Sampling, frequency distribution, graphs, measures of central tendency, measures of dispersion

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Sampling, frequency distribution, graphs, measures of central tendency, measures of dispersion"

Transcription

1 Statistics Basics Sampling, frequency distribution, graphs, measures of central tendency, measures of dispersion Part 1: Sampling, Frequency Distributions, and Graphs The method of collecting, organizing, analyzing, and interpreting data, as well as drawing conclusions based on the data is called statistics. Methodology is divided into two main areas. Descriptive Statistics: Collecting, organizing, summarizing, and presenting data. Inferential Statistics: Making generalizations about and drawing conclusions from the data collected. We have the following basic concepts in statistics: Population: Set containing all the people or objects whose properties are to be described and analyzed by the data collector. Sample: Subset or subgroup of the population. Representative Sample: A sample that exhibits characteristics typical of those possessed by the target population. A random sample is a sample obtained in such a way that every element in the population has an equal chance of being selected. Methodology: Identify each element in the population. Assign numbers to each element in the population. Randomly select numbers. Assign the elements in the population who have those numbers to the sample set. A frequency distribution is an arrangement of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample.

2 Ex: If 100 people rate a five-point Likert scale assessing their agreement with a statement on a scale on which 1 denotes strong agreement and 5 strong disagreement, the frequency distribution of their responses might look like: Rank Degree of agreement Number 1 Strongly agree 20 2 Agree somewhat 30 3 Not sure 20 4 Disagree somewhat 15 5 Strongly disagree 15 We can group the frequencies into classes that are meaningful for the data. Ex: The heights of the students in a class could be organized into the following frequency table. Height range Number of students Cumulative number feet feet feet feet The class has 4.5 as the lower class limit and 4.9 as the upper class limit. The class width is 0.5. A frequency distribution shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data e.g. to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc. A very used tool in statistics is the graph: Histogram: A bar graph with bars that touch can be used to visually display the data. Frequency Polygon: A line graph formed by connecting dots in the midpoint of each bar of the histogram Stem-and-Leaf Plots: This plot is constructed by separating each data item into two parts: Stem consists of the ten s digit and Leaf consists of the units digit. Ex: An example histogram of the heights of 31 Black Cherry trees:

3 Ex: A frequency polygon for a data set containing the scores 1,1,2,2,2,2,2,3,3,3,3,4,4,5: Ex: A steam-and-leaf plot suggesting the ages of people at a family reunion. In this table the steam 3 and leaf 4 means that one people has the age of 34 years.

4 Part 2: Measures of Central Tendency Mean: The sum of the data items divided by the number of items., where Σx represents the sum of all the data items and n represents the number of items. Ex: The arithmetic mean of six values: 34, 27, 45, 55, 22, 34 is When many data values occur more than once and a frequency distribution is used to organize the data, we can use the following formula to calculate the mean:, Where x represents each data value, f represents the frequency of that data value, and Σxf represents the sum of all the products obtained by multiplying each data value by its frequency. Here the number n represents the total frequency of the distribution. Ex: Ages of Statistics Students in Spring 2000: Ages Frequency

5 Estimate the mean for this set of data. Class Midpoint Frequency m f The sum of the product of the midpoints and frequencies is 1005 (add the values in the last column). Divide this number by 40 (the total of the frequencies), and we estimate the mean to be Median is the data item in the middle of each set of ranked, or ordered, data. To find the median of a group of data items: Ex: is 4. Arrange the data items in order, from smallest to largest. If the number of data items is odd, the median is the data item in the middle of the list. If the number of data items is even, the median is the mean of the two middle data items. a. The median for the set {2,2,5,3,2,5,4,7,4}: we have {2,2,2,3,4,4,5,5,7}, so the median b. The median for the set {4,5,2,9,1,4,9,6}: we have {1,2,4,4,5,6,9,9}, so we add the middle terms = 9 and divide by 2: the mean is 4.5. Ex: Finding the Median for a Frequency Distribution of the stress-level rating: Stress Rating x Frequency f

6 There are 151 data items in this table so n = 151. The median is the value in the 76 position. Count down the frequency column in the distribution until we identify the 76 th data item; we find it to be 7. So, the median stress-level rating is 7 The mode is the data value that occurs most often in a data set. If more than one data value has the highest frequency, then each of these data values is a mode. If no data items are repeated, then the data set has no mode. Ex: Find the mode for the following groups of data: 7, 2, 4, 7, 8, 10. The mode is 7. The midrange is found by adding the lowest and highest data values and dividing the sum by 2:. 2 Ex: The midrange for the data set {10, 23, 8, 9, 14, 11} is Part 3: Measures of Dispersion The range is used to describe the spread of data items in a data set. Two of the most common measures of dispersion are range and standard deviation. It is given by the difference between the highest and the lowest data values in a data set:

7 Range = highest data value lowest data value Ex: Honolulu s hottest day is 89º and its coldest day is 61º. The range in temperature is: 89º 61º = 28º. Ex: Find the deviations from the mean for 472 in the five data items 778, 472, 147, 106, and 82. First, the mean is = Deviation from mean = data item mean = Standard deviation is a used measurement of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average (mean, or expected value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. Computing the standard deviation for a data set: Find the mean; Find the deviation of each data item from the mean: (data item mean) Square each deviation: data item mean ; Add the squared deviations: data item mean ; Divide:, where n is the number of data items; Take the square root:. Ex: Find the standard deviation for the data set: 778, 472, 147, 106, and 82. The mean was found to be 317. Deviations: =461, =155, =-170, =-211, =-235. Square the deviations and add them: ,192. Because there are 5 items, we divide the previous number by 5-1=4 and obtain:

8 365,192 91, Finally, we apply the square root: 91, The standard deviation is approximately

A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes

A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes together with the number of data values from the set that

More information

Chapter 3: Central Tendency

Chapter 3: Central Tendency Chapter 3: Central Tendency Central Tendency In general terms, central tendency is a statistical measure that determines a single value that accurately describes the center of the distribution and represents

More information

Lecture I. Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions.

Lecture I. Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions. Lecture 1 1 Lecture I Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions. It is a process consisting of 3 parts. Lecture

More information

Frequency Distributions

Frequency Distributions Displaying Data Frequency Distributions After collecting data, the first task for a researcher is to organize and summarize the data to get a general overview of the results. Remember, this is the goal

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

Chapter 2 - Graphical Summaries of Data

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

More information

Table 2-1. Sucrose concentration (% fresh wt.) of 100 sugar beet roots. Beet No. % Sucrose. Beet No.

Table 2-1. Sucrose concentration (% fresh wt.) of 100 sugar beet roots. Beet No. % Sucrose. Beet No. Chapter 2. DATA EXPLORATION AND SUMMARIZATION 2.1 Frequency Distributions Commonly, people refer to a population as the number of individuals in a city or county, for example, all the people in California.

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

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

Organizing & Graphing Data

Organizing & Graphing Data AGSC 320 Statistical Methods Organizing & Graphing Data 1 DATA Numerical representation of reality Raw data: Data recorded in the sequence in which they are collected and before any processing Qualitative

More information

Summarizing and Displaying Categorical Data

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

More information

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

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

More information

We will use the following data sets to illustrate measures of center. DATA SET 1 The following are test scores from a class of 20 students:

We will use the following data sets to illustrate measures of center. DATA SET 1 The following are test scores from a class of 20 students: MODE The mode of the sample is the value of the variable having the greatest frequency. Example: Obtain the mode for Data Set 1 77 For a grouped frequency distribution, the modal class is the class having

More information

2. A is a subset of the population. 3. Construct a frequency distribution for the data of the grades of 25 students taking Math 11 last

2. A is a subset of the population. 3. Construct a frequency distribution for the data of the grades of 25 students taking Math 11 last Math 111 Chapter 12 Practice Test 1. If I wanted to survey 50 Cabrini College students about where they prefer to eat on campus, which would be the most appropriate way to conduct my survey? a. Find 50

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

Desciptive Statistics Qualitative data Quantitative data Graphical methods Numerical methods

Desciptive Statistics Qualitative data Quantitative data Graphical methods Numerical methods Desciptive Statistics Qualitative data Quantitative data Graphical methods Numerical methods Qualitative data Data are classified in categories Non numerical (although may be numerically codified) Elements

More information

Content DESCRIPTIVE STATISTICS. Data & Statistic. Statistics. Example: DATA VS. STATISTIC VS. STATISTICS

Content DESCRIPTIVE STATISTICS. Data & Statistic. Statistics. Example: DATA VS. STATISTIC VS. STATISTICS Content DESCRIPTIVE STATISTICS Dr Najib Majdi bin Yaacob MD, MPH, DrPH (Epidemiology) USM Unit of Biostatistics & Research Methodology School of Medical Sciences Universiti Sains Malaysia. Introduction

More information

Statistics Summary (prepared by Xuan (Tappy) He)

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.

More information

Chapter 2: Frequency Distributions and Graphs

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

More information

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

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),

More information

MBA 611 STATISTICS AND QUANTITATIVE METHODS

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

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

Use Measures of Central Tendency and Dispersion. Measures of Central Tendency

Use Measures of Central Tendency and Dispersion. Measures of Central Tendency 13.6 Use Measures of Central Tendency and Dispersion Before You analyzed surveys and samples. Now You will compare measures of central tendency and dispersion. Why? So you can analyze and compare data,

More information

Chapter 1: Using Graphs to Describe Data

Chapter 1: Using Graphs to Describe Data Department of Mathematics Izmir University of Economics Week 1 2014-2015 Introduction In this chapter we will focus on the definitions of population, sample, parameter, and statistic, the classification

More information

STATISTICS FOR PSYCH MATH REVIEW GUIDE

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.

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

Descriptive Statistics. Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion

Descriptive Statistics. Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Descriptive Statistics Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Statistics as a Tool for LIS Research Importance of statistics in research

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

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

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

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

Statistics Revision Sheet Question 6 of Paper 2

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

More information

13.2 Measures of Central Tendency

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

More information

MAT 142 College Mathematics Module #3

MAT 142 College Mathematics Module #3 MAT 142 College Mathematics Module #3 Statistics Terri Miller Spring 2009 revised March 24, 2009 1.1. Basic Terms. 1. Population, Sample, and Data A population is the set of all objects under study, a

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

Measures of Central Tendency and Variability: Summarizing your Data for Others

Measures of Central Tendency and Variability: Summarizing your Data for Others Measures of Central Tendency and Variability: Summarizing your Data for Others 1 I. Measures of Central Tendency: -Allow us to summarize an entire data set with a single value (the midpoint). 1. Mode :

More information

BNG 202 Biomechanics Lab. Descriptive statistics and probability distributions I

BNG 202 Biomechanics Lab. Descriptive statistics and probability distributions I BNG 202 Biomechanics Lab Descriptive statistics and probability distributions I Overview The overall goal of this short course in statistics is to provide an introduction to descriptive and inferential

More information

LEARNING OBJECTIVES SCALES OF MEASUREMENT: A REVIEW SCALES OF MEASUREMENT: A REVIEW DESCRIBING RESULTS DESCRIBING RESULTS 8/14/2016

LEARNING OBJECTIVES SCALES OF MEASUREMENT: A REVIEW SCALES OF MEASUREMENT: A REVIEW DESCRIBING RESULTS DESCRIBING RESULTS 8/14/2016 UNDERSTANDING RESEARCH RESULTS: DESCRIPTION AND CORRELATION LEARNING OBJECTIVES Contrast three ways of describing results: Comparing group percentages Correlating scores Comparing group means Describe

More information

Central Tendency and Variation

Central Tendency and Variation Contents 5 Central Tendency and Variation 161 5.1 Introduction............................ 161 5.2 The Mode............................. 163 5.2.1 Mode for Ungrouped Data................ 163 5.2.2 Mode

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

Northumberland Knowledge

Northumberland Knowledge Northumberland Knowledge Know Guide How to Analyse Data - November 2012 - This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about

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

Calculation example mean, median, midrange, mode, variance, and standard deviation for raw and grouped data

Calculation example mean, median, midrange, mode, variance, and standard deviation for raw and grouped data Calculation example mean, median, midrange, mode, variance, and standard deviation for raw and grouped data Raw data: 7, 8, 6, 3, 5, 5, 1, 6, 4, 10 Sorted data: 1, 3, 4, 5, 5, 6, 6, 7, 8, 10 Number of

More information

Mathematics. Probability and Statistics Curriculum Guide. Revised 2010

Mathematics. Probability and Statistics Curriculum Guide. Revised 2010 Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction

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

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

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

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

Math Chapter 2 review

Math Chapter 2 review Math 116 - Chapter 2 review Name Provide an appropriate response. 1) Suppose that a data set has a minimum value of 28 and a max of 73 and that you want 5 classes. Explain how to find the class width for

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

Each exam covers lectures from since the previous exam and up to the exam date.

Each exam covers lectures from since the previous exam and up to the exam date. Sociology 301 Exam Review Liying Luo 03.22 Exam Review: Logistics Exams must be taken at the scheduled date and time unless 1. You provide verifiable documents of unforeseen illness or family emergency,

More information

Utah Core Curriculum for Mathematics

Utah Core Curriculum for Mathematics Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions

More information

! x sum of the entries

! 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,

More information

Chapter 2 Summarizing and Graphing Data

Chapter 2 Summarizing and Graphing Data Chapter 2 Summarizing and Graphing Data 2-1 Review and Preview 2-2 Frequency Distributions 2-3 Histograms 2-4 Graphs that Enlighten and Graphs that Deceive Preview Characteristics of Data 1. Center: A

More information

CH.6 Random Sampling and Descriptive Statistics

CH.6 Random Sampling and Descriptive Statistics CH.6 Random Sampling and Descriptive Statistics Population vs Sample Random sampling Numerical summaries : sample mean, sample variance, sample range Stem-and-Leaf Diagrams Median, quartiles, percentiles,

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

The Big 50 Revision Guidelines for S1

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

More information

Sta 309 (Statistics And Probability for Engineers)

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

More information

Research Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement

Research Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value.

More information

Measures of Center Section 3-2 Definitions Mean (Arithmetic Mean)

Measures of Center Section 3-2 Definitions Mean (Arithmetic Mean) Measures of Center Section 3-1 Mean (Arithmetic Mean) AVERAGE the number obtained by adding the values and dividing the total by the number of values 1 Mean as a Balance Point 3 Mean as a Balance Point

More information

CHAPTER 3 CENTRAL TENDENCY ANALYSES

CHAPTER 3 CENTRAL TENDENCY ANALYSES CHAPTER 3 CENTRAL TENDENCY ANALYSES The next concept in the sequential statistical steps approach is calculating measures of central tendency. Measures of central tendency represent some of the most simple

More information

Methods for Describing Data Sets

Methods for Describing Data Sets 1 Methods for Describing Data Sets.1 Describing Data Graphically In this section, we will work on organizing data into a special table called a frequency table. First, we will classify the data into categories.

More information

Statistics revision. Dr. Inna Namestnikova. Statistics revision p. 1/8

Statistics revision. Dr. Inna Namestnikova. Statistics revision p. 1/8 Statistics revision Dr. Inna Namestnikova inna.namestnikova@brunel.ac.uk Statistics revision p. 1/8 Introduction Statistics is the science of collecting, analyzing and drawing conclusions from data. Statistics

More information

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1:

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1: Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 000: Page 1: DESCRIPTIVE STATISTICS - FREQUENCY DISTRIBUTIONS AND AVERAGES: Inferential and Descriptive Statistics: There are four

More information

909 responses responded via telephone survey in U.S. Results were shown by political affiliations (show graph on the board)

909 responses responded via telephone survey in U.S. Results were shown by political affiliations (show graph on the board) 1 2-1 Overview Chapter 2: Learn the methods of organizing, summarizing, and graphing sets of data, ultimately, to understand the data characteristics: Center, Variation, Distribution, Outliers, Time. (Computer

More information

Quantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality

Quantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality Quantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality 1 To help choose which type of quantitative data analysis to use either before

More information

Lean Six Sigma Training/Certification Book: Volume 1

Lean Six Sigma Training/Certification Book: Volume 1 Lean Six Sigma Training/Certification Book: Volume 1 Six Sigma Quality: Concepts & Cases Volume I (Statistical Tools in Six Sigma DMAIC process with MINITAB Applications Chapter 1 Introduction to Six Sigma,

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

2.2-Frequency Distributions

2.2-Frequency Distributions 2.2-Frequency Distributions When working with large data sets, it is often helpful to organize and summarize data by constructing a table called a frequency distribution, defined later. Because computer

More information

Graphical and Tabular. Summarization of Data OPRE 6301

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

More information

Probability and Statistics Vocabulary List (Definitions for Middle School Teachers)

Probability and Statistics Vocabulary List (Definitions for Middle School Teachers) Probability and Statistics Vocabulary List (Definitions for Middle School Teachers) B Bar graph a diagram representing the frequency distribution for nominal or discrete data. It consists of a sequence

More information

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

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)

More information

TYPES OF DATA TYPES OF VARIABLES

TYPES OF DATA TYPES OF VARIABLES TYPES OF DATA Univariate data Examines the distribution features of one variable. Bivariate data Explores the relationship between two variables. Univariate and bivariate analysis will be revised separately.

More information

Describing Data. Carolyn J. Anderson EdPsych 580 Fall Describing Data p. 1/42

Describing Data. Carolyn J. Anderson EdPsych 580 Fall Describing Data p. 1/42 Describing Data Carolyn J. Anderson EdPsych 580 Fall 2005 Describing Data p. 1/42 Describing Data Numerical Descriptions Single Variable Relationship Graphical displays Single variable. Relationships in

More information

Module 4: Data Exploration

Module 4: Data Exploration Module 4: Data Exploration Now that you have your data downloaded from the Streams Project database, the detective work can begin! Before computing any advanced statistics, we will first use descriptive

More information

Univariate Descriptive Statistics

Univariate Descriptive Statistics Univariate Descriptive Statistics Displays: pie charts, bar graphs, box plots, histograms, density estimates, dot plots, stemleaf plots, tables, lists. Example: sea urchin sizes Boxplot Histogram Urchin

More information

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

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

More information

Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013

Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013 Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.1-1.6) Objectives

More information

Session 1.6 Measures of Central Tendency

Session 1.6 Measures of Central Tendency Session 1.6 Measures of Central Tendency Measures of location (Indices of central tendency) These indices locate the center of the frequency distribution curve. The mode, median, and mean are three indices

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

Prestatistics. Review #3. Find the square root. 1) 144 A) 72 B) -12 C) 12 D) Not a real number. 2) A) -312 B) 25 C) -25 D) Not a real number

Prestatistics. Review #3. Find the square root. 1) 144 A) 72 B) -12 C) 12 D) Not a real number. 2) A) -312 B) 25 C) -25 D) Not a real number Prestatistics Review #3 Find the square root. 1) 144 A) 72 B) -12 C) 12 D) Not a real number 2) - 625 A) -312 B) 25 C) -25 D) Not a real number 3) 0.25 A) 0.005 B) 0.05 C) 5 D) 0.5 Find the cube root.

More information

Means, standard deviations and. and standard errors

Means, standard deviations and. and standard errors CHAPTER 4 Means, standard deviations and standard errors 4.1 Introduction Change of units 4.2 Mean, median and mode Coefficient of variation 4.3 Measures of variation 4.4 Calculating the mean and standard

More information

Data and Statistics. There are three measures of central tendency that you must know. All of these should be somewhat familiar to you:

Data and Statistics. There are three measures of central tendency that you must know. All of these should be somewhat familiar to you: Data and Statistics There are three measures of central tendency that you must know. All of these should be somewhat familiar to you: Mean: Commonly called the average. It is the sum of a set of values

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

Exploratory Data Analysis

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

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

MEASURES OF DISPERSION

MEASURES OF DISPERSION MEASURES OF DISPERSION Measures of Dispersion While measures of central tendency indicate what value of a variable is (in one sense or other) average or central or typical in a set of data, measures of

More information

Intro to Statistics 8 Curriculum

Intro to Statistics 8 Curriculum Intro to Statistics 8 Curriculum Unit 1 Bar, Line and Circle Graphs Estimated time frame for unit Big Ideas 8 Days... Essential Question Concepts Competencies Lesson Plans and Suggested Resources Bar graphs

More information

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

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

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

Descriptive Statistics and Exploratory Data Analysis

Descriptive Statistics and Exploratory Data Analysis Descriptive Statistics and Exploratory Data Analysis Dean s s Faculty and Resident Development Series UT College of Medicine Chattanooga Probasco Auditorium at Erlanger January 14, 2008 Marc Loizeaux,

More information

THE BINOMIAL DISTRIBUTION & PROBABILITY

THE BINOMIAL DISTRIBUTION & PROBABILITY REVISION SHEET STATISTICS 1 (MEI) THE BINOMIAL DISTRIBUTION & PROBABILITY The main ideas in this chapter are Probabilities based on selecting or arranging objects Probabilities based on the binomial distribution

More information

Statistical Concepts and Market Return

Statistical Concepts and Market Return Statistical Concepts and Market Return 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Some Fundamental Concepts... 2 3. Summarizing Data Using Frequency Distributions...

More information

2. Describing Data. We consider 1. Graphical methods 2. Numerical methods 1 / 56

2. Describing Data. We consider 1. Graphical methods 2. Numerical methods 1 / 56 2. Describing Data We consider 1. Graphical methods 2. Numerical methods 1 / 56 General Use of Graphical and Numerical Methods Graphical methods can be used to visually and qualitatively present data and

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

STA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance

STA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance Principles of Statistics STA-201-TE This TECEP is an introduction to descriptive and inferential statistics. Topics include: measures of central tendency, variability, correlation, regression, hypothesis

More information

Foundation of Quantitative Data Analysis

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

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

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

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

More information

( ) ( ) Central Tendency. Central Tendency

( ) ( ) Central Tendency. Central Tendency 1 Central Tendency CENTRAL TENDENCY: A statistical measure that identifies a single score that is most typical or representative of the entire group Usually, a value that reflects the middle of the distribution

More information