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

Save this PDF as:

Size: px
Start display at page:

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

## Transcription

1 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 be classified as being categorical (qualitative) or quantitative. Categorical variable measures attribute, it takes values from a set of categories. Examples are gender, make of automobile, color of eyes. Quantitative variable represents the amount or quantity of something. It could be discrete or continuous. Discrete quantitative variable takes numbers that are countable, such as 0, 1, 2, 3, Example: are number of female students in APSU. Continues quantitative variable takes values from an interval, such as [0, 5]. Examples: heights of students in a class, weather temperature. Example: Questions 2.3 and 2.4 page 29. 1

2 Page 2 of 16 A proportion of a category (or relative frequency of a category) = frequency of category total number of observation. Percentage of a category = proportion 100%. A frequency table is a list the possible variable values with the frequencies for each value. Example: In a survey concerning public education, 400 school administrators were asked to rate the quality of education in the US. Their responses are summarized in the following table Rating Frequency A 35 B 260 C 93 D 12 Based on this data, answer the following questions: a) What is the proportion for the rating A schools in the US. b) What is the percentage of rating A schools in the US. c) What is the grade for the schools in the US which they got the highest percentage? What is this percentage? What can you say about the quality of the education in US based on this data? d) Construct a relative frequency table for the data. 2

3 Page 3 of 16 Section 2: Graphs Graphs for Categorical variables: We use pie chart or bar chart to describe the categorical data. Example: For the previous data. a) Construct a pie chart to describe the data b) Construct a bar chart to describe the data. Graphs for quantitative variables: We use dot plots, stem and leaf plots, or histograms. The distribution of a set of data is a graph, table, or mathematical formula that indicates the different kinds of possible observations and how often they occur. Distributions of quantitative data have shape, and the shape of a distribution can be determined by looking at dot plots, stem and leaf plots, or histograms. Example: Construct a dot plot for the following data; 1,2,3,2,2,4,2,3,5,9,5,5,5,1 Discussion (shapes of distributions): Dotplot of data 1 Dotplot of data 2 Dotplot of data data data data

4 Page 4 of 16 Stem and leaf To construct a stem-and-leaf display: Partition each observation into a stem and a leaf. Usually the stem consists of all the digits except for the final one, which is the leaf. Order the stems from the smallest to the largest in a column. Ensure that all stems in the data range are included. Record the leaf for each observation in the row corresponding to its stem. The leaves should be ordered. Example: The following data represents the prices of 19 different brands of walking shoes. Construct a stem and leaf plot to display the distribution of the data Histogram - Divide the range of the data into intervals of equal width. For discrete variable use the actual values. - Use the frequency table to construct the histogram. 4

5 Page 5 of 16 Basic Shapes Right skewed Symmetric Left skewed Example: The following data represents number of quarts of milk purchased during a particular week. Construct a histogram to describe the distribution of the data Example: The following data represents the GPAs of 30 Bucknell University freshmen, recorded at the end of the freshman year. Construct a histogram to display the distribution of the data (Choose width=0.3 for each interval). Describe shape of the distribution of the data

6 Page 6 of 16 Example: Discussion (skewness, mode, unimodal, bimodal, spread, outliers) 6

7 Page 7 of 16 Section 3: Measures of Center Summation Notation Given numbers x 1, x 2, x 3,., x n, we can express their sum x 1 + x 2 + x 3 + x x n as Example: n x i i= 1 Mean, Median, Mode A measure of center is a one-number description of a distribution or data set, and we focus on three. Mean or average: The sum of numbers divided by the total number of the numbers: Mean = n i=1 n x i Median or 50th percentile: a number that separates the lower 50% and upper 50% of the numbers. Mode: the number that occurs most frequently in the set. There can be more than one mode. Example: In the 2002 Winter Olympics, figure skater Michelle Kwan competed in the short program ladies single event. She received the following scores for technical merit: Find the mean, median, and mode. Throw out the score of 5.5 and again find the mean, median and mode. 7

8 Page 8 of 16 Remark: Properties: Resistant measures are not sensitive to extreme data. The median is resistant, the mean is not. Example: Compare the mean and median of the salaries \$13,000 \$32,000 \$45,000 with the mean and median of the salaries \$13; 000 \$32; 000 \$250; 000 Population Mean and Sample Mean The population mean µ (pronounced myoo) of a population of size N is the average of all values x 1, x 2,, x N in the population: Population mean N xi i= µ = 1. N The sample mean x (pronounced x-bar) of a sample of size n is the average of all values x 1, x 2, x n in the sample: Sample mean n xi i= x = 1. n

9 Page 9 of 16 Example: The ages in years of all seven MATH 4270 students are Find the population mean for the students ages A random sample of size three was taken from the class. The random sample was Find the sample mean of the three students' ages. Example:

10 Page 10 of 16 Sec 4: Measures of Spread Measures of spread summarize how far data are spread out. We focus on the following measurements: Standard deviation: used when the mean is the measure of center. It is the most important measure of spread. Range: the largest value minus the smallest value. Interquartile range: used when the median is the measure of center (we will talk about it in sec 5). Other Important Sums (leading up to measuring the spread) Sum of distances from the mean: ( x i x) n i= 1 Sum of squared distances from the mean: ( x i x) n i= 1 Example: History Exam Scores for four students are Fill the following table 2 x x i x 2 ( x i x) Population and Sample Standard Deviation The standard deviation measures the variation in a data set by indicating how far, on average, each number is from the mean. Population standard deviation σ : σ = N i= 1 2 ( x x) i N Sample standard deviation s: s = n i= 1 ( x i x) n 1 2

11 Page 11 of 16 Example: The ages in years for a sample of three MATH 4270 students are Find the sample standard deviation and the range. Remarks about Standard Deviation The more variation among data in a sample, the larger the standard deviation. Like the mean, the standard deviation is not resistant because its value is affected by extreme data points. Empirical Rule: For bell-shaped distributions, - about 68.27% of all possible observations lie within one σ from µ. - about 95.45% of all possible observations lie within two σ s from µ. - about 99.73% of all possible observations lie within three σ s from µ.

12 Page 12 of 16 Section 5: Five-Number Summary, Boxplots, z-scores The 1rst quartile Q 1 is the 25th percentile, and it is the median of the lower half of the data. That is 25% of the data is lower than Q 1. The 2nd quartile Q 2 is the 50 th percentile, and it is the median of the data. That is 50% of the data is lower than Q 2. The 3rd quartile Q 3 is the 75th percentile, and it is the median of the upper half of the data. That is 75% of the data is lower than Q 3. Example: Eleven students report their exam score as: Find the quartiles Example: Sixteen people reportedly watched the following numbers of hours of TV weekly: Find the quartiles. The interquartile range (IQR) is compute as IQR = Q Q (this is our third measure of spread). 3 1 The IQR is not sensitive to extreme values and is therefore a resistant measure of spread. The IQR is used as the measure of spread. Example: Compute the range and IQR for the data in the previous example.

13 Page 13 of 16 The five- number summary of data consists of the min, Q 1, Q 2, Q 3 and max Example; Compute the five- number summary for the following 100 meter race times (in seconds): Outliers Outlier(s): data value(s) that is (are) far from most of the data. Lower limit: Q1 - (1.5)(IQR) (sometime called Inner fence lower limit) Upper limit: Q3 + (1.5)(IQR) (sometime called Inner fence upper limit) Data greater than the upper limit or less than the lower limit are potential outliers. Examples: Human heights of 9'. Miles per gallon rates greater than 95. Example: Use the lower limit and upper limit to identify any potential outliers in the previous example. Boxplots To create Boxplots do the following: - Determine the 5-number summary. - Compute lower & upper limits (Inner fence). - Mark and label the quartiles with vertical lines and box them in. - Indicate all potential outliers with * and label them. - Mark and label the smallest & largest values occurring within upper and lower limits with vertical lines, and connect the lines to the box (these are called adjacent values).

14 Example: The following data represent ages of a group of people. Make a boxplot for the data and identify any outliers Page 14 of 16 Advantage of Boxplots: - Graphically display the shape of distribution of the data. - Shows the potential outliers in the data. - Graphically display the spread of the data. Example: a) What is the shape of the distribution? b) Approximate each component of the five-number summary, and interpret them.

15 Page 15 of 16 z-scores (Standardized Data) Data can be standardized so that different data sets can be compared, or to compare values within the same data set. Example: The average height of men is 69 inches with a std. of 2.8 inches. The average height of women is 63.6 inches with a std. of 2.5 inches. Michael Jordan is 78 inches tall. Rebecca Lobo is 76 inches tall. Relatively speaking, who is taller? Jordan's and Lobo's heights should be standardized relative to those of their genders so their heights can be compared. x mean If x is a variable, then z = is the standardized version or z-score of x. Calculate the z- standard deviation scores of Jordan's and Lobo's heights. Facts About z-scores The mean of the z-scores of a population is always 0. The standard deviation of the z-scores of a population is always 1. Most z-scores will fall between -3 and 3. If the z-scores of x is less than -3 or greater than 3, then x is an outlier. z-scores never have units! Example: Body temperatures of healthy human children have mean = o F and standard deviation = 0.62 o F. Your child has temperature of 101 o F. What should you do?

16 Page 16 of 16 Section 6: Misleading Graphs Examples 2.85 and 2.87 Calculator commands: To use your calculator for evaluating the descriptive statistics and more (mean, standard deviation, quartile, ) do the following: STAT Edit Enter report your data in any column (say L1) STAT CALC 1-Var Stats Enter Scroll down to see more output. Example: Use your calculator to compute mean, mode, standard deviation, and the five- number summary for the following 100 meter race times (in seconds):

### 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,

### 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,

### 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

### 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.

### 13.2 Measures of Central Tendency

13.2 Measures of Central Tendency Measures of Central Tendency For a given set of numbers, it may be desirable to have a single number to serve as a kind of representative value around which all the numbers

### 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

### Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs

Types of Variables Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Quantitative (numerical)variables: take numerical values for which arithmetic operations make sense (addition/averaging)

### 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

### Chapter 2 - Graphical Summaries of Data

Chapter 2 - Graphical Summaries of Data Data recorded in the sequence in which they are collected and before they are processed or ranked are called raw data. Raw data is often difficult to make sense

### Descriptive Statistics

Chapter 2 Descriptive Statistics 2.1 Descriptive Statistics 1 2.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Display data graphically and interpret graphs:

### Classify the data as either discrete or continuous. 2) An athlete runs 100 meters in 10.5 seconds. 2) A) Discrete B) Continuous

Chapter 2 Overview Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify as categorical or qualitative data. 1) A survey of autos parked in

### 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

### 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)

### 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

### Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics

Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),

### Practice#1(chapter1,2) Name

Practice#1(chapter1,2) Name Solve the problem. 1) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or inferential statistics? A) inferential statistics

### Introduction to Environmental Statistics. The Big Picture. Populations and Samples. Sample Data. Examples of sample data

A Few Sources for Data Examples Used Introduction to Environmental Statistics Professor Jessica Utts University of California, Irvine jutts@uci.edu 1. Statistical Methods in Water Resources by D.R. Helsel

### Summarizing and Displaying Categorical Data

Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency

### 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

Using Your TI-NSpire Calculator: Descriptive Statistics Dr. Laura Schultz Statistics I This handout is intended to get you started using your TI-Nspire graphing calculator for statistical applications.

### AP Statistics Chapter 1 Test - Multiple Choice

AP Statistics Chapter 1 Test - Multiple Choice Name: 1. The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph, we may conclude

### 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.

### 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

### Histogram. Graphs, and measures of central tendency and spread. Alternative: density (or relative frequency ) plot /13/2004

Graphs, and measures of central tendency and spread 9.07 9/13/004 Histogram If discrete or categorical, bars don t touch. If continuous, can touch, should if there are lots of bins. Sum of bin heights

### 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

### Diagrams and Graphs of Statistical Data

Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in

### The Big Picture. Describing Data: Categorical and Quantitative Variables Population. Descriptive Statistics. Community Coalitions (n = 175)

Describing Data: Categorical and Quantitative Variables Population The Big Picture Sampling Statistical Inference Sample Exploratory Data Analysis Descriptive Statistics In order to make sense of data,

### Introduction to Statistics for Psychology. Quantitative Methods for Human Sciences

Introduction to Statistics for Psychology and Quantitative Methods for Human Sciences Jonathan Marchini Course Information There is website devoted to the course at http://www.stats.ox.ac.uk/ marchini/phs.html

### ! x sum of the entries

3.1 Measures of Central Tendency (Page 1 of 16) 3.1 Measures of Central Tendency Mean, Median and Mode! x sum of the entries a. mean, x = = n number of entries Example 1 Find the mean of 26, 18, 12, 31,

### Section 3.1 Measures of Central Tendency: Mode, Median, and Mean

Section 3.1 Measures of Central Tendency: Mode, Median, and Mean One number can be used to describe the entire sample or population. Such a number is called an average. There are many ways to compute averages,

### Graphical and Tabular. Summarization of Data OPRE 6301

Graphical and Tabular Summarization of Data OPRE 6301 Introduction and Re-cap... Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that useful 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

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

### 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

### Stats Review Chapters 3-4

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

### 1.5 NUMERICAL REPRESENTATION OF DATA (Sample Statistics)

1.5 NUMERICAL REPRESENTATION OF DATA (Sample Statistics) As well as displaying data graphically we will often wish to summarise it numerically particularly if we wish to compare two or more data sets.

### 32 Measures of Central Tendency and Dispersion

32 Measures of Central Tendency and Dispersion In this section we discuss two important aspects of data which are its center and its spread. The mean, median, and the mode are measures of central tendency

### 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

### 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

### 3: Summary Statistics

3: Summary Statistics Notation Let s start by introducing some notation. Consider the following small data set: 4 5 30 50 8 7 4 5 The symbol n represents the sample size (n = 0). The capital letter X denotes

### 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

### Exploratory Data Analysis

Exploratory Data Analysis Johannes Schauer johannes.schauer@tugraz.at Institute of Statistics Graz University of Technology Steyrergasse 17/IV, 8010 Graz www.statistics.tugraz.at February 12, 2008 Introduction

### 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

### Chapter 2: Frequency Distributions and Graphs

Chapter 2: Frequency Distributions and Graphs Learning Objectives Upon completion of Chapter 2, you will be able to: Organize the data into a table or chart (called a frequency distribution) Construct

### Interpreting Data in Normal Distributions

Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,

### Chapter 1: Exploring Data

Chapter 1: Exploring Data Chapter 1 Review 1. As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student

### 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

### Central Tendency. n Measures of Central Tendency: n Mean. n Median. n Mode

Central Tendency Central Tendency n A single summary score that best describes the central location of an entire distribution of scores. n Measures of Central Tendency: n Mean n The sum of all scores divided

### MBA 611 STATISTICS AND QUANTITATIVE METHODS

MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain

### 1.3 Measuring Center & Spread, The Five Number Summary & Boxplots. Describing Quantitative Data with Numbers

1.3 Measuring Center & Spread, The Five Number Summary & Boxplots Describing Quantitative Data with Numbers 1.3 I can n Calculate and interpret measures of center (mean, median) in context. n Calculate

### Lesson Plan. Mean Count

S.ID.: Central Tendency and Dispersion S.ID.: Central Tendency and Dispersion Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape

### MATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MATH 3/GRACEY PRACTICE EXAM/CHAPTERS 2-3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The frequency distribution

### Describing, Exploring, and Comparing Data

24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter

### Sta 309 (Statistics And Probability for Engineers)

Instructor: Prof. Mike Nasab Sta 309 (Statistics And Probability for Engineers) Chapter 2 Organizing and Summarizing Data Raw Data: When data are collected in original form, they are called raw data. The

### 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

### consider the number of math classes taken by math 150 students. how can we represent the results in one number?

ch 3: numerically summarizing data - center, spread, shape 3.1 measure of central tendency or, give me one number that represents all the data consider the number of math classes taken by math 150 students.

### Pie Charts. proportion of ice-cream flavors sold annually by a given brand. AMS-5: Statistics. Cherry. Cherry. Blueberry. Blueberry. Apple.

Graphical Representations of Data, Mean, Median and Standard Deviation In this class we will consider graphical representations of the distribution of a set of data. The goal is to identify the range of

### 4. Introduction to Statistics

Statistics for Engineers 4-1 4. Introduction to Statistics Descriptive Statistics Types of data A variate or random variable is a quantity or attribute whose value may vary from one unit of investigation

### Home Runs, Statistics, and Probability

NATIONAL MATH + SCIENCE INITIATIVE Mathematics American League AL Central AL West AL East National League NL West NL East Level 7 th grade in a unit on graphical displays Connection to AP* Graphical Display

### 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

### CC Investigation 5: Histograms and Box Plots

Content Standards 6.SP.4, 6.SP.5.c CC Investigation 5: Histograms and Box Plots At a Glance PACING 3 days Mathematical Goals DOMAIN: Statistics and Probability Display numerical data in histograms and

### Statistics Summary (prepared by Xuan (Tappy) He)

Statistics Summary (prepared by Xuan (Tappy) He) Statistics is the practice of collecting and analyzing data. The analysis of statistics is important for decision making in events where there are uncertainties.

### DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 1

DESCRIPTIVE STATISTICS - CHAPTERS 1 & 2 1 OVERVIEW STATISTICS PANIK...THE THEORY AND METHODS OF COLLECTING, ORGANIZING, PRESENTING, ANALYZING, AND INTERPRETING DATA SETS SO AS TO DETERMINE THEIR ESSENTIAL

### 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

### + Chapter 1 Exploring Data

Chapter 1 Exploring Data Introduction: Data Analysis: Making Sense of Data 1.1 Analyzing Categorical Data 1.2 Displaying Quantitative Data with Graphs 1.3 Describing Quantitative Data with Numbers Introduction

### 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

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

Exam Name 1) A recent report stated ʺBased on a sample of 90 truck drivers, there is evidence to indicate that, on average, independent truck drivers earn more than company -hired truck drivers.ʺ Does

### Box-and-Whisker Plots

Learning Standards HSS-ID.A. HSS-ID.A.3 3 9 23 62 3 COMMON CORE.2 Numbers of First Cousins 0 3 9 3 45 24 8 0 3 3 6 8 32 8 0 5 4 Box-and-Whisker Plots Essential Question How can you use a box-and-whisker

### STATISTICS FOR PSYCH MATH REVIEW GUIDE

STATISTICS FOR PSYCH MATH REVIEW GUIDE ORDER OF OPERATIONS Although remembering the order of operations as BEDMAS may seem simple, it is definitely worth reviewing in a new context such as statistics formulae.

### The Ordered Array. Chapter Chapter Goals. Organizing and Presenting Data Graphically. Before you continue... Stem and Leaf Diagram

Chapter - Chapter Goals After completing this chapter, you should be able to: Construct a frequency distribution both manually and with Excel Construct and interpret a histogram Chapter Presenting Data

### Lecture 2: Descriptive Statistics and Exploratory Data Analysis

Lecture 2: Descriptive Statistics and Exploratory Data Analysis Further Thoughts on Experimental Design 16 Individuals (8 each from two populations) with replicates Pop 1 Pop 2 Randomly sample 4 individuals

### SPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)

Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer

### 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

### AP Statistics Solutions to Packet 2

AP Statistics Solutions to Packet 2 The Normal Distributions Density Curves and the Normal Distribution Standard Normal Calculations HW #9 1, 2, 4, 6-8 2.1 DENSITY CURVES (a) Sketch a density curve that

### DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability

DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability RIT Score Range: Below 171 Below 171 Data Analysis and Statistics Solves simple problems based on data from tables* Compares

### Chapter 3. The Normal Distribution

Chapter 3. The Normal Distribution Topics covered in this chapter: Z-scores Normal Probabilities Normal Percentiles Z-scores Example 3.6: The standard normal table The Problem: What proportion of observations

### 2 Descriptive statistics with R

Biological data analysis, Tartu 2006/2007 1 2 Descriptive statistics with R Before starting with basic concepts of data analysis, one should be aware of different types of data and ways to organize data

### Statistics Chapter 2

Statistics Chapter 2 Frequency Tables A frequency table organizes quantitative data. partitions data into classes (intervals). shows how many data values are in each class. Test Score Number of Students

### 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

### Using SPSS, Chapter 2: Descriptive Statistics

1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,

### Foundation of Quantitative Data Analysis

Foundation of Quantitative Data Analysis Part 1: Data manipulation and descriptive statistics with SPSS/Excel HSRS #10 - October 17, 2013 Reference : A. Aczel, Complete Business Statistics. Chapters 1

### The Big 50 Revision Guidelines for S1

The Big 50 Revision Guidelines for S1 If you can understand all of these you ll do very well 1. Know what is meant by a statistical model and the Modelling cycle of continuous refinement 2. Understand

### 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

### HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

Mathematics Revision Guides Histograms, Cumulative Frequency and Box Plots Page 1 of 25 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

### 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.

### Recitation, Week 3: Basic Descriptive Statistics and Measures of Central Tendency:

Recitation, Week 3: Basic Descriptive Statistics and Measures of Central Tendency: 1. What does Healey mean by data reduction? a. Data reduction involves using a few numbers to summarize the distribution

### 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

### 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,

### Bar Graphs and Dot Plots

CONDENSED L E S S O N 1.1 Bar Graphs and Dot Plots In this lesson you will interpret and create a variety of graphs find some summary values for a data set draw conclusions about a data set based on graphs

### Chapter 10 - Practice Problems 1

Chapter 10 - Practice Problems 1 1. A researcher is interested in determining if one could predict the score on a statistics exam from the amount of time spent studying for the exam. In this study, the

### Statistics 101 Homework 2

Statistics 101 Homework 2 Solution Reading: January 23 January 25 Chapter 4 January 28 Chapter 5 Assignment: 1. As part of a physiology study participants had their heart rate (beats per minute) taken

### 4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"

Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses

### STAT355 - Probability & Statistics

STAT355 - Probability & Statistics Instructor: Kofi Placid Adragni Fall 2011 Chap 1 - Overview and Descriptive Statistics 1.1 Populations, Samples, and Processes 1.2 Pictorial and Tabular Methods in Descriptive

### 3.1 Measures of central tendency: mode, median, mean, midrange Dana Lee Ling (2012)

3.1 Measures of central tendency: mode, median, mean, midrange Dana Lee Ling (2012) Mode The mode is the value that occurs most frequently in the data. Spreadsheet programs such as Microsoft Excel or OpenOffice.org

### Summary of Formulas and Concepts. Descriptive Statistics (Ch. 1-4)

Summary of Formulas and Concepts Descriptive Statistics (Ch. 1-4) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume

### a. mean b. interquartile range c. range d. median

3. Since 4. The HOMEWORK 3 Due: Feb.3 1. A set of data are put in numerical order, and a statistic is calculated that divides the data set into two equal parts with one part below it and the other part

### The Normal Distribution

Chapter 6 The Normal Distribution 6.1 The Normal Distribution 1 6.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Recognize the normal probability distribution

### Statistics Revision Sheet Question 6 of Paper 2

Statistics Revision Sheet Question 6 of Paper The Statistics question is concerned mainly with the following terms. The Mean and the Median and are two ways of measuring the average. sumof values no. of