# 1 Lesson 3: Presenting Data Graphically

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 1 Lesson 3: Presenting Data Graphically 1.1 Types of graphs Once data is organized and arranged, it can be presented. Graphic representations of data are called graphs, plots or charts. There are an untold number of graph and chart types, and a myriad of names for these types. We will discuss a few of the more popular or common types, and we will use the names for them in many spreadsheets Scatter Plots The simplest type to start with are scatter plots. These are very popular in mathematics applications, and are a good choice when your data comes as pairs of numbers. (Each datum is a pair of numbers.) In a real application, the more data points drawn that can be plotted on a computer the better; in a hand drawn classroom exercise, the fewer the better. First a middle school example: Bags of jelly beans come in various sizes, and cost various amounts of money. The cart below gives the costs of bags of various sizes. Number of Beans Cost \$1.50 \$3.00 \$3.75 \$6.00 \$7.50 \$11.25 First we must make a note of the organization of the data: The data is organized as pairs of numbers written in columns, the rst column only being labels. All the entries are numbers. The data is arranged in increasing order along each row. There is a functional relationship in both directions of the pairs. A scatter plot of this data might look like \$12.00 Jelly Beans Cost \$10.00 \$8.00 \$6.00 \$4.00 \$2.00 Cost \$ Number of Beans 1

2 This has the cost on the vertical axis and the number on the horizontal axis. There is another choice which switches these positions. \$12.00 Jelly Beans Number of Beans \$10.00 \$8.00 \$6.00 \$4.00 \$2.00 \$0.00 \$0.00 \$2.00 \$4.00 \$6.00 \$8.00 \$10.00 \$12.00 Cost Notice, to get this second plot, you would say that we have rearranged the data. We might have rearranged the data by switching the two rows in our data table to Cost \$1.50 \$3.00 \$3.75 \$6.00 \$7.50 \$11.25 Number of Beans Even if we did not actually do it on paper, it should be considered a rearrangement. What is happening here is that we are choosing between the two functional relationships we have available. The cost of a bag of jelly beans is in a functional relationship with the cost of the bag. The "xvariable" is typically drawn on the horizontal axis, so we might say that the rst graph illustrates this functional relationship. If we look at the second graph, the cost is on the horizontal axis. We can interpret this as illustrating the functional relationship the number of jelly beans has with the cost. All we are doing is giving a mathematical context to the only slightly di erent graphical representations of the same thing. Mostly the distinction is just your point of view, but mathematicians do have a their own preference when it comes to functions. What if there is no functional relation in a table? Then a scatter plot is still a good choice. Consider the 2008 Philadelphia Eagles football team again. There are 80 players on the team mostly, but not all, big men. We can collect a table of the heights and weights of all these players. Without looking at the table, we know how it might be organized: The data is organized as columns of (First Name, Second Name, Height, Weight).. The rst two entries in a datum are names, the second two entries are numbers. The data is arranged alphabetical order by last name. 2

3 There is a functional relationship in both directions of the pairs. The players heights are in a functional relationship with the full names. The players weights are in a functional relationship with the full names. The players heights are not in a functional relationship with the weights. The players weights are not in a functional relationship with the full heights. These last four observations are worth a look at. No two players have the same rst and last names, so a player s full name uniquely identify him and thus both his height and weight. That is what we need for the rst two functional relationships with the player s full name. Without actually looking at the data, we are only guessing that players heights are not in a functional relationship with the weights. But them it seems rather likely that in a list of 80 people, two might have the same weight but have di erent heights. One example of that is enough to eliminate a functional relationship. The last observation is on more solid ground. We already saw that Andrews and Baskett are the same height, but di erent weights. So we know for certain that the players weights are not in a functional relationship with their heights. If we are interested in the player s sizes, and not the players themselves, we can rearrange the data by leaving out the players names. (Remember dropping data is just a rearrangement.) Now this leaves a data set made up of numbers, and better still the numbers are in pairs. Unfortunately, there are no functional relationships in these number pairs. A scatter plot still works. In fact, the good side of not having a functional relationship in pairs of numbers is that there is basically only one type of chart that we can use to display that data: a 3

4 scatter plot. 400 Philadelphia Eagles Weight Height Weight Each diamond represents a player; its place along the horizontal axis is the players height; it place along the vertical axis represents his weight. We can see that there are a number of players who are 6 1 tall, and their weights vary from about 170 pounds to about 350. So this there is not a functional relationship in this data, but the scatter chart gives a very clear picture of how large these players are. The scatter plot does not need a functional relationship is provide good visual information. (Notice how clearly the scatter plot shows the curious fact that no player is exactly 6 foot tall.) In summary, scatter graphs as good for data made up of pairs of numbers. They work whether or not there is a functional relationship. 4

5 1.1.2 Line graphs The example of the costs of jelly beans led us to the scatter plot \$12.00 Jelly Beans Number of Beans \$10.00 \$8.00 \$6.00 \$4.00 \$2.00 \$0.00 \$0.00 \$2.00 \$4.00 \$6.00 \$8.00 \$10.00 \$12.00 Cost There is such a strong pattern in this data, that it almost jumps o the graph. These points line up! If we were to accentuate this by drawing a line between the points, we would have the line graph \$12.00 Jelly Beans Number of Beans \$10.00 \$8.00 \$6.00 \$4.00 \$2.00 Cost \$ Cost This line graph is possible because the number of jelly beans is in a functional relationship with the cost. For a line graph to work, there must be a functional relationship. The data of Eagles football players heights and weights has nothing resembling a functional relationship, and there is no way of connecting the points in its scatter plot into a line graph. Line graphs are only possible when there is a functional relationship in pairs of numbers in the data. When the "input" data in the functional relationship has a natural order, line graphs are often a good choice. There only has to be a functional relationship in one direction for a line chart to work. In the last lesson we considered the grades on three tests earned 5

6 by a group of students. Name Test 1 Test 2 Test 3 April Barry Cindy David Eileen Frank Gena Harry Ivy Jacob Keri Larry Mary Norm At rst this data does not seem to t in the pattern of either a scatter plot or a line plot. However, if we look at one datum from this, we have a di erent situation. Name Test 1 Test 2 Test 3 Mary Here the data has the form Each datum is a pair of the form (Test #, Score) The score is in a functional relationship with the test number. The test number is not in a functional relationship with the score. Here is a set of data that can be illustrated using a line chart. 100 Mary Grade Test 1 Test 2 Test 3 Notice that we placed the tests along the horizontal axis. Typically the "input" item in a functional relationship is set along the horizontal axis, and the "output" item is placed on the vertical. 6

7 Now Mary is a good student, but this graph makes it look she improved quite a bit on the last test. However, she was an A student throughout, and this graph may not give the correct impression. We can change the scale of grades to correct this impression, although the result may be just as bad Mary Grade Test 1 Test 2 Test 3 For now, we will not worry that much about adjusting a chart or graph visually, but rather concentrate on simply selecting the best type of chart. Later we will revisit the idea of formatting a chart for visual e ect. Still the scale from 0 to 100 might work better for other students, and certainly if we want to compare several students. Consider the girls: Name Test 1 Test 2 Test 3 April Cindy Eileen Gena Ivy Keri Mary

8 We can give each girl her own line graph, and place them all in one chart. Test Scores April Cindy Eileen Gena Ivy Keri Mary 10 0 Test 1 Test 2 Test 3 For another example, consider the Department of Education program called Math and Science Partnerships. The Department distributes funds to the states for speci c projects, and the funds received by Arizona over since 2001 are given in the table: A rizona \$6,759,013 \$10,114,346 \$9, 655, 054 \$12, 202, 519 \$9,278,899 \$5,291,697 \$5,290,464 The data is organized as pairs written in columns; and so each row is a datum. The data can be thought of as made up of pairs of numbers. The money is in a functional relationship with the year. The data is arranged in increasing order of years. Since we have pairs of numbers, we could use a scatter plot. But there is a functional relationship, so we could just as well use a line plot. Since the years 8

9 have a natural order, a line plot is a good choice: Arizona MSP Funds Amount Notice, the only lines in this graph are the ones we added. All the line graph does is connect points in the scatter plot with straight line segments. In many cases, a line graph is a visual presentation of the data more than a mathematical representation. It is possible, and sometimes useful, to smooth out the plot by curving the lines through the points in the scatter plot. The results is still just a variation of the line graph. There are times when shading in the area below the lines in the line graph is a good idea for visual e ect, but mathematically such an "area" chart is only a variation of a line graph. Line graphs are very useful, and there are any number of major and minor variations of their basic idea that can come in handy Column charts and bar charts Consider the Arizona MSP data a second time A rizona \$6,759,013 \$10,114,346 \$9, 655, 054 \$12, 202, 519 \$9,278,899 \$5,291,697 \$5,290,464 The amount of money is in a functional relationship with the year. The lines between points in the Arizona MSP funding chart give the impression that the funds arrived uniformly during the year. This is not necessarily wrong, but it might not be the impression we want to give. A simple scatter plot looks too 9

10 sparse, and may be hard to read. \$12,000, Arizona MSP Funds \$10,000, \$8,000, \$6,000, \$4,000, \$2,000, \$ But because there is a functional relationship, and we can use a column chart. \$12,000, Arizona MSP Funds \$10,000, \$8,000, \$6,000, \$4,000, \$2,000, \$ The nice thing about column charts is that the "input" data in the functional relationship does not need to be numbers. You can use column charts when the data along the horizontal axis are numbers, names, words, or anything. These data need a functional relationship with numbers, but the results can be quite nice. There is no rule that the columns need to be simple; all sorts of shapes can be used. Three dimensional bars work \$10,000, \$9,000, \$8,000, \$7,000, \$6,000, \$5,000, \$4,000, \$3,000, \$2,000, \$1,000, \$0.00 Arizona MSP Funds

11 We could just a well use cylinders, pyramids, cones, dollar signs, people in cap and gown, or basically anything we can draw to scale. We can draw it sideways and turn it into a bar chart: 2007 Arizona MSP Funds \$0.00 \$2,000, \$4,000, \$6,000, \$8,000, \$10,000, \$12,000, Column and Bar charts work very well when there are only a few data items to illustrate, and even more so when the numbers represent a quantity of some sort. They are less useful when one numerical value is signi cantly larger than all the others. It is also very important to note the scale used when reading one of these charts. The scale used in a column chart may be chosen to visually exaggerate a di erence in the data. This is not necessarily bad, but it does require the reader to be alert. Any column or bar chart that does not have clear numerical labels in its scale should be viewed with scepticism Pie Charts Pie charts are a great choice for displaying percentages. Take, for example, the MSP funding again: A rizona \$6,759,013 \$10,114,346 \$9, 655, 054 \$12, 202, 519 \$9,278,899 \$5,291,697 \$5,290,464 Note again: The data is organized as pairs written in columns; and so each row is a datum. The data can be thought of as made up of pairs of numbers. The money is in a functional relationship with the year. The data is arranged in increasing order of years. Before we build a pie chart, we need to rearrange the data. total column First, we add a T o t a l A rizona \$6,759,013 \$10,114,346 \$9, 655, 054 \$12, 202, 519 \$9,278, 899 \$5, 291, 697 \$5, 290, 464 \$58, 591,

12 A pie chart needs a functional relationship to work, but more important, the output of the function needs to be a number. In this example, the amount of funds is in a functional relationship with the year. Each year has its own funding amount, and that will be represented with its own slice of a pie. The size of the slice is proportional to the amount of money received in that year. To draw the pie chart, we need to rearrange our data to include percentages: T o t a l A rizona \$6,759,013 \$10,114,346 \$9,655,054 \$12, 202, 519 \$9, 278, 899 \$5,291,697 \$5,290,464 \$58,591,992 P e r c e n t a g e 1 2 % 1 7 % 1 6 % 2 1 % 1 6 % 9 % 9 % % In a pie chart, the pie is made up entirely by the slices. In our case, each slice represents the funding in one year. The area of each slice is the same percentage of the whole pie as the percentage of the amount obtained in that year. Now the areas in pie slices are proportional to the degrees in their angles. Since a whole pie comes from an angle of 360 we rearrange the table one more time to give angles of the corresponding percentage: T o t a l A rizona \$6,759,013 \$10,114,346 \$9,655,054 \$12, 202, 519 \$9, 278, 899 \$5,291,697 \$5,290,464 \$58,591,992 P e r c e n t a g e 1 2 % 1 7 % 1 6 % 2 1 % 1 6 % 9 % 9 % % A n g le After this, it is just a matter of how you like to draw it. but not as much as a computer program: A protractor helps, Arizona MSP Funds % % % % % % % There are lots of ways to draw and label the same data: 12

13 Arizona MSP Funds 2001 \$7,016, \$3,908, \$4,055, \$8,794, \$7,260, \$9,690, \$9,868, Or if you want to split it up a bit, Arizona MSP Funds % % % % % % % We can easily see that the largest percentage of funds came in 2004, and the least in Now a pie chart does not need to be a pie, it can be a rectangle: 13

14 1.1.5 Stem and Leaf Plots; Frequency Graphs and Histograms There are many other types of graphs than scatter plots, line graphs, column and row charts, and pie charts. There are also various versions of each of these types. There are plenty of choices for representing data graphically. We do not have time to do more than outline the basic types above. There is, however, one last general type of graphic associated with data. we will consider three forms of this general type: Stem and Leaf Plots, Frequency Graphs, and Histograms. A "Stem and Leaf Plot" provides a graphic way to assemble or collect data in the form of numbers. Many times a completed stem and leaf plot will give at least some visual information about the data. In truth, a stem an leaf plot is tabulation of data more than a graphic representation of the data. However, it has a graphic element to it, and it can be seen as a primitive form of a histogram. In its simplest form a stem and leaf plot is used on data consisting of two digit numbers. In this case the "stem" of the graph is the rst digit of the number, and the "leaf" is the second. The stem numbers are most often stacked vertically, and the leaves are placed to one side horizontally. Consider our list of test scores. April 55 Barry 63 Cindy 88 David 97 Eileen 58 Frank 90 Gena 88 Harry 71 Ivy 65 Jacob 77 Keri 75 Larry 88 Mary 95 Norm 86 If we are interested in the test more than the student s scores, we rearrange the table by dropping the names so that each datum is just a test score. All we care about is the scores, so we rearrange the data by forgetting about the names in these rows. 55; 63; 88; 97; 58; 90; 88; 71; 65; 77; 75; 88; 95; 86: We end up with the most straightforward of all data sets: a simple list of numbers. Stem and Leaf Plots only work for data sets made up of numbers. Using 14

15 the rst digit as the stem and the second digit as the leaf, we get a plot like Stem Leaf We can easily see where Barry s score of 63 appears in this plot, its stem is 6 and leaf is 3. Unfortunately, we no longer know it belongs to Barry. As we can see, this works quite well on data sets made up of two digit numbers. But it is easy to see how to adapt it to other types of numbers. Consider the basic idea behind this stem and leaf plot. We start with a data set that is either given or being collected. The datum in the set are single objects, in the example, two digit test scores between 50 and 99. When we chose to use the rst digit of each number as a stem, we have actually broken the data into classes: 50-59, 60-69, 70-79, 80-89, and Once these classes have been assigned as the stems, the rest of the datum became the leaf. Since in the example the leaves are digits (numbers) we used the digits themselves to represent the leaves, and arranged them in increasing order. When numbers are involved, proper etiquette calls for the leaves to be listed in order. This general description of a stem and leaf plot leads us to a "Class and Frequency Plot." Data is divided into classes, and the classes play the role of the "stems." Since the remainder of a datum may not be a digit, or even a number, we might use any symbol to denote each leaf. Each piece of data appears as a symbol in the correct stem. In our example of test data, we might end up with something like Stem Leaf We de nitely lose information this way, and this is probably not an example where this is the best idea. However, there is information left that might be useful. The number of leaves in each stem shows the frequency that data occurs in this class. Thus the "Stem and Leaf Plot" has become a "Class and Frequency Plot." Consider a better example, namely the Eagles football team. Suppose that we have collected data in the form (First Name, Last Name, Height, Weight.) for all 80 players. We notice that the players are all between 68 and 80 inches tall. We will assign every measurement in this range as a class. The classes refer to only on part of each datum, and the rest of the datum is a bit complicated. 15

16 Still we will just denote the rest of each datum with a blue. true class and frequency graph: The result is a We easily see that 3 players are 77 inches tall. If we tilt it on its side, it looks like 16

17 If we merge the diamonds into columns, we get Notice all of these are class and frequency graphs drawn as columns or rows. Thus class and frequency graphs can appear as bar charts and column charts. In this example, the classes are the heights and are listed across one axis. The columns measure a count of the number of times that a datum falls in a particular class; that is to say, it gives the frequency of that class in the whole. Once we have a class and frequency chart, we are very close to our last type of chart, a histogram. In a proper histogram, we also select classes, and separate the data into those classes. Again we highlight the frequency with which each class occurs in the data. In a histogram, we use a shaded area above a class label - rather than a height - to indicate the frequency. Usually, but not strictly, the scale marking the frequency is either a percentage or a proportion out of 1. To emphasize the area aspect of the graph, regions of the graph are run together unless a class has a zero frequency of occurrence. 17

18 Here we used the actually numbers to scale the frequencies. When the units of the frequencies are uniform like this, there is no real distinction between the height and area. Thus relabeling to a proportion of 1 does not change the shape of the graph; Prepared by: Daniel Madden and Alyssa Keri: May

### Biostatistics: A QUICK GUIDE TO THE USE AND CHOICE OF GRAPHS AND CHARTS

Biostatistics: A QUICK GUIDE TO THE USE AND CHOICE OF GRAPHS AND CHARTS 1. Introduction, and choosing a graph or chart Graphs and charts provide a powerful way of summarising data and presenting them in

### 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

### 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

### 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

### Data Chart Types From Jet Reports

Data Chart Types From Jet Reports Variable Width Column Chart Bar Chart Column Chart Circular Area Chart Line Chart Column Chart Line Chart Two Variables Per Item Many Items Few Items Cyclical Data Non-Cyclical

### MATH CHAPTER 2 EXAMPLES & DEFINITIONS

MATH 10043 CHAPTER 2 EXAMPLES & DEFINITIONS Section 2.2 Definition: Frequency distribution a chart or table giving the values of a variable together with their corresponding frequencies. A frequency distribution

### There are some general common sense recommendations to follow when presenting

Presentation of Data The presentation of data in the form of tables, graphs and charts is an important part of the process of data analysis and report writing. Although results can be expressed within

### 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

### A Picture Really Is Worth a Thousand Words

4 A Picture Really Is Worth a Thousand Words Difficulty Scale (pretty easy, but not a cinch) What you ll learn about in this chapter Why a picture is really worth a thousand words How to create a histogram

### Column Charts. Line Charts

1 of 1 There are a vast number of different types of charts that you can create in Excel. This document with the help of Microsoft Help will outline the different categories of charts and the different

### 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

### Presentation of data

2 Presentation of data Using various types of graph and chart to illustrate data visually In this chapter we are going to investigate some basic elements of data presentation. We shall look at ways in

### 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

### Microsoft Excel 2010 Charts and Graphs

Microsoft Excel 2010 Charts and Graphs Email: training@health.ufl.edu Web Page: http://training.health.ufl.edu Microsoft Excel 2010: Charts and Graphs 2.0 hours Topics include data groupings; creating

### Graphical methods for presenting data

Chapter 2 Graphical methods for presenting data 2.1 Introduction We have looked at ways of collecting data and then collating them into tables. Frequency tables are useful methods of presenting data; they

### San Jose State University Engineering 10 1

KY San Jose State University Engineering 10 1 Select Insert from the main menu Plotting in Excel Select All Chart Types San Jose State University Engineering 10 2 Definition: A chart that consists of multiple

### Unit 21 Student s t Distribution in Hypotheses Testing

Unit 21 Student s t Distribution in Hypotheses Testing Objectives: To understand the difference between the standard normal distribution and the Student's t distributions To understand the difference between

PRESENTING YOUR DATA GRAPHICALLY OVERVIEW This paper outlines best practices for the graphical presentation of data. It begins with a brief discussion of various aspects of giving a presentation. It then

### Business Statistics & Presentation of Data BASIC MATHEMATHICS MATH0101

Business Statistics & Presentation of Data BASIC MATHEMATHICS MATH0101 1 STATISTICS??? Numerical facts eg. the number of people living in a certain town, or the number of cars using a traffic route each

### Data Handling Progression in Maths. May 2014

Data Handling Progression in Maths May 2014 Purpose of Policy Data handling is a significant part of the Mathematics Primary Curriculum. This policy will form the basis upon which we map out the learning

### Excel Types of charts and their uses.

Microsoft Excel supports many types of charts to help you display data in ways that are meaningful to your audience. When you create a chart or change the type of an existing chart in Microsoft Excel or

### Years after 2000. US Student to Teacher Ratio 0 16.048 1 15.893 2 15.900 3 15.900 4 15.800 5 15.657 6 15.540

To complete this technology assignment, you should already have created a scatter plot for your data on your calculator and/or in Excel. You could do this with any two columns of data, but for demonstration

### What Does the Normal Distribution Sound Like?

What Does the Normal Distribution Sound Like? Ananda Jayawardhana Pittsburg State University ananda@pittstate.edu Published: June 2013 Overview of Lesson In this activity, students conduct an investigation

### Unit 9 Describing Relationships in Scatter Plots and Line Graphs

Unit 9 Describing Relationships in Scatter Plots and Line Graphs Objectives: To construct and interpret a scatter plot or line graph for two quantitative variables To recognize linear relationships, non-linear

### Presenting numerical data

Student Learning Development Presenting numerical data This guide offers practical advice on how to incorporate numerical information into essays, reports, dissertations, posters and presentations. The

### 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

### 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

### 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)

### 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.

### Plotting Data with Microsoft Excel

Plotting Data with Microsoft Excel Here is an example of an attempt to plot parametric data in a scientifically meaningful way, using Microsoft Excel. This example describes an experience using the Office

### 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

### Question 2: How do you evaluate a limit from a graph?

Question 2: How do you evaluate a limit from a graph? In the question before this one, we used a table to observe the output values from a function as the input values approach some value from the left

### Other useful guides from Student Learning Development: Histograms, Pie charts, Presenting numerical data

Student Learning Development Bar charts This guide explains what bar charts are and outlines the different ways in which they can be used to present data. It also provides some design tips to ensure that

### Grade 6 Math Circles Winter 2013 Mean, Median, Mode

1 University of Waterloo Faculty of Mathematics Grade 6 Math Circles Winter 2013 Mean, Median, Mode Mean, Median and Mode The word average is a broad term. There are in fact three kinds of averages: mean,

### Consultation paper Presenting data in graphs, charts and tables science subjects

Consultation paper Presenting data in graphs, charts and tables science subjects This edition: November 2015 (version 1.0) Scottish Qualifications Authority 2015 Contents Presenting data in graphs, charts

### Interactive Math Glossary Terms and Definitions

Terms and Definitions Absolute Value the magnitude of a number, or the distance from 0 on a real number line Additive Property of Area the process of finding an the area of a shape by totaling the areas

### First Grade CCSS Math Vocabulary Word List *Terms with an asterisk are meant for teacher knowledge only students do not need to learn them.

First Grade CCSS Math Vocabulary Word List *Terms with an asterisk are meant for teacher knowledge only students do not need to learn them. Add To combine; put together two or more quantities. Addend Any

### In this course, we will consider the various possible types of presentation of data and justification for their use in given situations.

PRESENTATION OF DATA 1.1 INTRODUCTION Once data has been collected, it has to be classified and organised in such a way that it becomes easily readable and interpretable, that is, converted to information.

### 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

### Drawing a histogram using Excel

Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to

### Year 1 Maths Expectations

Times Tables I can count in 2 s, 5 s and 10 s from zero. Year 1 Maths Expectations Addition I know my number facts to 20. I can add in tens and ones using a structured number line. Subtraction I know all

### Bivariate Descriptive Statistics: Unsing Spreadsheets to View and Summarize Data

Connexions module: m47471 1 Bivariate Descriptive Statistics: Unsing Spreadsheets to View and Summarize Data Irene Mary Duranczyk Suzanne Loch Janet Stottlemyer This work is produced by The Connexions

### 31 Misleading Graphs and Statistics

31 Misleading Graphs and Statistics It is a well known fact that statistics can be misleading. They are often used to prove a point, and can easily be twisted in favour of that point! The purpose of this

### and Relativity Frequency Polygons for Discrete Quantitative Data We can use class boundaries to represent a class of data

Section - A: Frequency Polygons and Relativity Frequency Polygons for Discrete Quantitative Data We can use class boundaries to represent a class of data In the past section we created Frequency Histograms.

### Grade 8 Classroom Assessments Based on State Standards (CABS)

Grade 8 Classroom Assessments Based on State Standards (CABS) A. Mathematical Processes and E. Statistics and Probability (From the WKCE-CRT Mathematics Assessment Framework, Beginning of Grade 10) A.

### KINDERGARTEN Practice addition facts to 5 and related subtraction facts. 1 ST GRADE Practice addition facts to 10 and related subtraction facts.

MATH There are many activities parents can involve their children in that are math related. Children of all ages can always practice their math facts (addition, subtraction, multiplication, division) in

### TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

### 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.

### Session 7 Bivariate Data and Analysis

Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares

### 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.

### 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

### Exploring Mathematics Through Problem-Solving and Student Voice

Exploring Mathematics Through Problem-Solving and Student Voice Created By: Lisa Bolduc, Aileen Burke-Tsakmakas, Shelby Monaco, Antonietta Scalzo Contributions By: Churchill Public School Professional

### BEST GUESS - JUNE 2016 EDEXCEL LINEAR PAPER 2 (Higher)

BEST GUESS - JUNE 2016 EDEXCEL LINEAR PAPER 2 (Higher) This paper has been made up of questions for the topics that we believe are worth revising prior to paper 2 (Edexcel Linear) as with all these things

### 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

### Data Analysis: Displaying Data - Graphs

Accountability Modules WHAT IT IS Return to Table of Contents WHEN TO USE IT TYPES OF GRAPHS Bar Graphs Data Analysis: Displaying Data - Graphs Graphs are pictorial representations of the relationships

### 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...

### Creating Charts in Microsoft Excel A supplement to Chapter 5 of Quantitative Approaches in Business Studies

Creating Charts in Microsoft Excel A supplement to Chapter 5 of Quantitative Approaches in Business Studies Components of a Chart 1 Chart types 2 Data tables 4 The Chart Wizard 5 Column Charts 7 Line charts

### Prentice Hall Mathematics: Course 1 2008 Correlated to: Arizona Academic Standards for Mathematics (Grades 6)

PO 1. Express fractions as ratios, comparing two whole numbers (e.g., ¾ is equivalent to 3:4 and 3 to 4). Strand 1: Number Sense and Operations Every student should understand and use all concepts and

### Excel Lesson 1: Microsoft Excel Basics

Excel Lesson 1: Microsoft Excel Basics 1. Active cell: The cell in the worksheet in which you can type data. 2. Active worksheet: The worksheet that is displayed in the work area. 3. Adjacent range: All

### MD5-26 Stacking Blocks Pages 115 116

MD5-26 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.

### 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

### Part 1: Background - Graphing

Department of Physics and Geology Graphing Astronomy 1401 Equipment Needed Qty Computer with Data Studio Software 1 1.1 Graphing Part 1: Background - Graphing In science it is very important to find and

### 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

### 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

### Chapter 14: Production Possibility Frontiers

Chapter 14: Production Possibility Frontiers 14.1: Introduction In chapter 8 we considered the allocation of a given amount of goods in society. We saw that the final allocation depends upon the initial

### Chapter 27: Taxation. 27.1: Introduction. 27.2: The Two Prices with a Tax. 27.2: The Pre-Tax Position

Chapter 27: Taxation 27.1: Introduction We consider the effect of taxation on some good on the market for that good. We ask the questions: who pays the tax? what effect does it have on the equilibrium

### Lab 11. Simulations. The Concept

Lab 11 Simulations In this lab you ll learn how to create simulations to provide approximate answers to probability questions. We ll make use of a particular kind of structure, called a box model, that

### 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

### OA3-10 Patterns in Addition Tables

OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20

### Glossary of numeracy terms

Glossary of numeracy terms These terms are used in numeracy. You can use them as part of your preparation for the numeracy professional skills test. You will not be assessed on definitions of terms during

### Granny s Balloon Trip

Granny s Balloon Trip This problem gives you the chance to: represent data using tables and graphs On her eightieth birthday, Sarah s granny went for a trip in a hot air balloon. This table shows the schedule

### Appendix E: Graphing Data

You will often make scatter diagrams and line graphs to illustrate the data that you collect. Scatter diagrams are often used to show the relationship between two variables. For example, in an absorbance

### Introduction to the Practice of Statistics Fifth Edition Moore, McCabe

Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 1.3 Homework Answers 1.80 If you ask a computer to generate "random numbers between 0 and 1, you uniform will get observations

### Pareto Chart What is a Pareto Chart? Why should a Pareto Chart be used? When should a Pareto Chart be used?

Pareto Chart What is a Pareto Chart? The Pareto Chart is named after Vilfredo Pareto, a 19 th century economist who postulated that a large share of wealth is owned by a small percentage of the population.

### 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

### GRADE 2 MATHEMATICS. Students are expected to know content and apply skills from previous grades.

GRADE 2 MATHEMATICS Students are expected to know content and apply skills from previous grades. Mathematical reasoning and problem solving processes should be incorporated throughout all mathematics standards.

### 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,

### NUMB3RS Activity: A Stab in the Dark. Episode: Hot Shot

Teacher Page 1 NUMB3RS Activity: A Stab in the Dark Topic: Histograms, relative frequency, and probability Grade Level: 7-12 Objective: Connect histograms and relative frequencies to probability Time:

### GCSE Mathematics Calculator Foundation Tier Free Practice Set 6 1 hour 30 minutes ANSWERS. Marks shown in brackets for each question (2)

MathsMadeEasy 3 GCSE Mathematics Calculator Foundation Tier Free Practice Set 6 1 hour 30 minutes ANSWERS Marks shown in brackets for each question Typical Grade Boundaries C D E F G 76 60 47 33 20 Legend

### Math 016. Materials With Exercises

Math 06 Materials With Exercises June 00, nd version TABLE OF CONTENTS Lesson Natural numbers; Operations on natural numbers: Multiplication by powers of 0; Opposite operations; Commutative Property of

### Models for Discrete Variables

Probability Models for Discrete Variables Our study of probability begins much as any data analysis does: What is the distribution of the data? Histograms, boxplots, percentiles, means, standard deviations

### Performance Assessment Task Baseball Players Grade 6. Common Core State Standards Math - Content Standards

Performance Assessment Task Baseball Players Grade 6 The task challenges a student to demonstrate understanding of the measures of center the mean, median and range. A student must be able to use the measures

T O P I C 1 2 Techniques and tools for data analysis Preview Introduction In chapter 3 of Statistics In A Day different combinations of numbers and types of variables are presented. We go through these

### Appendix A. Comparison. Number Concepts and Operations. Math knowledge learned not matched by chess

Appendix A Comparison Number Concepts and Operations s s K to 1 s 2 to 3 Recognize, describe, and use numbers from 0 to 100 in a variety of familiar settings. Demonstrate and use a variety of methods to

### Module 2: Introduction to Quantitative Data Analysis

Module 2: Introduction to Quantitative Data Analysis Contents Antony Fielding 1 University of Birmingham & Centre for Multilevel Modelling Rebecca Pillinger Centre for Multilevel Modelling Introduction...

### Chapter 17: Aggregation

Chapter 17: Aggregation 17.1: Introduction This is a technical chapter in the sense that we need the results contained in it for future work. It contains very little new economics and perhaps contains

### Students will understand 1. use numerical bases and the laws of exponents

Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?

### AP STATISTICS 2006 SCORING GUIDELINES (Form B) Question 1

AP STATISTICS 2006 SCORING GUIDELINES (Form B) Question 1 Intent of Question The primary purpose of this question is to assess a student s ability to read, interpret, and explain information contained

### 0 Introduction to Data Analysis Using an Excel Spreadsheet

Experiment 0 Introduction to Data Analysis Using an Excel Spreadsheet I. Purpose The purpose of this introductory lab is to teach you a few basic things about how to use an EXCEL 2010 spreadsheet to do

### 12-1 Representations of Three-Dimensional Figures

Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

### Common Tools for Displaying and Communicating Data for Process Improvement

Common Tools for Displaying and Communicating Data for Process Improvement Packet includes: Tool Use Page # Box and Whisker Plot Check Sheet Control Chart Histogram Pareto Diagram Run Chart Scatter Plot

### Graphing Exercise 1. Create a Pie Graph by Selecting a Data Table

Graphing Exercise 1. Create a Pie Graph by Selecting a Data Table This exercise selects the data in an existing data table and creates a pie graph of the data (Figure G1-1). Figure G1-1. Tree species sampled

### chapter >> Making Decisions Section 2: Making How Much Decisions: The Role of Marginal Analysis

chapter 7 >> Making Decisions Section : Making How Much Decisions: The Role of Marginal Analysis As the story of the two wars at the beginning of this chapter demonstrated, there are two types of decisions:

### 2. THE x-y PLANE 7 C7

2. THE x-y PLANE 2.1. The Real Line When we plot quantities on a graph we can plot not only integer values like 1, 2 and 3 but also fractions, like 3½ or 4¾. In fact we can, in principle, plot any real

### High School Algebra Reasoning with Equations and Inequalities Solve systems of equations.

Performance Assessment Task Graphs (2006) Grade 9 This task challenges a student to use knowledge of graphs and their significant features to identify the linear equations for various lines. A student

### Numeracy and mathematics Experiences and outcomes

Numeracy and mathematics Experiences and outcomes My learning in mathematics enables me to: develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different

### Math Dictionary Terms for Grades K-1:

Math Dictionary Terms for Grades K-1: A Addend - one of the numbers being added in an addition problem Addition - combining quantities And - 1) combine, 2) shared attributes, 3) represents decimal point

### Introducing the. Tools for. Continuous Improvement

Introducing the Tools for Continuous Improvement The Concept In today s highly competitive business environment it has become a truism that only the fittest survive. Organisations invest in many different