA 111 - Summer 2013 Term II July 2, 2013 Lecture Plan 1 Types of data 2 Describing the data with plots 3 Summary statistics for central tendency and spread 4 Histograms
More informationMath146 - Chapter 3 Handouts. The Greek Alphabet. Source: Page 1 of 39
Source: www.mathwords.com The Greek Alphabet Page 1 of 39 Some Miscellaneous Tips on Calculations Examples: Round to the nearest thousandth 0.92431 0.75693 CAUTION! Do not truncate numbers! Example: 1
More informationOverview/Outline. Moving beyond raw data. PSY 464 Advanced Experimental Design. Describing and Exploring Data The Normal Distribution
PSY 464 Advanced Experimental Design Describing and Exploring Data The Normal Distribution 1 Overview/Outline Questions-problems? Exploring/Describing data Organizing/summarizing data Graphical presentations
More informationFINALS REVIEW BELL RINGER. Simplify the following expressions without using your calculator. 1) 6 2/3 + 1/2 2) 2 * 3(1/2 3/5) 3) 5/ /2 4
FINALS REVIEW BELL RINGER Simplify the following expressions without using your calculator. 1) 6 2/3 + 1/2 2) 2 * 3(1/2 3/5) 3) 5/3 + 7 + 1/2 4 4) 3 + 4 ( 7) + 3 + 4 ( 2) 1) 36/6 4/6 + 3/6 32/6 + 3/6 35/6
More information1) What is the range of the data shown in the box and whisker plot? 2) True or False: 75% of the data falls between 6 and 12.
DO NOW 1) What is the range of the data shown in the box and whisker plot? 2) True or False: 75% of the data falls between 6 and 12. May 21 7:19 AM 1. 3 2. 2 3. 1 4. 4 5. 2 6. Min = 17, Q 1 = 18.5, Med
More informationDATA SUMMARIZATION AND VISUALIZATION
APPENDIX DATA SUMMARIZATION AND VISUALIZATION PART 1 SUMMARIZATION 1: BUILDING BLOCKS OF DATA ANALYSIS 294 PART 2 PART 3 PART 4 VISUALIZATION: GRAPHS AND TABLES FOR SUMMARIZING AND ORGANIZING DATA 296
More informationUNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences. STAB22H3 Statistics I Duration: 1 hour and 45 minutes
UNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences STAB22H3 Statistics I Duration: 1 hour and 45 minutes Last Name: First Name: Student number: Aids allowed: - One handwritten
More information(a) salary of a bank executive (measured in dollars) quantitative. (c) SAT scores of students at Millersville University quantitative
Millersville University Name Answer Key Department of Mathematics MATH 130, Elements of Statistics I, Test 1 February 8, 2010, 10:00AM-10:50AM Please answer the following questions. Your answers will be
More informationMath Take Home Quiz on Chapter 2
Math 116 - Take Home Quiz on Chapter 2 Show the calculations that lead to the answer. Due date: Tuesday June 6th Name Time your class meets Provide an appropriate response. 1) A newspaper surveyed its
More informationMeasures of Central Tendency Lecture 5 22 February 2006 R. Ryznar
Measures of Central Tendency 11.220 Lecture 5 22 February 2006 R. Ryznar Today s Content Wrap-up from yesterday Frequency Distributions The Mean, Median and Mode Levels of Measurement and Measures of Central
More informationBoth the quizzes and exams are closed book. However, For quizzes: Formulas will be provided with quiz papers if there is any need.
Both the quizzes and exams are closed book. However, For quizzes: Formulas will be provided with quiz papers if there is any need. For exams (MD1, MD2, and Final): You may bring one 8.5 by 11 sheet of
More informationTutorial Handout Statistics, CM-0128M Descriptive Statistics
Tutorial Handout Statistics, CM-0128M January 18, 2013 Exercise 1. The following figures show the annual salaries in of 20 workers in a small firm. Calculate the arithmetic mean, median and mode salaries.
More informationChapter 3 Descriptive Statistics: Numerical Measures Part A
Slides Prepared by JOHN S. LOUCKS St. Edward s University Slide 1 Chapter 3 Descriptive Statistics: Numerical Measures Part A Measures of Location Measures of Variability Slide Measures of Location Mean
More informationCenter and Spread. Measures of Center and Spread. Example: Mean. Mean: the balance point 2/22/2009. Describing Distributions with Numbers.
Chapter 3 Section3-: Measures of Center Section 3-3: Measurers of Variation Section 3-4: Measures of Relative Standing Section 3-5: Exploratory Data Analysis Describing Distributions with Numbers The overall
More informationNumerical Measurements
El-Shorouk Academy Acad. Year : 2013 / 2014 Higher Institute for Computer & Information Technology Term : Second Year : Second Department of Computer Science Statistics & Probabilities Section # 3 umerical
More informationReview: Chebyshev s Rule. Measures of Dispersion II. Review: Empirical Rule. Review: Empirical Rule. Auto Batteries Example, p 59.
Review: Chebyshev s Rule Measures of Dispersion II Tom Ilvento STAT 200 Is based on a mathematical theorem for any data At least ¾ of the measurements will fall within ± 2 standard deviations from the
More informationFrequency Distribution and Summary Statistics
Frequency Distribution and Summary Statistics Dongmei Li Department of Public Health Sciences Office of Public Health Studies University of Hawai i at Mānoa Outline 1. Stemplot 2. Frequency table 3. Summary
More informationStat 101 Exam 1 - Embers Important Formulas and Concepts 1
1 Chapter 1 1.1 Definitions Stat 101 Exam 1 - Embers Important Formulas and Concepts 1 1. Data Any collection of numbers, characters, images, or other items that provide information about something. 2.
More information22.2 Shape, Center, and Spread
Name Class Date 22.2 Shape, Center, and Spread Essential Question: Which measures of center and spread are appropriate for a normal distribution, and which are appropriate for a skewed distribution? Eplore
More informationDays Traveling Frequency Relative Frequency Percent Frequency % % 35 and above 1 Total %
Math 1351 Activity 1(Chapter 10)(Due by end of class Feb. 15) Group # 1. A business magazine was conducting a study into the amount of travel required for managers across the U.S. Seventy-five managers
More informationWeek 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics.
Week 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics. Convergent validity: the degree to which results/evidence from different tests/sources, converge on the same conclusion.
More informationMgtOp 215 TEST 1 (Golden) Spring 2016 Dr. Ahn. Read the following instructions very carefully before you start the test.
MgtOp 15 TEST 1 (Golden) Spring 016 Dr. Ahn Name: ID: Section (Circle one): 4, 5, 6 Read the following instructions very carefully before you start the test. This test is closed book and notes; one summary
More informationSTATISTICAL DISTRIBUTIONS AND THE CALCULATOR
STATISTICAL DISTRIBUTIONS AND THE CALCULATOR 1. Basic data sets a. Measures of Center - Mean ( ): average of all values. Characteristic: non-resistant is affected by skew and outliers. - Median: Either
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name The bar graph shows the number of tickets sold each week by the garden club for their annual flower show. ) During which week was the most number of tickets sold? ) A) Week B) Week C) Week 5
More informationMAT 1371 Midterm. This is a closed book examination. However one sheet is permitted. Only non-programmable and non-graphic calculators are permitted.
MAT 1371 Midterm Duration: 80 minutes Professor G. Lamothe Student Number: Last Name: First Name: This is a closed book examination. However one sheet is permitted. Only non-programmable and non-graphic
More informationPSYCHOLOGICAL STATISTICS
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B Sc COUNSELLING PSYCHOLOGY (2011 Admission Onwards) II Semester Complementary Course PSYCHOLOGICAL STATISTICS QUESTION BANK 1. The process of grouping
More informationA LEVEL MATHEMATICS ANSWERS AND MARKSCHEMES SUMMARY STATISTICS AND DIAGRAMS. 1. a) 45 B1 [1] b) 7 th value 37 M1 A1 [2]
1. a) 45 [1] b) 7 th value 37 [] n c) LQ : 4 = 3.5 4 th value so LQ = 5 3 n UQ : 4 = 9.75 10 th value so UQ = 45 IQR = 0 f.t. d) Median is closer to upper quartile Hence negative skew [] Page 1 . a) Orders
More informationThe Range, the Inter Quartile Range (or IQR), and the Standard Deviation (which we usually denote by a lower case s).
We will look the three common and useful measures of spread. The Range, the Inter Quartile Range (or IQR), and the Standard Deviation (which we usually denote by a lower case s). 1 Ameasure of the center
More informationThe Central Limit Theorem: Homework
The Central Limit Theorem: Homework EXERCISE 1 X N(60, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let X be the random variable of sums.
More information( ) P = = =
1. On a lunch counter, there are 5 oranges and 6 apples. If 3 pieces of fruit are selected, find the probability that 1 orange and apples are selected. Order does not matter Combinations: 5C1 (1 ) 6C P
More informationMath 140 Introductory Statistics. First midterm September
Math 140 Introductory Statistics First midterm September 23 2010 Box Plots Graphical display of 5 number summary Q1, Q2 (median), Q3, max, min Outliers If a value is more than 1.5 times the IQR from the
More informationStat 201: Business Statistics I Additional Exercises on Chapter Chapter 3
Stat 201: Business Statistics I Additional Exercises on Chapter Chapter 3 Student Name: Solve the problem. 1) A sociologist recently conducted a survey of senior citizens who have net worths too high to
More informationName PID Section # (enrolled)
STT 315 - Lecture 3 Instructor: Aylin ALIN 02/19/2014 Midterm # 1 A Name PID Section # (enrolled) * The exam is closed book and 80 minutes. * You may use a calculator and the formula sheet that you brought
More information2 DESCRIPTIVE STATISTICS
Chapter 2 Descriptive Statistics 47 2 DESCRIPTIVE STATISTICS Figure 2.1 When you have large amounts of data, you will need to organize it in a way that makes sense. These ballots from an election are rolled
More informationThe Central Limit Theorem: Homework
The Central Limit Theorem: Homework EXERCISE 1 X N(60, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let X be the random variable of sums.
More information1 Exercise One. 1.1 Calculate the mean ROI. Note that the data is not grouped! Below you find the raw data in tabular form:
1 Exercise One Note that the data is not grouped! 1.1 Calculate the mean ROI Below you find the raw data in tabular form: Obs Data 1 18.5 2 18.6 3 17.4 4 12.2 5 19.7 6 5.6 7 7.7 8 9.8 9 19.9 10 9.9 11
More informationDescriptive Statistics
Chapter 3 Descriptive Statistics Chapter 2 presented graphical techniques for organizing and displaying data. Even though such graphical techniques allow the researcher to make some general observations
More informationSTA 248 H1S Winter 2008 Assignment 1 Solutions
1. (a) Measures of location: STA 248 H1S Winter 2008 Assignment 1 Solutions i. The mean, 100 1=1 x i/100, can be made arbitrarily large if one of the x i are made arbitrarily large since the sample size
More informationSOLUTIONS: DESCRIPTIVE STATISTICS
SOLUTIONS: DESCRIPTIVE STATISTICS Please note that the data is ordered from lowest value to highest value. This is necessary if you wish to compute the medians and quartiles by hand. You do not have to
More informationIntroduction to Computational Finance and Financial Econometrics Descriptive Statistics
You can t see this text! Introduction to Computational Finance and Financial Econometrics Descriptive Statistics Eric Zivot Summer 2015 Eric Zivot (Copyright 2015) Descriptive Statistics 1 / 28 Outline
More informationUnit 2 Statistics of One Variable
Unit 2 Statistics of One Variable Day 6 Summarizing Quantitative Data Summarizing Quantitative Data We have discussed how to display quantitative data in a histogram It is useful to be able to describe
More informationChapter 3: Displaying and Describing Quantitative Data Quiz A Name
Chapter 3: Displaying and Describing Quantitative Data Quiz A Name 3.1.1 Find summary statistics; create displays; describe distributions; determine 1. Following is a histogram of salaries (in $) for a
More informationDATA ANALYSIS EXAM QUESTIONS
DATA ANALYSIS EXAM QUESTIONS Question 1 (**) The number of phone text messages send by 11 different students is given below. 14, 25, 31, 36, 37, 41, 51, 52, 55, 79, 112. a) Find the lower quartile, the
More information1.2 Describing Distributions with Numbers, Continued
1.2 Describing Distributions with Numbers, Continued Ulrich Hoensch Thursday, September 6, 2012 Interquartile Range and 1.5 IQR Rule for Outliers The interquartile range IQR is the distance between the
More information9/17/2015. Basic Statistics for the Healthcare Professional. Relax.it won t be that bad! Purpose of Statistic. Objectives
Basic Statistics for the Healthcare Professional 1 F R A N K C O H E N, M B B, M P A D I R E C T O R O F A N A L Y T I C S D O C T O R S M A N A G E M E N T, LLC Purpose of Statistic 2 Provide a numerical
More informationEdexcel past paper questions
Edexcel past paper questions Statistics 1 Chapters 2-4 (Discrete) Statistics 1 Chapters 2-4 (Discrete) Page 1 Stem and leaf diagram Stem-and-leaf diagrams are used to represent data in its original form.
More informationSection 6-1 : Numerical Summaries
MAT 2377 (Winter 2012) Section 6-1 : Numerical Summaries With a random experiment comes data. In these notes, we learn techniques to describe the data. Data : We will denote the n observations of the random
More informationMonte Carlo Simulation (Random Number Generation)
Monte Carlo Simulation (Random Number Generation) Revised: 10/11/2017 Summary... 1 Data Input... 1 Analysis Options... 6 Summary Statistics... 6 Box-and-Whisker Plots... 7 Percentiles... 9 Quantile Plots...
More informationThe Central Limit Theorem: Homework
EERCISE 1 The Central Limit Theorem: Homework N(60, 9). Suppose that you form random samples of 25 from this distribution. Let be the random variable of averages. Let be the random variable of sums. For
More informationMATH FOR LIBERAL ARTS REVIEW 2
MATH FOR LIBERAL ARTS REVIEW 2 Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 1) A die is rolled. The set of equally likely
More informationMisleading Graphs. Examples Compare unlike quantities Truncate the y-axis Improper scaling Chart Junk Impossible to interpret
Misleading Graphs Examples Compare unlike quantities Truncate the y-axis Improper scaling Chart Junk Impossible to interpret 1 Pretty Bleak Picture Reported AIDS cases 2 But Wait..! 3 Turk Incorporated
More informationChapter 15: Sampling distributions
=true true Chapter 15: Sampling distributions Objective (1) Get "big picture" view on drawing inferences from statistical studies. (2) Understand the concept of sampling distributions & sampling variability.
More informationSome Characteristics of Data
Some Characteristics of Data Not all data is the same, and depending on some characteristics of a particular dataset, there are some limitations as to what can and cannot be done with that data. Some key
More informationSummarising Data. Summarising Data. Examples of Types of Data. Types of Data
Summarising Data Summarising Data Mark Lunt Arthritis Research UK Epidemiology Unit University of Manchester Today we will consider Different types of data Appropriate ways to summarise these data 17/10/2017
More informationExploring Data and Graphics
Exploring Data and Graphics Rick White Department of Statistics, UBC Graduate Pathways to Success Graduate & Postdoctoral Studies November 13, 2013 Outline Summarizing Data Types of Data Visualizing Data
More informationDistributions and their Characteristics
Distributions and their Characteristics 1. A distribution of a variable is merely a list of all values the variable can take, and the corresponding frequencies. Distributions may be represented or displayed
More informationSTAT Chapter 6 The Standard Deviation (SD) as a Ruler and The Normal Model
STAT 203 - Chapter 6 The Standard Deviation (SD) as a Ruler and The Normal Model In Chapter 5, we introduced a few measures of center and spread, and discussed how the mean and standard deviation are good
More informationCHAPTER 6. ' From the table the z value corresponding to this value Z = 1.96 or Z = 1.96 (d) P(Z >?) =
Solutions to End-of-Section and Chapter Review Problems 225 CHAPTER 6 6.1 (a) P(Z < 1.20) = 0.88493 P(Z > 1.25) = 1 0.89435 = 0.10565 P(1.25 < Z < 1.70) = 0.95543 0.89435 = 0.06108 (d) P(Z < 1.25) or Z
More informationSTAT Chapter 6 The Standard Deviation (SD) as a Ruler and The Normal Model
STAT 203 - Chapter 6 The Standard Deviation (SD) as a Ruler and The Normal Model In Chapter 5, we introduced a few measures of center and spread, and discussed how the mean and standard deviation are good
More informationStandard Deviation. Lecture 18 Section Robb T. Koether. Hampden-Sydney College. Mon, Sep 26, 2011
Standard Deviation Lecture 18 Section 5.3.4 Robb T. Koether Hampden-Sydney College Mon, Sep 26, 2011 Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Sep 26, 2011 1 / 42 Outline 1 Variability
More informationNotes 12.8: Normal Distribution
Notes 12.8: Normal Distribution For many populations, the distribution of events are relatively close to the average or mean. The further you go out both above and below the mean, there are fewer number
More information1) 3 points Which of the following is NOT a measure of central tendency? a) Median b) Mode c) Mean d) Range
February 19, 2004 EXAM 1 : Page 1 All sections : Geaghan Read Carefully. Give an answer in the form of a number or numeric expression where possible. Show all calculations. Use a value of 0.05 for any
More information