# Frequency distributions, central tendency & variability. Displaying data

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Frequency distributions, central tendency & variability Displaying data

2 Software SPSS Excel/Numbers/Google sheets Social Science Statistics website (socscistatistics.com)

3 Creating and SPSS file Open the Excel data file Tidy up the data Open SPSS type in new data Copy and paste the Excel data into the SPSS spreadsheet Go to Variable View and select the correct measurement scale Recode string variables into numerical variables: Transform -> Recode into same variables Add labels: choose Variable View and in the Values column add the labels

4 Displaying data Histogram (frequency polygon): shows the frequency (or probability) of each value of the dependent variable Classic bar chart: shows the average value of the dependent variable at each level of the independent variable Scatterplot: shows the relationship between two dependent variables

5 Frequency Distributions For Nominal or Ordinal data: Eye colour Brown, brown, hazel, blue, blue, grey, blue, brown, hazel, grey, green, blue, brown World cup: How may times each country finished 1 st or 2 nd place For scale (ratio or interval) data: Height (cm) 176, 178, 184, 172, 180, 178, 165, 160, 172, 171, 176, 166, 176, 183, 165, 158, 165, 173, 162, 185

6 Frequency Table: Steps Find Max and Min. scores Determine Range (Max-Min+1) Determine number of bins More art than science, judgment call Decide bottom number From Highest to lowest, count number of scores that belongs in each bin.

7 Frequency table Height Frequency Percent Cumulative percent

8 Histogram: Steps Define X-axis Define the range of X-axis variable. Define range of frequency on the Y-axis. CHOOSE the bin size (wisely).

9 Number of people Histogram Height group (cm)

10 Number of people Frequency polygon Height group (cm)

11 Number of people Histogram: cheating Height group (cm)

12 Normal distribution (bell-shaped)

13 Skewed distributions

14 Exercises 1 What would the histograms look like for English Test 1 (ceiling effect) English Test 2 (floor effect)? 2 By hand: Draw a histogram for number of Facebook friends 3 By hand: Draw histograms for hours of sleep on Saturday vs. Tuesday 4 No do both in SPSS. Get SPSS to draw a normal curve over the histogram and to display a frequency table. Analyse > Desriptive Statistics > Frequencies 6 Look at the various options the SPSS dialogue gives you. Try to guess what they are. 5 Did SPSS choose the right bin size? If not, change it. (Double click chart. Bin/un-bin element.)

15 A histogram is NOT the same as a bar chart showing averages

16 Beer and labour

17 What graph is this? (Multiple choice tests)

18 scatterplots Correlation between two variables The variables have several levels The horizontal axis shows one variable and vertical axis the other variable The points correspond to individuals

19 A scatterplot (interval, ratio or ordinal data)

20 Contingency table (nominal data) Lives in Buda Lives in Pest By bike 8 3 Public transport Other way 2 1 Total Total

21 Exercise 1. From your homework data Which relationships would be best displayed in a bar chart? Which relationships would be best displayed in a scatterplot? Which relationships would be best displayed in a contingency table? 2. Create a bar chart, a scatterplot and a contingency table In SPSS go to Graphs for a bar chart and a scatterplot For a contingency table, go to Analyze -> Descriptive Statistics -> Crosstabs and choose the two variables (In Excel: bar chart and scatterplot from charts For a histograme, choose bins, calculate frequncies and create a bar chart with the frequencz values. Then reduce the gap between the bars. For a contingency table use Pivot table function)

22 Characterising a data set Two important characteristics: Central tendency: the middle value of the set of data Definition of the middle depends on the type of data: for a normal curve, the middle of the histogram Variability: to what extent scores deviate from the middle value The spread of the histogram

23 Measures of Central Tendency Mean: the arithmetic average Most commonly used central tendency measure Used in later inferential statistics For interval/ratio data Median: the middle score in a distribution Less affected than the mean by a few extreme scores Mode: the most frequently occurring score Easy to compute from frequency distribution Can be used for any type of data including nominal

24 Computing the sample Mean (M or x bar) Compute the mean of 3, 4, 2, 5, 7, & 5 Sum the numbers (26) Count the number of scores (6) Plug these values into the equations Excel: =AVERAGE() X X N X

25 symbols μ = population mean ( mew ) M or (x bar) = sample mean = Sigma, summation ( add all of these ) N = sample size

26 Computing the Median Order the scores from smallest to largest Determine the middle score [(N+1)/2] If 7 scores, the middle is the fourth score [(7+1)/2]=4 Median of [11, 27, 32, 43, 46, 47, 51] = 43 If 8 scores, the middle score is half way between the 4 th and 5 th scores [(8+1)/2]=4.5 Median of [11, 27, 32, 43, 46, 47, 51, 56] = 44.5 Excel: =Median() It has no symbol! (Median, Mdn)

27 Outliers Outliers are extreme values: very high or very low in comparison with the rest of the scores Use Number of Facebook friends, Hours of sleep or Units of alcohol 1. Create a frequency table 2. Draw a histogram does it look normal? 3. Are there any outliers? 4. Estimate the mode, mean and the median from the histogram 5. Calculate the mean and the median are they similar? 6. You can do all that in SPSS: Analyze -> Descriptives -> Frequencies

28 Multi-modal distribution

29 Measuring Dispersion Measures of dispersion show us how well the mean (median, mode) represents the sample and the population Range: distance between lowest and highest score Simple but outliers are a big problem Variance: average squared distance from the mean Used in later inferential statistics Standard Deviation: square root of variance (inter-quartile range)

30 Variance & Standard Deviation (for set of observations) σ = Standard Deviation = square root of variance (for population) SD = Standard Deviation = square root of variance (for sample)

31 The Variance Computing the Variance Compute the mean (M) Compute the distance of each score from the mean (X M) Square those distances (X M) 2 Sum those squared distances: Sum of Squares: SS Divide by the number of observations (N) for the set of observations (population) the degrees of freedom (N - 1) for the population estimate from the sample Excel: =VAR.P() or VAR.S() Good statistical properties, but this measure of variability is in squared units

32 The Standard Deviation Computing the Standard Deviation Compute the variance Take the square root of the variance Excel: =STDEV.P() or STDEV.S() This measure, like the variance, has good statistical properties and is measured in the same units as the mean

33 Symbols Target Sample (from which you generalise) Population (just the observations) Standard Deviation Variance SD, s SD 2, s 2 N σ σ 2 n Number of observation

34 What does the standard deviation mean? Dogs heights at the shoulders (mm): 600, 470, 170, 430, 300 Mathisfun.com SD (set of observations) = 147 mm A dog up to 147 mm taller or shorter than average, is within the standard range (those even shorter or even taller are tiny or huge) SD (population estimate) = 164 mm Allows for slightly greater variation to compensate for an imperfect sample

35 The Normal Distribution Described by: Shape: unimodal Central Tendency: mean = median = mode Variability: 68% of values are within 1 SD of the mean 95% of values are within 2 SD of the mean 99.7% of values are within 3 SD of the mean 35

36

37 percentiles Pth percentile: the value for which P percent of the scores are less than that value Deciles: 10 th, 20 th, etc percentiles Quartiles: 25 th, 50 th and 75 th percentiles Another measure of variability: Interquartile range: third quartile first quartile

38 Growth chart

39 Box-Plot Box Bottom = 1 st quartile Box Midline = 2 nd quartile (Median) Box Top = 3 rd Quartile Whiskers = Values closest to 1.5 times the interquartile range above or below the box (or sometimes above or below the median) Beyond the whiskers: outliers and extreme outliers

40 exercise Take the data of units of alcohol for those who went out and those who did not go out Draw histogram and box plot, find mode, median, mean, SD interquartile range and outliers You can do this separately for the two groups via Analyze -> Descriptive statistics -> Frequencies + the Box plot via Graphs Or in one go via Analyze -> Descriptive statistics -> Explore Calculate the percentile for the number of hours you slept on Saturday How much alcohol does the data predict you would have had if you had/had not gone out that night?

42 How To Lie with Graphs

43 Tricks in Describing Stats If you omit Zero in your scale, must indicate with ellipsis Simulated Survey Orientation Rt (ms) Simulated Survey and Egocentric Orientation: Sex Differences Egocentric Survey Scale and Load Female Male Ln (Rt) Heavy Light Load and Angle Conditions Large Small

44 Starting Point Mayor Marcus is running for a second term against a challenger. Which graph should he send to the local journalist who is reporting on crime rates?

45 What s wrong with this picture?

46 What s wrong with this picture?

47 Homework Mary Claire magazine s observation of shopping habits: Put the data into an SPSS file, draw histograms, calculate means and standard deviations, draw boxplots and identify outliers, draw scatterplots (Their conclusion was that shopping was good for you because of all the exercise you get.) Men Minutes spent shopping Kilometres walked Women Minutes spend shopping Kilometres walked

### 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.

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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,

### 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

### 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

### 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

### 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,

### 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

### 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

### 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

### 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,

### 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.

### 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,

### 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

### 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.

### WHICH TYPE OF GRAPH SHOULD YOU CHOOSE?

PRESENTING GRAPHS WHICH TYPE OF GRAPH SHOULD YOU CHOOSE? CHOOSING THE RIGHT TYPE OF GRAPH You will usually choose one of four very common graph types: Line graph Bar graph Pie chart Histograms LINE GRAPHS

### 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

### 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

### 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

### 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

### 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)

### 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

### 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

### 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

### 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.

### 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

### Descriptive Statistics and Measurement Scales

Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample

### 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

### 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

### 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

### Statistical Analysis Using Gnumeric

Statistical Analysis Using Gnumeric There are many software packages that will analyse data. For casual analysis, a spreadsheet may be an appropriate tool. Popular spreadsheets include Microsoft Excel,

### 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.

### 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

### 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

### Introduction to Descriptive Statistics

Mathematics Learning Centre Introduction to Descriptive Statistics Jackie Nicholas c 1999 University of Sydney Acknowledgements Parts of this booklet were previously published in a booklet of the same

### 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

### 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

### 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

### 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

### Sheffield Hallam University. Faculty of Health and Wellbeing Professional Development 1 Quantitative Analysis. Glossary

Sheffield Hallam University Faculty of Health and Wellbeing Professional Development 1 Quantitative Analysis Glossary 2 Using the Glossary This does not set out to tell you everything about the topics

### 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

### Descriptive Statistics. Understanding Data: Categorical Variables. Descriptive Statistics. Dataset: Shellfish Contamination

Descriptive Statistics Understanding Data: Dataset: Shellfish Contamination Location Year Species Species2 Method Metals Cadmium (mg kg - ) Chromium (mg kg - ) Copper (mg kg - ) Lead (mg kg - ) Mercury

### 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

### Data exploration with Microsoft Excel: univariate analysis

Data exploration with Microsoft Excel: univariate analysis Contents 1 Introduction... 1 2 Exploring a variable s frequency distribution... 2 3 Calculating measures of central tendency... 16 4 Calculating

### 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

### Homework 3. Part 1. Name: Score: / null

Name: Score: / Homework 3 Part 1 null 1 For the following sample of scores, the standard deviation is. Scores: 7, 2, 4, 6, 4, 7, 3, 7 Answer Key: 2 2 For any set of data, the sum of the deviation scores

### 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,

### 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

### Statistics Chapter 3 Averages and Variations

Statistics Chapter 3 Averages and Variations Measures of Central Tendency Average a measure of the center value or central tendency of a distribution of values. Three types of average: Mode Median Mean

### 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

### Introduction to Stata: Graphic Displays of Data and Correlation

Math 143 Lab #1 Introduction to Stata: Graphic Displays of Data and Correlation Overview Thus far in the course, you have produced most of our graphical displays by hand, calculating summaries and correlations

### 1 Measures for location and dispersion of a sample

Statistical Geophysics WS 2008/09 7..2008 Christian Heumann und Helmut Küchenhoff Measures for location and dispersion of a sample Measures for location and dispersion of a sample In the following: Variable

### 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

### Seminar paper Statistics

Seminar paper Statistics The seminar paper must contain: - the title page - the characterization of the data (origin, reason why you have chosen this analysis,...) - the list of the data (in the table)

### Analysis Tools in Geochemistry for ArcGIS

Analysis Tools in Geochemistry for ArcGIS The database that is used to store all of the geographic information in Geochemistry for ArcGIS is Esri s file Geodatabase (fgdb). This is a collection of tables

### An introduction to using Microsoft Excel for quantitative data analysis

Contents An introduction to using Microsoft Excel for quantitative data analysis 1 Introduction... 1 2 Why use Excel?... 2 3 Quantitative data analysis tools in Excel... 3 4 Entering your data... 6 5 Preparing

### 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:

### III. GRAPHICAL METHODS

Pie Charts and Bar Charts: III. GRAPHICAL METHODS Pie charts and bar charts are used for depicting frequencies or relative frequencies. We compare examples of each using the same data. Sources: AT&T (1961)

### 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

### 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

### Data Exploration Data Visualization

Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select

### 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

### 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

### 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),

### Statistics. Measurement. Scales of Measurement 7/18/2012

Statistics Measurement Measurement is defined as a set of rules for assigning numbers to represent objects, traits, attributes, or behaviors A variableis something that varies (eye color), a constant does

### 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

### 2. Filling Data Gaps, Data validation & Descriptive Statistics

2. Filling Data Gaps, Data validation & Descriptive Statistics Dr. Prasad Modak Background Data collected from field may suffer from these problems Data may contain gaps ( = no readings during this period)

### Chapter 7 What to do when you have the data

Chapter 7 What to do when you have the data We saw in the previous chapters how to collect data. We will spend the rest of this course looking at how to analyse the data that we have collected. Stem and

### ( ) ( ) 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

### PROPERTIES OF MEAN, MEDIAN

PROPERTIES OF MEAN, MEDIAN In the last class quantitative and numerical variables bar charts, histograms(in recitation) Mean, Median Suppose the data set is {30, 40, 60, 80, 90, 120} X = 70, median = 70

### 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

### What is Statistics? Statistics is about Collecting data Organizing data Analyzing data Presenting data

Introduction What is Statistics? Statistics is about Collecting data Organizing data Analyzing data Presenting data What is Statistics? Statistics is divided into two areas: descriptive statistics and

### 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

### 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.

### ! 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,

### 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

### 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

### 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

### Unit 16 Normal Distributions

Unit 16 Normal Distributions Objectives: To obtain relative frequencies (probabilities) and percentiles with a population having a normal distribution While there are many different types of distributions

### 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...

### 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

### 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

### Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering

Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques

### Visual Display of Data in Stata

Lab 2 Visual Display of Data in Stata In this lab we will try to understand data not only through numerical summaries, but also through graphical summaries. The data set consists of a number of variables

### This activity will show you how to use Excel to draw cumulative frequency graphs. 0 < x < x < x

Pay rates for men and women Excel 2003 activity This activity will show you how to use Excel to draw cumulative frequency graphs. Information sheet The table gives the results from a survey about hourly

### Why do we measure central tendency? Basic Concepts in Statistical Analysis

Why do we measure central tendency? Basic Concepts in Statistical Analysis Chapter 4 Too many numbers Simplification of data Descriptive purposes What is central tendency? Measure of central tendency A

### 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

### Exploratory Data Analysis. Psychology 3256

Exploratory Data Analysis Psychology 3256 1 Introduction If you are going to find out anything about a data set you must first understand the data Basically getting a feel for you numbers Easier to find

### 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