Stats Review Chapters 3-4

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Stats Review Chapters 3-4"

Transcription

1 Stats Review Chapters 3-4 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test Generator from Pearson Revised 12/13

2 Note: This review is composed of questions the textbook and the test generator. This review is meant to highlight basic concepts from the course. It does not cover all concepts presented by your instructor. Refer back to your notes, unit objectives, handouts, etc. to further prepare for your exam. A copy of this review can be found at The final answers are displayed in red and the chapter/section number is the corner.

3 Find the Mean, Median, Mode Data Set: 71, 74, 67, 64, 72, 71, 65, 66, 69,70 Mean: add up all the numbers and divide by the amount of numbers = Median: Arrange numbers from smallest to largest then find the middle number 64, 65,66, 67,69,70,71, 71, 72, 74 The middle number is between 69 and 70. Finding the mean of these two numbers will give us the median which is 69.5 Mode: The most repeated number (can have none, one, or more than one) The mode is

4 Find the Range and Sample Standard Deviation Data Set: 71, 74, 67, 64, 72, 71, 65, 66, 69,70 Range: The highest number the smallest number 74-64=10 Sample Standard Deviation: Use Excel or Calculator You get

5 Find the Five-Number Summary: Part 1 of 2 Data Set: 64, 65, 66, 67, 69, 70, 71, 71, 72, 74 Min: the smallest number 64 Max: the largest number 74 Median: the middle number 69.5 Q1: Find the median of the numbers from the minimum and the median (do not include the median) These numbers are 64, 65, 66, 67, 69. The median of these numbers are 66. So Q1 is

6 Find the Five-Number Summary: Part 2 of 2 Q3: Find the median of the numbers from the median (not included) to the maximum. These numbers are 70, 71, 71, 72, 74. The median of these numbers are 71. So Q1 is 71. The five-number summary is

7 Find the Upper and Lower Fences Data Set: 71, 74, 67, 64, 72, 71, 65, 66, 69, 70 1) Find the IQR. IQR=Q3-Q1=71-66=5 2) Multiply the IQR by 1.5: 5*1.5=7.5 3) Upper Fence: Add 7.5 to Q3; =78.5 4) Lower Fence: Subtract 7.5 from Q1; =58.5 Any numbers outside this range would be considered outliers. 3.4

8 Construct a Boxplot Construct a box plot given the five-number summary

9 Relationship between Mean, Median and Shape Match the shape to the relationship between mean and median. Mean>Median Mean=Median Mean<Median Skewed Left Mean<Median Symmetric Mean=Median Skewed right Mean>Median If data is skewed, median is more representative of the typical observation. 3.1

10 Empirical Rule to Find the Probability: Part 1 of 2 At a tennis tournament, a statistician keeps track of every serve. She reported that the mean serve speed of a particular player was 104 mph and the standard deviation of the serve speeds was 8 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was bell shaped. Using the Empirical Rule, what proportion of the player's serves are expected to be between 112 mph and 120 mph? 3.2

11 Empirical Rule to Find the Probability: Part 1 of 2 Start by drawing the bell curve Compare this to the empirical rule curve on page 149 or find the percents as described on page 149. We can see that the probability is 13.5% or.135. *You could also find the z-scores, then find the probability. 3.2

12 Find the Mean: Part 1 of 2 Days Frequency Step 1: Find the midpoint of each class (days) Days Class Midpoint, x i Frequency, f i =

13 Find the Mean: Part 2 of 2 Step 2: Multiply the class midpoint by frequency Days Class Midpoint, x i Frequency, f i x i f i *2=3 = Step 3: Find the sum of the x i f i column: =546.5 Step 4: Find the sum of the frequency column: 83 Step 5: Divide the number from step 3 by the number from step 4: 546.5/83=6.6 The mean is

14 Find the Sample Standard Deviation: Part 1 of 2 (from previous problem) Step 1: Find the mean (see previous 2 slides). Mean=6.6 Step 2: Complete the following table (the first three columns were done in the previous 2 slides and column 4 is the mean) Days Class Midpoint, x i Frequency, f i x x i -x (x i x) 2 f i = =-5.1 ( 5.1) 2 2 =

15 Find the Sample Standard Deviation: Part 2 of 2 (from previous problem) Days Class Midpoint, x i Frequency, f i x x i -x (x i x) 2 f i =-5.1 ( 5.1) = = Step 3: Find the total of the (x i x ) 2 f i column. Total = Step 4: Find the total of the frequency column. Total =83. Take this number and subtract =82 Step 5: Take the number from Step 3 and divide by the number from step /82= Step 6: Take the square root of the number from step =

16 Correlation Coefficient Match the Correlation with the Graph r=-.6 r=0 r=.99 should not use correlation r= r= r= Should not use correlation 4.1

17 Least-Squares Regression Line: Part 1 of 3 The data are the average one-way commute times (in minutes) for selected students and the number of absences for those students during the term. a) Find the equation of the regression line for the given data. Round the regression line values to the nearest hundredth. b) What would be the predicted number of absences if the commute time was 40 minutes? Is this a reasonable question? c) Interpret the Slope Commute time (x) Number of absences (y)

18 Least-Squares Regression Line: Part 2 of 3 a) Find the regression Line With Calculator y =.45x 30.3 By Hand First find the mean of x and y (labeled x and y), the sample standard deviation of x and y (labeled s x and s y ), and the correlation (r). x =86.556, y=8.556, s x =9.593, s y =4.39, r=.98 Slope (b 1 )=r s y s x = =.45 Y-Intercept (b 0 )= y-b1 x = (86.556)=-30.3 The regression Line is y = b 1 x + b o so ours is y =.45x

19 Least-Squares Regression Line: Part 3 of 3 b) What would be the predicted number of absences if the commute time was 40 minutes? Is this a reasonable question? Tine is 40 minutes or x=40. Put this value into our least-squares regression line y =.45(40) 30.3=-12.3 This means that when the commute time is 40 minutes, than the number of absences is This is not a reasonable question since 40 is outside the scope (i.e. 40 is not within the given range of x values). c) Interpret the slope The slope is.45. This means that for every minute we increase our commute the number of absences increases by

20 Sum Of Residuals: Part 1 of 2 Find the sum of residuals Step 1: Find the least squares regression line (see previous slides) Step 2: Find the predicted y values (y) for each x Commute time (x) Number of absences (y) Predicted y =.45(72)-30.3=

21 Sum Of Residuals: Part 2 of 2 Step 3: Calculate the residuals: observed predicted or y-y Step 4: Calculate the residuals squared: (observed predicted) 2 or (y-y) 2 Step 5: Find the sum of the numbers in the column from step 4. This is the sum of residuals which equals Commute time (x) Number of absences (y) Predicted y Step 3 y-y Step 4 (y-y)

22 Coefficient of Determination (R 2 ) If the coefficient of determination (R 2 ) is 86.44% and the data shows a negative association, what is the linear correlation coefficient (r)? r = r 2 =.8644 =.9297 Since it has a negative association, r = Interpret R 2 = 86.44% 86.44% of the variability in y (the response variable) is explained by the least-squares regression line. 4.3

23 Residual Plots What does the residual plot to the right suggest? There is an outlier Removing the outlier, what does the residual plot suggest? No pattern, linear model is appropriate

24 Contingency Tables: Part 1 of 3 Is there an association between party affliction and gender? The following represents the gender and party affliction of registered voters based on random sample 802 adults. Female Male Republican Democratic Independent a) Construct a frequency marginal distribution b) Construct a relative frequency marginal distribution c) Construct a conditional distribution of party affiliation by gender d) Is gender associated with party affiliation? If so, how? 4.4

25 Contingency Tables: Part 2 of 3 a) Construct a frequency marginal distribution Gender Party Female Male frequency marginal distribution Republican = =220 Democratic Independent = = To do: Find the total for each row and column b) Construct a relative frequency marginal distribution Gender Party Female Male relative frequency marginal distribution Republican Democratic Independent =405/802= To do: Divide the row/column total by the sample size 4.4

26 Contingency Tables: Part 3 of 3 c) Construct a conditional distribution of party affiliation by gender Gender Party Female Male Republican =105/405=.259 =115/397=.290 Democratic Independent Total 1 1 To do: Divide the each cell by its column total d) Is gender associated with party affiliation? If so, how? Yes; males are more likely to be Independents and less likely to be democrats. 4.4

Stats Review chapters 7-8

Stats Review chapters 7-8 Stats Review chapters 7-8 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

More information

IQR Rule for Outliers

IQR Rule for Outliers 1. Arrange data in order. IQR Rule for Outliers 2. Calculate first quartile (Q1), third quartile (Q3) and the interquartile range (IQR=Q3-Q1). CO2 emissions example: Q1=0.9, Q3=6.05, IQR=5.15. 3. Compute

More information

Technology Step-by-Step Using StatCrunch

Technology Step-by-Step Using StatCrunch Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate

More information

Chapter 2: Exploring Data with Graphs and Numerical Summaries. Graphical Measures- Graphs are used to describe the shape of a data set.

Chapter 2: Exploring Data with Graphs and Numerical Summaries. Graphical Measures- Graphs are used to describe the shape of a data set. Page 1 of 16 Chapter 2: Exploring Data with Graphs and Numerical Summaries Graphical Measures- Graphs are used to describe the shape of a data set. Section 1: Types of Variables In general, variable can

More information

Chapter 3 Descriptive Statistics: Numerical Measures. Learning objectives

Chapter 3 Descriptive Statistics: Numerical Measures. Learning objectives Chapter 3 Descriptive Statistics: Numerical Measures Slide 1 Learning objectives 1. Single variable Part I (Basic) 1.1. How to calculate and use the measures of location 1.. How to calculate and use the

More information

Exercise 1.12 (Pg. 22-23)

Exercise 1.12 (Pg. 22-23) Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

More information

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number 1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression

More information

Data Mining Part 2. Data Understanding and Preparation 2.1 Data Understanding Spring 2010

Data Mining Part 2. Data Understanding and Preparation 2.1 Data Understanding Spring 2010 Data Mining Part 2. and Preparation 2.1 Spring 2010 Instructor: Dr. Masoud Yaghini Introduction Outline Introduction Measuring the Central Tendency Measuring the Dispersion of Data Graphic Displays References

More information

College of the Canyons Math 140 Exam 1 Amy Morrow. Name:

College of the Canyons Math 140 Exam 1 Amy Morrow. Name: Name: Answer the following questions NEATLY. Show all necessary work directly on the exam. Scratch paper will be discarded unread. One point each part unless otherwise marked. 1. Owners of an exercise

More information

Exploratory data analysis (Chapter 2) Fall 2011

Exploratory data analysis (Chapter 2) Fall 2011 Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,

More information

F. Farrokhyar, MPhil, PhD, PDoc

F. Farrokhyar, MPhil, PhD, PDoc Learning objectives Descriptive Statistics F. Farrokhyar, MPhil, PhD, PDoc To recognize different types of variables To learn how to appropriately explore your data How to display data using graphs How

More information

Name: Date: Use the following to answer questions 2-3:

Name: Date: Use the following to answer questions 2-3: Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student

More information

Chapter 3: Data Description Numerical Methods

Chapter 3: Data Description Numerical Methods Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,

More information

Stats Review Chapters 5-6

Stats Review Chapters 5-6 Stats Review Chapters 5-6 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

More information

Calculate Confidence Intervals Using the TI Graphing Calculator

Calculate Confidence Intervals Using the TI Graphing Calculator Calculate Confidence Intervals Using the TI Graphing Calculator Confidence Interval for Population Proportion p Confidence Interval for Population μ (σ is known 1 Select: STAT / TESTS / 1-PropZInt x: number

More information

10-3 Measures of Central Tendency and Variation

10-3 Measures of Central Tendency and Variation 10-3 Measures of Central Tendency and Variation So far, we have discussed some graphical methods of data description. Now, we will investigate how statements of central tendency and variation can be used.

More information

UNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences Midterm Test March 2014

UNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences Midterm Test March 2014 UNIVERSITY OF TORONTO SCARBOROUGH Department of Computer and Mathematical Sciences Midterm Test March 2014 STAB22H3 Statistics I Duration: 1 hour and 45 minutes Last Name: First Name: Student number: Aids

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 3 (b) 51

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 3 (b) 51 Chapter 2- Problems to look at Use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class. 1) Height (in inches) 1)

More information

Variables. Exploratory Data Analysis

Variables. Exploratory Data Analysis Exploratory Data Analysis Exploratory Data Analysis involves both graphical displays of data and numerical summaries of data. A common situation is for a data set to be represented as a matrix. There is

More information

The Dummy s Guide to Data Analysis Using SPSS

The Dummy s Guide to Data Analysis Using SPSS The Dummy s Guide to Data Analysis Using SPSS Mathematics 57 Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved TABLE OF CONTENTS PAGE Helpful Hints for All Tests...1 Tests

More information

STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI

STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI STATS8: Introduction to Biostatistics Data Exploration Babak Shahbaba Department of Statistics, UCI Introduction After clearly defining the scientific problem, selecting a set of representative members

More information

Introduction to Regression. Dr. Tom Pierce Radford University

Introduction to Regression. Dr. Tom Pierce Radford University Introduction to Regression Dr. Tom Pierce Radford University In the chapter on correlational techniques we focused on the Pearson R as a tool for learning about the relationship between two variables.

More information

Stats Review Chapters 9-10

Stats Review Chapters 9-10 Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

More information

Descriptive Statistics. Frequency Distributions and Their Graphs 2.1. Frequency Distributions. Chapter 2

Descriptive Statistics. Frequency Distributions and Their Graphs 2.1. Frequency Distributions. Chapter 2 Chapter Descriptive Statistics.1 Frequency Distributions and Their Graphs Frequency Distributions A frequency distribution is a table that shows classes or intervals of data with a count of the number

More information

First Midterm Exam (MATH1070 Spring 2012)

First Midterm Exam (MATH1070 Spring 2012) First Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notecard. Calculators are allowed, but other electronics are prohibited. 1. [40pts] Multiple Choice Problems

More information

Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.

Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p. Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under

More information

Final Exam Practice Problem Answers

Final Exam Practice Problem Answers Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal

More information

MTH 140 Statistics Videos

MTH 140 Statistics Videos MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative

More information

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

More information

Elementary Statistics. Summarizing Raw Data. In Frequency Distribution Table

Elementary Statistics. Summarizing Raw Data. In Frequency Distribution Table Summarizing Raw Data In Frequency Distribution Table 1 / 37 What is a Raw Data? Raw Data (sometimes called source data) is data that has not been processed for meaningful use. What is a Frequency Distribution

More information

2. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2006 model motor vehicles.

2. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2006 model motor vehicles. Math 1530-017 Exam 1 February 19, 2009 Name Student Number E There are five possible responses to each of the following multiple choice questions. There is only on BEST answer. Be sure to read all possible

More information

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96 1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

More information

Copyright 2013 by Laura Schultz. All rights reserved. Page 1 of 6

Copyright 2013 by Laura Schultz. All rights reserved. Page 1 of 6 Using Your TI-NSpire Calculator: Linear Correlation and Regression Dr. Laura Schultz Statistics I This handout describes how to use your calculator for various linear correlation and regression applications.

More information

x Measures of Central Tendency for Ungrouped Data Chapter 3 Numerical Descriptive Measures Example 3-1 Example 3-1: Solution

x Measures of Central Tendency for Ungrouped Data Chapter 3 Numerical Descriptive Measures Example 3-1 Example 3-1: Solution Chapter 3 umerical Descriptive Measures 3.1 Measures of Central Tendency for Ungrouped Data 3. Measures of Dispersion for Ungrouped Data 3.3 Mean, Variance, and Standard Deviation for Grouped Data 3.4

More information

Example: Boats and Manatees

Example: Boats and Manatees Figure 9-6 Example: Boats and Manatees Slide 1 Given the sample data in Table 9-1, find the value of the linear correlation coefficient r, then refer to Table A-6 to determine whether there is a significant

More information

Statistics and research

Statistics and research Statistics and research Usaneya Perngparn Chitlada Areesantichai Drug Dependence Research Center (WHOCC for Research and Training in Drug Dependence) College of Public Health Sciences Chulolongkorn University,

More information

Minitab Guide. This packet contains: A Friendly Guide to Minitab. Minitab Step-By-Step

Minitab Guide. This packet contains: A Friendly Guide to Minitab. Minitab Step-By-Step Minitab Guide This packet contains: A Friendly Guide to Minitab An introduction to Minitab; including basic Minitab functions, how to create sets of data, and how to create and edit graphs of different

More information

MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW. Ch 1-3. One problem similar to the problems below will be included in the final

MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW. Ch 1-3. One problem similar to the problems below will be included in the final MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW Ch 1-3 One problem similar to the problems below will be included in the final 1.This table presents the price distribution of shoe styles offered

More information

Inferential Statistics

Inferential Statistics Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

More information

MAT 12O ELEMENTARY STATISTICS I

MAT 12O ELEMENTARY STATISTICS I LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 12O ELEMENTARY STATISTICS I 3 Lecture Hours, 1 Lab Hour, 3 Credits Pre-Requisite:

More information

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo Readings: Ha and Ha Textbook - Chapters 1 8 Appendix D & E (online) Plous - Chapters 10, 11, 12 and 14 Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability

More information

5/31/2013. 6.1 Normal Distributions. Normal Distributions. Chapter 6. Distribution. The Normal Distribution. Outline. Objectives.

5/31/2013. 6.1 Normal Distributions. Normal Distributions. Chapter 6. Distribution. The Normal Distribution. Outline. Objectives. The Normal Distribution C H 6A P T E R The Normal Distribution Outline 6 1 6 2 Applications of the Normal Distribution 6 3 The Central Limit Theorem 6 4 The Normal Approximation to the Binomial Distribution

More information

The right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median

The right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median CONDENSED LESSON 2.1 Box Plots In this lesson you will create and interpret box plots for sets of data use the interquartile range (IQR) to identify potential outliers and graph them on a modified box

More information

Chapter 15 Multiple Choice Questions (The answers are provided after the last question.)

Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) 1. What is the median of the following set of scores? 18, 6, 12, 10, 14? a. 10 b. 14 c. 18 d. 12 2. Approximately

More information

Lecture 1: Review and Exploratory Data Analysis (EDA)

Lecture 1: Review and Exploratory Data Analysis (EDA) Lecture 1: Review and Exploratory Data Analysis (EDA) Sandy Eckel seckel@jhsph.edu Department of Biostatistics, The Johns Hopkins University, Baltimore USA 21 April 2008 1 / 40 Course Information I Course

More information

Numerical Measures of Central Tendency

Numerical Measures of Central Tendency Numerical Measures of Central Tendency Often, it is useful to have special numbers which summarize characteristics of a data set These numbers are called descriptive statistics or summary statistics. A

More information

Descriptive Statistics

Descriptive Statistics Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

More information

StatTools Assignment #1, Winter 2007 This assignment has three parts.

StatTools Assignment #1, Winter 2007 This assignment has three parts. StatTools Assignment #1, Winter 2007 This assignment has three parts. Before beginning this assignment, be sure to carefully read the General Instructions document that is located on the StatTools Assignments

More information

GCSE HIGHER Statistics Key Facts

GCSE HIGHER Statistics Key Facts GCSE HIGHER Statistics Key Facts Collecting Data When writing questions for questionnaires, always ensure that: 1. the question is worded so that it will allow the recipient to give you the information

More information

Describing Data. We find the position of the central observation using the formula: position number =

Describing Data. We find the position of the central observation using the formula: position number = HOSP 1207 (Business Stats) Learning Centre Describing Data This worksheet focuses on describing data through measuring its central tendency and variability. These measurements will give us an idea of what

More information

Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools. Tools for Summarizing Data Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

More information

Week 11 Lecture 2: Analyze your data: Descriptive Statistics, Correct by Taking Log

Week 11 Lecture 2: Analyze your data: Descriptive Statistics, Correct by Taking Log Week 11 Lecture 2: Analyze your data: Descriptive Statistics, Correct by Taking Log Instructor: Eakta Jain CIS 6930, Research Methods for Human-centered Computing Scribe: Chris(Yunhao) Wan, UFID: 1677-3116

More information

E205 Final: Version B

E205 Final: Version B Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random

More information

Numerical Summarization of Data OPRE 6301

Numerical Summarization of Data OPRE 6301 Numerical Summarization of Data OPRE 6301 Motivation... In the previous session, we used graphical techniques to describe data. For example: While this histogram provides useful insight, other interesting

More information

Graphing Data Presentation of Data in Visual Forms

Graphing Data Presentation of Data in Visual Forms Graphing Data Presentation of Data in Visual Forms Purpose of Graphing Data Audience Appeal Provides a visually appealing and succinct representation of data and summary statistics Provides a visually

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data. 1) Bill kept track of the number of hours he spent

More information

Mind on Statistics. Chapter 2

Mind on Statistics. Chapter 2 Mind on Statistics Chapter 2 Sections 2.1 2.3 1. Tallies and cross-tabulations are used to summarize which of these variable types? A. Quantitative B. Mathematical C. Continuous D. Categorical 2. The table

More information

Statistics 151 Practice Midterm 1 Mike Kowalski

Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and

More information

Can Gas Prices be Predicted?

Can Gas Prices be Predicted? Can Gas Prices be Predicted? Chris Vaughan, Reynolds High School A Statistical Analysis of Annual Gas Prices from 1976-2005 Level/Course: This lesson can be used and modified for teaching High School Math,

More information

vs. relative cumulative frequency

vs. relative cumulative frequency Variable - what we are measuring Quantitative - numerical where mathematical operations make sense. These have UNITS Categorical - puts individuals into categories Numbers don't always mean Quantitative...

More information

Chapter 2. Objectives. Tabulate Qualitative Data. Frequency Table. Descriptive Statistics: Organizing, Displaying and Summarizing Data.

Chapter 2. Objectives. Tabulate Qualitative Data. Frequency Table. Descriptive Statistics: Organizing, Displaying and Summarizing Data. Objectives Chapter Descriptive Statistics: Organizing, Displaying and Summarizing Data Student should be able to Organize data Tabulate data into frequency/relative frequency tables Display data graphically

More information

Algebra I: Lesson 5-4 (5074) SAS Curriculum Pathways

Algebra I: Lesson 5-4 (5074) SAS Curriculum Pathways Two-Variable Quantitative Data: Lesson Summary with Examples Bivariate data involves two quantitative variables and deals with relationships between those variables. By plotting bivariate data as ordered

More information

Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

More information

Multiple Choice Questions

Multiple Choice Questions Multiple Choice Questions 1. A fast- food restaurant chain with 700 outlets in the United States describes the geographic location of its restaurants with the accompanying table of percentages. A restaurant

More information

MEASURES OF VARIATION

MEASURES OF VARIATION NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are

More information

AP * Statistics Review. Descriptive Statistics

AP * Statistics Review. Descriptive Statistics AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

More information

, has mean A) 0.3. B) the smaller of 0.8 and 0.5. C) 0.15. D) which cannot be determined without knowing the sample results.

, has mean A) 0.3. B) the smaller of 0.8 and 0.5. C) 0.15. D) which cannot be determined without knowing the sample results. BA 275 Review Problems - Week 9 (11/20/06-11/24/06) CD Lessons: 69, 70, 16-20 Textbook: pp. 520-528, 111-124, 133-141 An SRS of size 100 is taken from a population having proportion 0.8 of successes. An

More information

Applied Statistics Handbook

Applied Statistics Handbook Applied Statistics Handbook Phil Crewson Version 1. Applied Statistics Handbook Copyright 006, AcaStat Software. All rights Reserved. http://www.acastat.com Protected under U.S. Copyright and international

More information

Data Analysis: Describing Data - Descriptive Statistics

Data Analysis: Describing Data - Descriptive Statistics WHAT IT IS Return to Table of ontents Descriptive statistics include the numbers, tables, charts, and graphs used to describe, organize, summarize, and present raw data. Descriptive statistics are most

More information

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

c. Construct a boxplot for the data. Write a one sentence interpretation of your graph. MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?

More information

MATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!

MATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing! MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics

More information

2 Describing, Exploring, and

2 Describing, Exploring, and 2 Describing, Exploring, and Comparing Data This chapter introduces the graphical plotting and summary statistics capabilities of the TI- 83 Plus. First row keys like \ R (67$73/276 are used to obtain

More information

Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),

Chapter 10. Key Ideas Correlation, Correlation Coefficient (r), Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables

More information

DESCRIPTIVE STATISTICS & DATA PRESENTATION*

DESCRIPTIVE STATISTICS & DATA PRESENTATION* Level 1 Level 2 Level 3 Level 4 0 0 0 0 evel 1 evel 2 evel 3 Level 4 DESCRIPTIVE STATISTICS & DATA PRESENTATION* Created for Psychology 41, Research Methods by Barbara Sommer, PhD Psychology Department

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. STA 2023 WEISS Ch apters 1, 2 3 4 Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The table below shows

More information

Center: Finding the Median. Median. Spread: Home on the Range. Center: Finding the Median (cont.)

Center: Finding the Median. Median. Spread: Home on the Range. Center: Finding the Median (cont.) Center: Finding the Median When we think of a typical value, we usually look for the center of the distribution. For a unimodal, symmetric distribution, it s easy to find the center it s just the center

More information

AP Statistics 2011 Scoring Guidelines

AP Statistics 2011 Scoring Guidelines AP Statistics 2011 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2 (b) 1

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2 (b) 1 Unit 2 Review Name Use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class. 1) Miles (per day) 1-2 9 3-4 22 5-6

More information

EXAM #1 (Example) Instructor: Ela Jackiewicz. Relax and good luck!

EXAM #1 (Example) Instructor: Ela Jackiewicz. Relax and good luck! STP 231 EXAM #1 (Example) Instructor: Ela Jackiewicz Honor Statement: I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.

More information

STAT 155 Introductory Statistics. Lecture 5: Density Curves and Normal Distributions (I)

STAT 155 Introductory Statistics. Lecture 5: Density Curves and Normal Distributions (I) The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Lecture 5: Density Curves and Normal Distributions (I) 9/12/06 Lecture 5 1 A problem about Standard Deviation A variable

More information

CALCULATIONS & STATISTICS

CALCULATIONS & STATISTICS CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents

More information

Chapter 23. Inferences for Regression

Chapter 23. Inferences for Regression Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily

More information

MCQ S OF MEASURES OF CENTRAL TENDENCY

MCQ S OF MEASURES OF CENTRAL TENDENCY MCQ S OF MEASURES OF CENTRAL TENDENCY MCQ No 3.1 Any measure indicating the centre of a set of data, arranged in an increasing or decreasing order of magnitude, is called a measure of: (a) Skewness (b)

More information

How Does My TI-84 Do That

How Does My TI-84 Do That How Does My TI-84 Do That A guide to using the TI-84 for statistics Austin Peay State University Clarksville, Tennessee How Does My TI-84 Do That A guide to using the TI-84 for statistics Table of Contents

More information

SOME NOTES ON STATISTICAL INTERPRETATION. Below I provide some basic notes on statistical interpretation for some selected procedures.

SOME NOTES ON STATISTICAL INTERPRETATION. Below I provide some basic notes on statistical interpretation for some selected procedures. 1 SOME NOTES ON STATISTICAL INTERPRETATION Below I provide some basic notes on statistical interpretation for some selected procedures. The information provided here is not exhaustive. There is more to

More information

Homework Questions? A Look at Categorical Variables. Math 140. Chapter 3 1. Two Types of Questions

Homework Questions? A Look at Categorical Variables. Math 140. Chapter 3 1. Two Types of Questions Homework Questions? Two Types of Questions 1. Conceptual questions Answered in the beginning of class, as part of class Just ask. 2. HW questions on specific problems Answered during office hours Answered

More information

GCSE Statistics Revision notes

GCSE Statistics Revision notes GCSE Statistics Revision notes Collecting data Sample This is when data is collected from part of the population. There are different methods for sampling Random sampling, Stratified sampling, Systematic

More information

A Guide for a Selection of SPSS Functions

A Guide for a Selection of SPSS Functions A Guide for a Selection of SPSS Functions IBM SPSS Statistics 19 Compiled by Beth Gaedy, Math Specialist, Viterbo University - 2012 Using documents prepared by Drs. Sheldon Lee, Marcus Saegrove, Jennifer

More information

Monopoly and Regression

Monopoly and Regression Math Objectives Students will analyze the linear association between two variables and interpret the association in the context of a given scenario. Students will calculate a least-squares regression line

More information

Simple Regression Theory II 2010 Samuel L. Baker

Simple Regression Theory II 2010 Samuel L. Baker SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the

More information

ACTM State Exam-Statistics

ACTM State Exam-Statistics ACTM State Exam-Statistics For the 25 multiple-choice questions, make your answer choice and record it on the answer sheet provided. Once you have completed that section of the test, proceed to the tie-breaker

More information

Exam # 1 STAT The number of people from the state of Alaska الاسكا) (ولاية who voted for a Republican

Exam # 1 STAT The number of people from the state of Alaska الاسكا) (ولاية who voted for a Republican King Abdulaziz University Faculty of Sciences Statistics Department Name: ID No: Exam # 1 STAT 11 First Term 149-143H Section: 6 You have 6 questions in 7 pages. You have 1 minutes to solve the exam. Please

More information

Report of for Chapter 2 pretest

Report of for Chapter 2 pretest Report of for Chapter 2 pretest Exam: Chapter 2 pretest Category: Organizing and Graphing Data 1. "For our study of driving habits, we recorded the speed of every fifth vehicle on Drury Lane. Nearly every

More information

Mathematics Online Instructional Materials Correlation to the 2009 Algebra I Standards of Learning and Curriculum Framework

Mathematics Online Instructional Materials Correlation to the 2009 Algebra I Standards of Learning and Curriculum Framework Provider York County School Division Course Syllabus URL http://yorkcountyschools.org/virtuallearning/coursecatalog.aspx Course Title Algebra I AB Last Updated 2010 - A.1 The student will represent verbal

More information

Lecture 7 Cogsci 109. Thurs. Oct. 12, 2006

Lecture 7 Cogsci 109. Thurs. Oct. 12, 2006 Lecture 7 Cogsci 109 Thurs. Oct. 12, 2006 Announcements Homework 2 is posted. Office hours Midterm is coming up somewhere in the next couple of weeks Anything lectured on, presented in section, in the

More information

Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY

Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY 1. Introduction Besides arriving at an appropriate expression of an average or consensus value for observations of a population, it is important to

More information

Mathematics. GSE Algebra II/ Advanced Algebra Unit 7: Inferences & Conclusions from Data

Mathematics. GSE Algebra II/ Advanced Algebra Unit 7: Inferences & Conclusions from Data Georgia Standards of Excellence Curriculum Frameworks Mathematics GSE Algebra II/ Advanced Algebra Unit 7: Inferences & Conclusions from Data These materials are for nonprofit educational purposes only.

More information

Chapter 3 Central Tendency

Chapter 3 Central Tendency Chapter 3 Central Tendency PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh Edition by Frederick J Gravetter and Larry B. Wallnau Learning Outcomes 1 2 3 4 5 6 Understand

More information

AP Statistics Semester Exam Review Chapters 1-3

AP Statistics Semester Exam Review Chapters 1-3 AP Statistics Semester Exam Review Chapters 1-3 1. Here are the IQ test scores of 10 randomly chosen fifth-grade students: 145 139 126 122 125 130 96 110 118 118 To make a stemplot of these scores, you

More information