Q 1 = 23.8 M = Q 3 = 29.8 IQR = 6 The numbers are in order and there are 18 pieces of data so the median is the average of the 9th and 10th
|
|
- Rosalind Lee
- 6 years ago
- Views:
Transcription
1 Sample Exam #1, Math Use the data set given below to answer all of the following questions. 14.0, 18.4, 1.6,.1, 3.8, 4.3, 5.9, 6.5, 7.5, 9., 9.3, 9.4, 9.7, 9.8, 30., 30.8, 31.9, 33.5 HaL Use the statistical capability of your scientific calculator to find the mean, standard deviation, and variance of the data: êê x = 6.55 s = variance = HbL Find by hand the first quartile Q 1, median M, third quartile Q 3, and the IQR. Q 1 = 3.8 M = 8.35 Q 3 = 9.8 IQR = 6 The numbers are in order and there are 18 pieces of data so the median is the average of the 9th and 10th pieces of data. M = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅ = 8.35 Q 1 is the median of the first half of the data, or the 5th piece of data and Q is the median of the second half of the data, or the 14th piece of data. HcL Create a boxplot for these data: HdL Create a split stemplot for these data: First, round to the nearest whole number HeL Which measure would be a better measure for the center of this distribution? Justify your choice. Since the distribution is skewed and not very symmetric the median is the best measure for the center.
2 . The histogram below shows the distribution of a set of observations: HaL Is the distribution symmetric, skewed to the left, or skewed to the right? The distribution is skewed to the left. HbL Is the mean less than or greater than the median? Since the mean follows the skew, the mean is less than the median. HcL How many data values are in the data set? Adding up the height of each bar, we get: = 141 HdL Use the histogram to accurately estimate the median. The position of the median is found by: n+1 ÅÅÅÅÅÅÅÅÅ = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅ = ÅÅÅÅÅÅÅÅ 14 = 71 is the 71st entry, so M is between 130 and Use Table A to answer the following questions. Find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. HaL z From Table A, we find the p-value to be =.0009 or.09% HbL -1.5 z We look up both -1.5 and 0.54 in Table A. Using these we find the p-value to be =.5998 or 59.98%
3 HcL 58% of the observations are greater than what z value? Since Table A uses the area to the left, we subtract 100%-58% and we look up 4% or.4 in table A to find the z value. The closest we can get is.4168, which gives z = Estimate the mean and standard deviation for the normal distribution whose density curve is shown. m = 16 (This is the center.) s = 3 (This is the distance from the center to the inflection points, ie. the steepest point on the curve.) The scores on the math section of the SAT test for Washington students (006) are normally distributed with mean 53 and standard deviation 103. HaL What proportion of students received a score between 500 and 650? First we'll find the z values for 500 and 650. z 1 = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ º z = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ º Using table A the number of students scoring less than 500 is 37.83% and the number of students scoring less than 650 is 87.49%. So the number of students scoring between 500 and 650 is =49.66%.
4 HbL 83% of the test scores were less than what value? The percentage closest to 83% from table A is %. This gives a z value of z =.96. We'll use this to solve for the test score..96 = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅ x = x - 53 x º 631 So 83% of the test scores were less than 631. x 6. Match the scatterplot with the correlation values given below: Scatterplot #1 Scatterplot # Scatterplot #3 Scatterplot #4 Scatterplot #5 Scatterplot #6 HaL r = goes with Scatterplot # 4_ HbL r = 1.00 goes with Scatterplot # 6_ HcL r = goes with Scatterplot # 1_ HdL r = 0.68 goes with Scatterplot # 3_ HeL r = 0.59 goes with Scatterplot # 5_ HfL r = -0.9 goes with Scatterplot # 7. A new teacher is analyzing whether or not there is an association between scores earned by students on their first exam in the course and the course grade earned by students at the end of the term. Exams are scored using a 100 point scale (0 to 100 points) and course grades use a 100% scale (0% to 100%). There are 35 students in the course. HaL Decide which variable, Exam 1 Score or Course Grade, is the explanatory variable and which is the response variable. Circle the scatterplot below that matches your decision. Explanatory Variable: Exam 1 Score
5 Response Variable: Course Grade Course Grade Exam 1 HbL Find the equation of the regression line ỳ = a + b x. The mean and standard deviation for the Course Grade variable is and 0.13 The mean and standard deviation for the Exam 1 Score variable is and The correlation is Be very sensitive to roundoff errors. We'll use the formula, ỳ = a + b x, with b = r s y ÅÅÅÅÅÅ and a = êê y - b êê x. s x b =.7845 H ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ L º a = H83.943L º So the regression line is given by ỳ = x. HcL Predict the course grade for a student who scores a 91 on their first exam. Use the equation of the regression line found in (b). ỳ = H91L º.86 HdL There is an obvious outlier present in the data set - what is its coordinate on the scatterplot? Describe what happened to the student represented by the outlier. The coordinate is approximately H96,.56L. The student did well on the first exam, scoring a 96 out of 100, but didn't pass the class with a 56% overall. HeL What proportion of the 35 students earned an A for the course? Any Course Grade between 90% and 100% would be assigned the A letter grade. There are 4 of students that have scores above.9. So ÅÅÅÅÅÅ 4 º.114 or 11.4 % of the students earned an A. 35 Depending on the quarter and instructor some of the previous exercise may not appear until exam. 8. Use the data set to answer the following questions:,,,4,4,5,5,5,7,7,7,7,8,11,11 HaL Find the five number summary for the given data. There are 15 pieces of data, so the median is the 8th or middle piece. M = 5 The median of the first half of the data is the 4th piece. Q 1 = 4 The median of the second half of the data is the 1th piece. Q 3 = 7 This gives a five number summary of Min =, Q 1 = 4, M = 5, Q 3 = 7, Max = 11
6 HbL Create a boxplot for the data For the data set from the previous problem, describe the distribution of the data and determine if the five number summary was the best representation of the spread. The distribution is skewed and so the five number summary is the best representation of the spread, because mean and standard deviation are better suited for symmetric distributions. 10. Create a split stemplot for the following data and describe the distribution: 11,1,16,19,,3,5,5,6,8,9,30,3,34,38, For the data set in the previous problem determine the best summary and give justification for your answer. (Just state the type of summary, don't compute it.) Either summary could be justified. It is single peaked and somewhat symmetric, so mean and standard deviation could be used. On the other hand, there is a little bit of skewness, so the five number summary may be more desirable. 1. The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 66 days and standard deviation 16 days. Use the rule to answer the following questions. HaL Between what values do the lengths of the middle 99.7% of all pregnancies fall? The middle 99.7% of the pregnancies will fall within 3 standard deviations from the mean. 66 ± 3 H16L 66 ± to 314 days
7 That is, 99.7% of the pregnancies will fall between 18 and 314 days HbL How long are the longest.5% of all pregnancies? The longest.5% of all pregnancies will fall above standard deviations from the mean H16L = 98 So the longest.5% of all pregnancies last 98 or more days. 13. Use table A to answer the following questions HaL What percentage of human pregnancies last less than 70 days? z = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ = From table A, we get PHz.5L =.5987 HbL What percentage of human pregnancies last between 50 and 70 days? z 1 = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ =
8 PHz 1.5L =.5987 z = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ = PHz -1L =.1587 So the percentage of human pregnancies between 50 and 70 days is = Below how many days do 67% of all human pregnancies last? Using table A, we'll find the value of z that corresponds to We find z =.44. Solving.44 = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅ x-66 for x, we get x = H.44L = days. So x should be less than 74 days Use the histogram to answer the following questions: Histogram Frequency More Bin Frequency HaL Describe the distribution of the data set. The distribution is single peaked with a slight skew to the right. HbL How many observations are represented by the histogram? = 5 HcL Find the median and mean on the histogram and justify your answers. Median º 7 (Find either the 13th entry or the point where the areas on either side are equal.) Mean º 31 (The average gets pulled towards the skew, so it should be more than the median.) Note: Actual answers may vary, but the relationships described above need to be true. 16. The following table gives information about a sample of sports cars that were test driven. Determine who the individuals are in the study, what the variables are, and whether each variable is categorical or quantitative. City mpg Highway mpg color Audi TT Quattro 0 8 white BMW M Coupe 17 5 black Ford Thunderbird 17 3 red The individuals are the cars being tested. The variables are city mpg, highway mpg and color. The two mpg variables are quantitative and color is categorical.
9 17. êê Compute the mean and standard deviation for the city mpg for all the cars in the study from problem 9. x = ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅ = 18 3 s = "################################ H0-18L +H17-18L +H17-18L ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ############## ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ =
Chapter 5: Exploring Data: Distributions Lesson Plan
Lesson Plan Exploring Data Displaying Distributions: Histograms For All Practical Purposes Mathematical Literacy in Today s World, 7th ed. Interpreting Histograms Displaying Distributions: Stemplots Describing
More informationAP Final Review II Exploring Data (20% 30%)
AP Final Review II Exploring Data (20% 30%) Quantitative vs Categorical Variables Quantitative variables are numerical values for which arithmetic operations such as means make sense. It is usually a measure
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 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 informationPractice Questions for Exam 1
Practice Questions for Exam 1 1. A used car lot evaluates their cars on a number of features as they arrive in the lot in order to determine their worth. Among the features looked at are miles per gallon
More informationChapter 5: Exploring Data: Distributions Lesson Plan
Lesson Plan Exploring Data Displaying Distributions: Histograms Interpreting Histograms Displaying Distributions: Stemplots Describing Center: Mean and Median Describing Variability: The Quartiles The
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 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 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 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 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 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 informationCHAPTER 1 Univariate data
Chapter Answers Page 1 of 17 CHAPTER 1 Univariate data Exercise 1A Types of data 1 Numerical a, b, c, g, h Categorical d, e, f, i, j, k, l, m 2 Discrete c, g Continuous a, b, h 3 C 4 C Exercise 1B Stem
More informationThe response variable depends on the explanatory variable.
A response variable measures an outcome of study. > dependent variables An explanatory variable attempts to explain the observed outcomes. > independent variables The response variable depends on the explanatory
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 informationUniversity of California, Berkeley, Statistics 131A: Statistical Inference for the Social and Life Sciences. Michael Lugo, Spring 2012
University of California, Berkeley, Statistics 3A: Statistical Inference for the Social and Life Sciences Michael Lugo, Spring 202 Solutions to Exam Friday, March 2, 202. [5: 2+2+] Consider the stemplot
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 informationSem. 1 Review Ch. 1-3
AP Stats Sem. 1 Review Ch. 1-3 Name 1. You measure the age, marital status and earned income of an SRS of 1463 women. The number and type of variables you have measured is a. 1463; all quantitative. b.
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 informationM 225 Test 1 B Name SHOW YOUR WORK FOR FULL CREDIT! Problem Max. Points Your Points Total 75
M 225 Test 1 B Name SHOW YOUR WORK FOR FULL CREDIT! Problem Max. Points Your Points 1-13 13 14 3 15 8 16 4 17 10 18 9 19 7 20 3 21 16 22 2 Total 75 1 Multiple choice questions (1 point each) 1. Look at
More informationChapter 6. Exploring Data: Relationships. Solutions. Exercises:
Chapter 6 Exploring Data: Relationships Solutions Exercises: 1. (a) It is more reasonable to explore study time as an explanatory variable and the exam grade as the response variable. (b) It is more reasonable
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 informationAP STATISTICS: Summer Math Packet
Name AP STATISTICS: Summer Math Packet DIRECTIONS: Complete all problems on this packet. Packet due by the end of the first week of classes. Attach additional paper if needed. Calculator may be used. 1.
More informationM 140 Test 1 B Name (1 point) SHOW YOUR WORK FOR FULL CREDIT! Problem Max. Points Your Points Total 75
M 140 est 1 B Name (1 point) SHOW YOUR WORK FOR FULL CREDI! Problem Max. Points Your Points 1-10 10 11 10 12 3 13 4 14 18 15 8 16 7 17 14 otal 75 Multiple choice questions (1 point each) For questions
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 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 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 informationMath 223 Lecture Notes 3/15/04 From The Basic Practice of Statistics, bymoore
Math 223 Lecture Notes 3/15/04 From The Basic Practice of Statistics, bymoore Chapter 3 continued Describing distributions with numbers Measuring spread of data: Quartiles Definition 1: The interquartile
More informationStatistics for Managers using Microsoft Excel 6 th Edition
Statistics for Managers using Microsoft Excel 6 th Edition Chapter 3 Numerical Descriptive Measures 3-1 Learning Objectives In this chapter, you learn: To describe the properties of central tendency, variation,
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 informationSociology 6Z03 Review I
Sociology 6Z03 Review I John Fox McMaster University Fall 2016 John Fox (McMaster University) Sociology 6Z03 Review I Fall 2016 1 / 19 Outline: Review I Introduction Displaying Distributions Describing
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 informationSTATISTICS 1 REVISION NOTES
STATISTICS 1 REVISION NOTES Statistical Model Representing and summarising Sample Data Key words: Quantitative Data This is data in NUMERICAL FORM such as shoe size, height etc. Qualitative Data This is
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 informationThe empirical ( ) rule
The empirical (68-95-99.7) rule With a bell shaped distribution, about 68% of the data fall within a distance of 1 standard deviation from the mean. 95% fall within 2 standard deviations of the mean. 99.7%
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 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 informationMultiple Choice Circle the letter corresponding to the best answer for each of the problems below (4 pts each)
Math 221 Hypothetical Exam 1, Wi2008, (Chapter 1-5 in Moore, 4th) April 3, 2063 S. K. Hyde, S. Barton, P. Hurst, K. Yan Name: Show all your work to receive credit. All answers must be justified to get
More informationReview Packet for Test 8 - Statistics. Statistical Measures of Center: and. Statistical Measures of Variability: and.
Name: Teacher: Date: Section: Review Packet for Test 8 - Statistics Part I: Measures of CENTER vs. Measures of VARIABILITY Statistical Measures of Center: and. Statistical Measures of Variability: and.
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 informationDescriptive Univariate Statistics and Bivariate Correlation
ESC 100 Exploring Engineering Descriptive Univariate Statistics and Bivariate Correlation Instructor: Sudhir Khetan, Ph.D. Wednesday/Friday, October 17/19, 2012 The Central Dogma of Statistics used to
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 information********************************************************************************************************
QUESTION # 1 1. Let the random variable X represent the number of telephone lines in use by the technical support center of a software manufacturer at noon each day. The probability distribution of X is
More informationScatterplots. 3.1: Scatterplots & Correlation. Scatterplots. Explanatory & Response Variables. Section 3.1 Scatterplots and Correlation
3.1: Scatterplots & Correlation Scatterplots A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal
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 informationStatistics 1. Edexcel Notes S1. Mathematical Model. A mathematical model is a simplification of a real world problem.
Statistics 1 Mathematical Model A mathematical model is a simplification of a real world problem. 1. A real world problem is observed. 2. A mathematical model is thought up. 3. The model is used to make
More informationChapter 4. Displaying and Summarizing. Quantitative Data
STAT 141 Introduction to Statistics Chapter 4 Displaying and Summarizing Quantitative Data Bin Zou (bzou@ualberta.ca) STAT 141 University of Alberta Winter 2015 1 / 31 4.1 Histograms 1 We divide the range
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 informationChapter2 Description of samples and populations. 2.1 Introduction.
Chapter2 Description of samples and populations. 2.1 Introduction. Statistics=science of analyzing data. Information collected (data) is gathered in terms of variables (characteristics of a subject that
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 informationAP Statistics Bivariate Data Analysis Test Review. Multiple-Choice
Name Period AP Statistics Bivariate Data Analysis Test Review Multiple-Choice 1. The correlation coefficient measures: (a) Whether there is a relationship between two variables (b) The strength of the
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 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 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 informationMAT Mathematics in Today's World
MAT 1000 Mathematics in Today's World Last Time 1. Three keys to summarize a collection of data: shape, center, spread. 2. Can measure spread with the fivenumber summary. 3. The five-number summary can
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 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 informationMath 138 Summer Section 412- Unit Test 1 Green Form, page 1 of 7
Math 138 Summer 1 2013 Section 412- Unit Test 1 Green Form page 1 of 7 1. Multiple Choice. Please circle your answer. Each question is worth 3 points. (a) Social Security Numbers are illustrations of which
More informationShape, Outliers, Center, Spread Frequency and Relative Histograms Related to other types of graphical displays
Histograms: Shape, Outliers, Center, Spread Frequency and Relative Histograms Related to other types of graphical displays Sep 9 1:13 PM Shape: Skewed left Bell shaped Symmetric Bi modal Symmetric Skewed
More informationHonors Algebra 1 - Fall Final Review
Name: Period Date: Honors Algebra 1 - Fall Final Review This review packet is due at the beginning of your final exam. In addition to this packet, you should study each of your unit reviews and your notes.
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 informationDescribing Distributions with Numbers
Topic 2 We next look at quantitative data. Recall that in this case, these data can be subject to the operations of arithmetic. In particular, we can add or subtract observation values, we can sort them
More informationUnits. Exploratory Data Analysis. Variables. Student Data
Units Exploratory Data Analysis Bret Larget Departments of Botany and of Statistics University of Wisconsin Madison Statistics 371 13th September 2005 A unit is an object that can be measured, such as
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 information(i) The mean and mode both equal the median; that is, the average value and the most likely value are both in the middle of the distribution.
MATH 183 Normal Distributions Dr. Neal, WKU Measurements that are normally distributed can be described in terms of their mean µ and standard deviation!. These measurements should have the following properties:
More informationInt Math 1 Statistic and Probability. Name:
Name: Int Math 1 1. Juan wants to rent a house. He gathers data on many similar houses. The distance from the center of the city, x, and the monthly rent for each house, y, are shown in the scatter plot.
More informationPrentice Hall Stats: Modeling the World 2004 (Bock) Correlated to: National Advanced Placement (AP) Statistics Course Outline (Grades 9-12)
National Advanced Placement (AP) Statistics Course Outline (Grades 9-12) Following is an outline of the major topics covered by the AP Statistics Examination. The ordering here is intended to define the
More informationP8130: Biostatistical Methods I
P8130: Biostatistical Methods I Lecture 2: Descriptive Statistics Cody Chiuzan, PhD Department of Biostatistics Mailman School of Public Health (MSPH) Lecture 1: Recap Intro to Biostatistics Types of Data
More informationTopic 3: Introduction to Statistics. Algebra 1. Collecting Data. Table of Contents. Categorical or Quantitative? What is the Study of Statistics?!
Topic 3: Introduction to Statistics Collecting Data We collect data through observation, surveys and experiments. We can collect two different types of data: Categorical Quantitative Algebra 1 Table of
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 informationA graph for a quantitative variable that divides a distribution into 25% segments.
STATISTICS Unit 2 STUDY GUIDE Topics 6-10 Part 1: Vocabulary For each word, be sure you know the definition, the formula, or what the graph looks like. Name Block A. association M. mean absolute deviation
More informationLecture 1: Description of Data. Readings: Sections 1.2,
Lecture 1: Description of Data Readings: Sections 1.,.1-.3 1 Variable Example 1 a. Write two complete and grammatically correct sentences, explaining your primary reason for taking this course and then
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 informationTables Table A Table B Table C Table D Table E 675
BMTables.indd Page 675 11/15/11 4:25:16 PM user-s163 Tables Table A Standard Normal Probabilities Table B Random Digits Table C t Distribution Critical Values Table D Chi-square Distribution Critical Values
More informationChapter 1 Introduction & 1.1: Analyzing Categorical Data
Chapter 1 Chapter 1 Introduction & 1.1: Analyzing Categorical Data Population Sample Make an inference about the population. Collect data from a representative sample... Perform Data Analysis, keeping
More informationDescribing Center: Mean and Median Section 5.4
Describing Center: Mean and Median Section 5.4 Look at table 5.2 at the right. We are going to make the dotplot of the city gas mileages of midsize cars. How to describe the center of a distribution: x
More informationExam: practice test 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam: practice test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. ) Using the information in the table on home sale prices in
More informationMATH-A Day 8 - Stats Exam not valid for Paper Pencil Test Sessions
MATH-A Day 8 - Stats Exam not valid for Paper Pencil Test Sessions [Exam ID:1LCDDJ 1 Karen knows that the z-score for a specific element within a set of data is.97. Karen can conclude that the element
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 informationChapter 3: Displaying and summarizing quantitative data p52 The pattern of variation of a variable is called its distribution.
Chapter 3: Displaying and summarizing quantitative data p52 The pattern of variation of a variable is called its distribution. 1 Histograms p53 The breakfast cereal data Study collected data on nutritional
More informationChapter 6 Assessment. 3. Which points in the data set below are outliers? Multiple Choice. 1. The boxplot summarizes the test scores of a math class?
Chapter Assessment Multiple Choice 1. The boxplot summarizes the test scores of a math class? Test Scores 3. Which points in the data set below are outliers? 73, 73, 7, 75, 75, 75, 77, 77, 77, 77, 7, 7,
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 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 information(i) The mean and mode both equal the median; that is, the average value and the most likely value are both in the middle of the distribution.
MATH 382 Normal Distributions Dr. Neal, WKU Measurements that are normally distributed can be described in terms of their mean µ and standard deviation σ. These measurements should have the following properties:
More informationHistograms allow a visual interpretation
Chapter 4: Displaying and Summarizing i Quantitative Data s allow a visual interpretation of quantitative (numerical) data by indicating the number of data points that lie within a range of values, called
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 informationComplement: 0.4 x 0.8 = =.6
Homework The Normal Distribution Name: 1. Use the graph below 1 a) Why is the total area under this curve equal to 1? Rectangle; A = LW A = 1(1) = 1 b) What percent of the observations lie above 0.8? 1
More informationFinding Quartiles. . Q1 is the median of the lower half of the data. Q3 is the median of the upper half of the data
Finding Quartiles. Use the median to divide the ordered data set into two halves.. If n is odd, do not include the median in either half. If n is even, split this data set exactly in half.. Q1 is the median
More informationMath 120 Introduction to Statistics Mr. Toner s Lecture Notes 3.1 Measures of Central Tendency
Math 1 Introduction to Statistics Mr. Toner s Lecture Notes 3.1 Measures of Central Tendency The word average: is very ambiguous and can actually refer to the mean, median, mode or midrange. Notation:
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 informationChapter 3: The Normal Distributions
Chapter 3: The Normal Distributions http://www.yorku.ca/nuri/econ2500/econ2500-online-course-materials.pdf graphs-normal.doc / histogram-density.txt / normal dist table / ch3-image Ch3 exercises: 3.2,
More informationAnnouncements. Lecture 1 - Data and Data Summaries. Data. Numerical Data. all variables. continuous discrete. Homework 1 - Out 1/15, due 1/22
Announcements Announcements Lecture 1 - Data and Data Summaries Statistics 102 Colin Rundel January 13, 2013 Homework 1 - Out 1/15, due 1/22 Lab 1 - Tomorrow RStudio accounts created this evening Try logging
More informationChapter 2 Class Notes Sample & Population Descriptions Classifying variables
Chapter 2 Class Notes Sample & Population Descriptions Classifying variables Random Variables (RVs) are discrete quantitative continuous nominal qualitative ordinal Notation and Definitions: a Sample is
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 informationStatistics I Chapter 2: Univariate data analysis
Statistics I Chapter 2: Univariate data analysis Chapter 2: Univariate data analysis Contents Graphical displays for categorical data (barchart, piechart) Graphical displays for numerical data data (histogram,
More informationPractice problems from chapters 2 and 3
Practice problems from chapters and 3 Question-1. For each of the following variables, indicate whether it is quantitative or qualitative and specify which of the four levels of measurement (nominal, ordinal,
More informationSTT 315 This lecture is based on Chapter 2 of the textbook.
STT 315 This lecture is based on Chapter 2 of the textbook. Acknowledgement: Author is thankful to Dr. Ashok Sinha, Dr. Jennifer Kaplan and Dr. Parthanil Roy for allowing him to use/edit some of their
More information