In this investigation you will use the statistics skills that you learned the to display and analyze a cup of peanut M&Ms.
|
|
- Emery Morrison
- 6 years ago
- Views:
Transcription
1 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 number of each color of peanut M&Ms: Your numbers Class numbers Red Orange Yellow Green Blue Brown Total 2. Now calculate the percentage of each color in your cup and for the whole class: Your percentages Class percentages Official percentages Red Orange Yellow Green Blue Brown Total 10% 20% 20% 20% 20% 10% 100% 3. Make a three-way bar graph showing your percentages, the class percentages and the official percentages.
2 Quantitative Analysis: M&M Weight Distribution Part II: Peanut M&Ms: 1. Record the weight of each peanut M&M in your cup: 2. Find the Five Number Summary for your data Min = Q1 = Median= Q3= Max = 3. Identify any outliers using 1.5xIQR 4. Draw the boxplot for this data with the outliers identified by *:
3 5. Choose 10 of your data points. Find the mean and the standard deviation for your data Total = Mean = X X mean (x mean) 2 Sum= Steps for finding Standard Deviation 1. Enter the weights in the x-column 2. Find the mean of the values 3. Fill in the 3 rd column by subtracting the mean from each x-value 4. Fill in the last column by squaring each value in the 3 rd column 5. Add all the values in the last column. 6. Divide this number by N Take the square root of this value. Standard deviation = 6. Group data: Make a frequency table for the weights of the plain M&Ms and make a histogram of the percentages Class Tally Frequ ency Percent age Total
4 7. Class data: Make a frequency table for the weights of the peanut M&Ms and make a histogram of the percentages. Use the classes specified by your instructor. To find the Midpoint of each data, add the start of one class with the start of the next class and divide by 2. Class Midpoint Frequency Percentage Total Histogram of Class Data for Plain M&Ms 8. Mark the midpoint of each class at the top of each bar. Join the points with a smooth curve to create a continuous frequency graph.
5 9. Find the Five Number Summary for the class data: Min = Q1 = Median = Q3 = Max = 10. Identify outliers using 1.5xIQR: 11. Draw the boxplot for this data with the outliers identified by *: 12. Find the mean and standard deviation for the class data. Because there are many values for the class data, we will calculate these values using the frequency table rather than the raw data. The results are approximate but they are easier to calculate. Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Class Midpoint, X Frequency, f X*f (X Mean) 2 (X Mean) 2 * f Σ f = Σ X*f = Σ (X Mean) 2 * f = Mean = Σ X*f/ Σ f =
6 Here are the steps for this calculation: 1. Enter the classes in the first column. 2. Find the midpoint of each class: (start of class 1 + start of class 2)/2 3. Enter the frequencies in column 3. Find the sum of all frequencies and write the total a the bottom of the column, where it says: Σ f = 4. Multiply the values in the 2 nd column with the values in the 3 rd column to fill the 4 th column. Find the sum of all the values in the 4 th column and enter the answer where it says: Σ X*f = 5. Find the mean of the values using the formula: Mean = Σ X*f/ Σ f 6. Find the differences between the values in the 2 nd column and the mean and square these differences. Enter the answers in column Multiply the values in the 3 rd column with the values in the 5 th column and enter the answers in column 6. Find the sum of all the values in the 6 th column and write the answer where it says: Σ (X Mean) 2 * f = 8. Use the formula for SD to find the standard deviation. Divide the value that you got at the bottom of the 6 th column by the value of Σ X*f = that you have at the bottom of the 4 th column. Then take the square root of the answer. 13. Identify outliers using the standard deviation and the mean. A data point is considered an outlier if it is more than 3 standard deviation larger than the mean OR less than 3 standard deviations away from the mean. Upper boundary = mean + 3* SD = Lower boundary = mean 3*SD = List your outliers: 14. On the histogram for the class data, mark the values of the mean, median and the mode and any outliers by using * s. 15. Is the frequency symmetric, left-skewed or right-skewed? For symmetric, the mean is approximately equal to the median. For left-skewed, the mean is less than the median For right-skewed, the mean is more than the median. 16. If the distribution is approximately bell-shaped and symmetric, the mean and standard deviation are better measures of center and range than the median and IQR. What is more appropriate to use here: the mean and standard deviation OR the median and IQR.
Chapter 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 informationStats Review Chapter 3. Mary Stangler Center for Academic Success Revised 8/16
Stats Review Chapter Revised 8/16 Note: This review is composed of questions similar to those found in the chapter review and/or chapter test. This review is meant to highlight basic concepts from the
More 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 informationThe Normal Distribution. Chapter 6
+ The Normal Distribution Chapter 6 + Applications of the Normal Distribution Section 6-2 + The Standard Normal Distribution and Practical Applications! We can convert any variable that in normally distributed
More informationMEASURING THE SPREAD OF DATA: 6F
CONTINUING WITH DESCRIPTIVE STATS 6E,6F,6G,6H,6I MEASURING THE SPREAD OF DATA: 6F othink about this example: Suppose you are at a high school football game and you sample 40 people from the student section
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 information3.3. Section. Measures of Central Tendency and Dispersion from Grouped Data. Copyright 2013, 2010 and 2007 Pearson Education, Inc.
Section 3.3 Measures of Central Tendency and Dispersion from Grouped Data Objectives 1. Approximate the mean of a variable from grouped data 2. Compute the weighted mean 3. Approximate the standard deviation
More informationChapter 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 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 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 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 informationHomework Example Chapter 1 Similar to Problem #14
Chapter 1 Similar to Problem #14 Given a sample of n = 129 observations of shower-flow-rate, do this: a.) Construct a stem-and-leaf display of the data. b.) What is a typical, or representative flow rate?
More informationCHAPTER 2: Describing Distributions with Numbers
CHAPTER 2: Describing Distributions with Numbers The Basic Practice of Statistics 6 th Edition Moore / Notz / Fligner Lecture PowerPoint Slides Chapter 2 Concepts 2 Measuring Center: Mean and Median Measuring
More 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 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 informationChapter. Numerically Summarizing Data. Copyright 2013, 2010 and 2007 Pearson Education, Inc.
Chapter 3 Numerically Summarizing Data Section 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
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 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 information8/4/2009. Describing Data with Graphs
Describing Data with Graphs 1 A variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration. Examples: Hair color, white blood cell count,
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 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 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 informationM & M Project. Think! Crunch those numbers! Answer!
M & M Project Think! Crunch those numbers! Answer! Chapters 1-2 Exploring Data and Describing Location in a Distribution Univariate Data: Length Stemplot and Frequency Table Stem (Units Digit) 0 1 1 Leaf
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 informationFREQUENCY DISTRIBUTIONS AND PERCENTILES
FREQUENCY DISTRIBUTIONS AND PERCENTILES New Statistical Notation Frequency (f): the number of times a score occurs N: sample size Simple Frequency Distributions Raw Scores The scores that we have directly
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 informationWhat is Statistics? Statistics is the science of understanding data and of making decisions in the face of variability and uncertainty.
What is Statistics? Statistics is the science of understanding data and of making decisions in the face of variability and uncertainty. Statistics is a field of study concerned with the data collection,
More 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 information+ Check for Understanding
n Measuring Position: Percentiles n One way to describe the location of a value in a distribution is to tell what percent of observations are less than it. Definition: The p th percentile of a distribution
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 informationChapter 7: Statistics Describing Data. Chapter 7: Statistics Describing Data 1 / 27
Chapter 7: Statistics Describing Data Chapter 7: Statistics Describing Data 1 / 27 Categorical Data Four ways to display categorical data: 1 Frequency and Relative Frequency Table 2 Bar graph (Pareto chart)
More informationSection 3. Measures of Variation
Section 3 Measures of Variation Range Range = (maximum value) (minimum value) It is very sensitive to extreme values; therefore not as useful as other measures of variation. Sample Standard Deviation The
More 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 informationIntroduction to Statistics
Introduction to Statistics Data and Statistics Data consists of information coming from observations, counts, measurements, or responses. Statistics is the science of collecting, organizing, analyzing,
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 information3.1 Measure of Center
3.1 Measure of Center Calculate the mean for a given data set Find the median, and describe why the median is sometimes preferable to the mean Find the mode of a data set Describe how skewness affects
More informationReview for Exam #1. Chapter 1. The Nature of Data. Definitions. Population. Sample. Quantitative data. Qualitative (attribute) data
Review for Exam #1 1 Chapter 1 Population the complete collection of elements (scores, people, measurements, etc.) to be studied Sample a subcollection of elements drawn from a population 11 The Nature
More informationFurther Mathematics 2018 CORE: Data analysis Chapter 2 Summarising numerical data
Chapter 2: Summarising numerical data Further Mathematics 2018 CORE: Data analysis Chapter 2 Summarising numerical data Extract from Study Design Key knowledge Types of data: categorical (nominal and ordinal)
More informationALGEBRAIC PRINCIPLES
ALGEBRAIC PRINCIPLES Numbers and Operations Standard: 1 Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers,
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 informationLearning Objectives for Stat 225
Learning Objectives for Stat 225 08/20/12 Introduction to Probability: Get some general ideas about probability, and learn how to use sample space to compute the probability of a specific event. Set Theory:
More informationDensity Curves and the Normal Distributions. Histogram: 10 groups
Density Curves and the Normal Distributions MATH 2300 Chapter 6 Histogram: 10 groups 1 Histogram: 20 groups Histogram: 40 groups 2 Histogram: 80 groups Histogram: 160 groups 3 Density Curve Density Curves
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 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 informationChapter. Numerically Summarizing Data Pearson Prentice Hall. All rights reserved
Chapter 3 Numerically Summarizing Data Section 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
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 informationMeasures of center. The mean The mean of a distribution is the arithmetic average of the observations:
Measures of center The mean The mean of a distribution is the arithmetic average of the observations: x = x 1 + + x n n n = 1 x i n i=1 The median The median is the midpoint of a distribution: the number
More 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 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 informationLecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series. Slide 1
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 3 Statistics for Describing, Exploring, and Comparing Data 3-1 Overview 3-2 Measures
More informationProbability Distributions
Probability Distributions Probability This is not a math class, or an applied math class, or a statistics class; but it is a computer science course! Still, probability, which is a math-y concept underlies
More informationQ 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
Sample Exam #1, Math 01 1. 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
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 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 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 informationStatistics Add Ins.notebook. November 22, Add ins
Add ins We have LOADS of things we need to know for the IGCSE that you haven't learnt as part of the Bavarian Curriculum. We are now going to shoehorn in some of those topics and ideas. Nov 12 11:50 Main
More 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 information2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 2 Methods for Describing Sets of Data Summary of Central Tendency Measures Measure Formula Description Mean x i / n Balance Point Median ( n +1) Middle Value
More informationCHAPTER 2 Modeling Distributions of Data
CHAPTER 2 Modeling Distributions of Data 2.1 Describing Location in a Distribution The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Describing Location
More informationBag RED ORANGE GREEN YELLOW PURPLE Candies per Bag
Skittles Project For this project our entire class when out and bought a standard 2.17 ounce bag of skittles. Before we ate them, we recorded all of our data, the amount of skittles in our bag and the
More informationUnit 2. Describing Data: Numerical
Unit 2 Describing Data: Numerical Describing Data Numerically Describing Data Numerically Central Tendency Arithmetic Mean Median Mode Variation Range Interquartile Range Variance Standard Deviation Coefficient
More 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 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 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 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 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 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 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 informationOBJECTIVES INTRODUCTION
M7 Chapter 3 Section 1 OBJECTIVES Suarize data using easures of central tendency, such as the ean, edian, ode, and idrange. Describe data using the easures of variation, such as the range, variance, and
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 informationLecture 41 Sections Wed, Nov 12, 2008
Lecture 41 Sections 14.1-14.3 Hampden-Sydney College Wed, Nov 12, 2008 Outline 1 2 3 4 5 6 7 one-proportion test that we just studied allows us to test a hypothesis concerning one proportion, or two categories,
More informationCIVL 7012/8012. Collection and Analysis of Information
CIVL 7012/8012 Collection and Analysis of Information Uncertainty in Engineering Statistics deals with the collection and analysis of data to solve real-world problems. Uncertainty is inherent in all real
More informationReview. Midterm Exam. Midterm Review. May 6th, 2015 AMS-UCSC. Spring Session 1 (Midterm Review) AMS-5 May 6th, / 24
Midterm Exam Midterm Review AMS-UCSC May 6th, 2015 Spring 2015. Session 1 (Midterm Review) AMS-5 May 6th, 2015 1 / 24 Topics Topics We will talk about... 1 Review Spring 2015. Session 1 (Midterm Review)
More informationST Presenting & Summarising Data Descriptive Statistics. Frequency Distribution, Histogram & Bar Chart
ST2001 2. Presenting & Summarising Data Descriptive Statistics Frequency Distribution, Histogram & Bar Chart Summary of Previous Lecture u A study often involves taking a sample from a population that
More 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 informationDescribing Distributions with Numbers
Describing Distributions with Numbers Using graphs, we could determine the center, spread, and shape of the distribution of a quantitative variable. We can also use numbers (called summary statistics)
More 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 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 informationLesson ACTIVITY: Tree Growth
Lesson 3.1 - ACTIVITY: Tree Growth Obj.: use arrow diagrams to represent expressions. evaluate expressions. write expressions to model realworld situations. Algebraic expression - A symbol or combination
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 informationA C E. Answers Investigation 4. Applications
Answers Applications 1. 1 student 2. You can use the histogram with 5-minute intervals to determine the number of students that spend at least 15 minutes traveling to school. To find the number of students,
More information200 participants [EUR] ( =60) 200 = 30% i.e. nearly a third of the phone bills are greater than 75 EUR
Ana Jerončić 200 participants [EUR] about half (71+37=108) 200 = 54% of the bills are small, i.e. less than 30 EUR (18+28+14=60) 200 = 30% i.e. nearly a third of the phone bills are greater than 75 EUR
More informationØ Set of mutually exclusive categories. Ø Classify or categorize subject. Ø No meaningful order to categorization.
Statistical Tools in Evaluation HPS 41 Fall 213 Dr. Joe G. Schmalfeldt Types of Scores Continuous Scores scores with a potentially infinite number of values. Discrete Scores scores limited to a specific
More informationDetermining the Spread of a Distribution
Determining the Spread of a Distribution 1.3-1.5 Cathy Poliak, Ph.D. cathy@math.uh.edu Department of Mathematics University of Houston Lecture 3-2311 Lecture 3-2311 1 / 58 Outline 1 Describing Quantitative
More informationStatistics 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 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 informationLecture 3. The Population Variance. The population variance, denoted σ 2, is the sum. of the squared deviations about the population
Lecture 5 1 Lecture 3 The Population Variance The population variance, denoted σ 2, is the sum of the squared deviations about the population mean divided by the number of observations in the population,
More informationDescriptive Statistics C H A P T E R 5 P P
Descriptive Statistics C H A P T E R 5 P P 1 1 0-130 Graphing data Frequency distributions Bar graphs Qualitative variable (categories) Bars don t touch Histograms Frequency polygons Quantitative variable
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 informationReminders. Homework due tomorrow Quiz tomorrow
Reminders Homework due tomorrow Quiz tomorrow 1 Warm Up - ACT Math Scores Distribution of ACT Math Scores Density 0 5 10 15 20 25 30 35 scores What percent of scores are between 12 and 24? Options: 38%,
More informationReview: Central Measures
Review: Central Measures Mean, Median and Mode When do we use mean or median? If there is (are) outliers, use Median If there is no outlier, use Mean. Example: For a data 1, 1.2, 1.5, 1.7, 1.8, 1.9, 2.3,
More 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 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 informationLesson Plan. Answer Questions. Summary Statistics. Histograms. The Normal Distribution. Using the Standard Normal Table
Lesson Plan Answer Questions Summary Statistics Histograms The Normal Distribution Using the Standard Normal Table 1 2. Summary Statistics Given a collection of data, one needs to find representations
More informationPhysicsAndMathsTutor.com
1 (i) 0 6 1 5 8 2 1 5 8 3 1 1 3 5 8 9 Key 1 8 represents 18 people Stem (in either order) and leaves Sorted and aligned Key Do not allow leaves 21,25, 28 etc Ignore commas between leaves Allow stem 0,
More informationDescriptive statistics
Patrick Breheny February 6 Patrick Breheny to Biostatistics (171:161) 1/25 Tables and figures Human beings are not good at sifting through large streams of data; we understand data much better when it
More informationLecture Slides. Elementary Statistics Twelfth Edition. by Mario F. Triola. and the Triola Statistics Series. Section 3.1- #
Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series by Mario F. Triola Chapter 3 Statistics for Describing, Exploring, and Comparing Data 3-1 Review and Preview 3-2 Measures
More informationx y x y ax bx c x Algebra I Course Standards Gap 1 Gap 2 Comments a. Set up and solve problems following the correct order of operations (including proportions, percent, and absolute value) with rational
More informationDescriptive Statistics Solutions COR1-GB.1305 Statistics and Data Analysis
Descriptive Statistics Solutions COR-GB.0 Statistics and Data Analysis Types of Data. The class survey asked each respondent to report the following information: gender; birth date; GMAT score; undergraduate
More information