SlideShare a Scribd company logo
1 of 24
Yes, that’s right. I know we’re in science. You still need to do math.
MATH AND GRAPHS
IN SCIENCE
Estimation
 An approximation of a
number based on
reasonable
assumptions.
 Everyone take a guess!
 Winner gets 2
tickets!!!!
Estimation! (Theartof guessing!)
How many marbles???
Accuracy
 How close a
measurement is to the
true or actual value.
Accuracy
All aimed for bulls eye: all in
Reproducible
 How close a group of
measurements are to
each other.
Reproducibility
This is also reproducible. What
if the darts were in a corner?
What is this??
 Neither!!!
Accurate? Reproducible?
Sig-Figs:
 This measurement
includes all digits that
have been measured
exactly plus one digit
whose value has been
estimated.
 How many sig-figs ???
Significant Figures!
My phone is 4.75 inches
long!
3!!!!!
Precision
 This tells you how
exact your
measurement is.
4.7563 inches long
Precision, precision, precision.
Which is more precise?
 My phone is 4.75
inches long
 OR
 My phone is 4.7563
inches long
Yep, more math… almost done!!
(it’s worth it, trust me)
Graphs:
 A visual representation of your
data (easiest way to know what
your data is “saying”)
Origin
 Where the two axes meet
(where the graph starts)
 Origin
Horizontal Axis (x-axis)
 Think “Horizon” as in- what you
see when you watch the sunset!
 This axis should be labeled with
the manipulated variable.
Vertical Axis (y-axis)
 Think “the other one”
 This axis should be labeled with
the responding variable.
Coordinates
 A pair of numbers used to
determine the position of a
point on a graph
 This is used in locations on a
map as well (maps are just
like graphs!!)
Data Points
 The point where the
coordinates intersect (points of
data that are plotted on a graph)
What is it??
 A smooth line that reflects the
general pattern of a graph
Why is it useful??
 This allows you to see the
general trend of the data.
Linear Graph:
 The linear graph is a result of
the data points falling in a
straight line naturally on the
graph.
 This data is very predictable
Non-Linear Graph:
 Any graph who’s data points
don’t naturally land on a
straight line.
 This is most typical of graphs
Slope:
 The steepness of the graph line
 The slope of the line tells you
how much “y” changes for
every change in “x”
 To calculate the slope, use the
following equation:
Slope = Rise/Run
SawTooth= BAD!!!!!
 In science, we never have a broken graph (saw
tooth).
 This is how people make graphs look misleading!
 Most people will use a saw tooth because it makes
their graph look more interesting. This is why you
should NOT do that! If it’s a boring graph, it’s boring
for a reason and should reflect your boring data!!
 DON’T BE MISLEADING!!!
Let’sAnalyze Some Graphs!
•What Do you notice about these graphs?
•What’s good about them?
•What’s bad about them?
•What are they telling you?
Math in science
Math in science
Math in science
Math in science
Math in science
Math in science
Math in science

More Related Content

What's hot

What's hot (12)

Statistics
StatisticsStatistics
Statistics
 
Charts And Graphs
Charts And GraphsCharts And Graphs
Charts And Graphs
 
Types of Chart
Types of ChartTypes of Chart
Types of Chart
 
Interpreting charts and graphs
Interpreting charts and graphsInterpreting charts and graphs
Interpreting charts and graphs
 
Correlation Session
Correlation SessionCorrelation Session
Correlation Session
 
Charts and graphs
Charts and graphsCharts and graphs
Charts and graphs
 
Tutorial Sense News What Is Sense Chart
Tutorial   Sense News   What Is Sense ChartTutorial   Sense News   What Is Sense Chart
Tutorial Sense News What Is Sense Chart
 
Scale and scale factor
Scale and scale factorScale and scale factor
Scale and scale factor
 
Assesment in education
Assesment in educationAssesment in education
Assesment in education
 
Excel Lesson 15
Excel Lesson 15Excel Lesson 15
Excel Lesson 15
 
Excel-bar-graph
Excel-bar-graphExcel-bar-graph
Excel-bar-graph
 
12 ways to visalize data
12 ways to visalize data12 ways to visalize data
12 ways to visalize data
 

Similar to Math in science

Graphicalrepresntationofdatausingstatisticaltools2019_210902_105156.pdf
Graphicalrepresntationofdatausingstatisticaltools2019_210902_105156.pdfGraphicalrepresntationofdatausingstatisticaltools2019_210902_105156.pdf
Graphicalrepresntationofdatausingstatisticaltools2019_210902_105156.pdfHimakshi7
 
Analysing charts and graphics
Analysing charts and graphicsAnalysing charts and graphics
Analysing charts and graphicsŠkola Futura
 
Geographical Skills
Geographical SkillsGeographical Skills
Geographical Skillsclemaitre
 
Standard deviationnormal distributionshow
Standard deviationnormal distributionshowStandard deviationnormal distributionshow
Standard deviationnormal distributionshowBiologyIB
 
Lecture 2-PPT.pdf
Lecture 2-PPT.pdfLecture 2-PPT.pdf
Lecture 2-PPT.pdfRAJKAMAL282
 
Lecture 2-PPT statistics.pdf
Lecture 2-PPT statistics.pdfLecture 2-PPT statistics.pdf
Lecture 2-PPT statistics.pdfDrSJayashree
 
Data handling Presentation with solved examples
Data handling Presentation with solved examplesData handling Presentation with solved examples
Data handling Presentation with solved examplesrithikkapoor7
 
4-types-of-graphs.pptx
4-types-of-graphs.pptx4-types-of-graphs.pptx
4-types-of-graphs.pptxMJGamboa2
 
1-7 Presenting Data
1-7 Presenting Data1-7 Presenting Data
1-7 Presenting Datarkelch
 
Data Handling
Data Handling Data Handling
Data Handling 75193
 
Top 7 types of Statistics Graphs for Data Representation
Top 7 types of Statistics Graphs for Data RepresentationTop 7 types of Statistics Graphs for Data Representation
Top 7 types of Statistics Graphs for Data RepresentationStat Analytica
 
Chapter 4 Problem 31. For problem three in chapter four, a teac.docx
Chapter 4 Problem 31. For problem three in chapter four,   a teac.docxChapter 4 Problem 31. For problem three in chapter four,   a teac.docx
Chapter 4 Problem 31. For problem three in chapter four, a teac.docxrobertad6
 
Lecture 3 making data sets into tables and graphs
Lecture 3   making data sets into tables and graphsLecture 3   making data sets into tables and graphs
Lecture 3 making data sets into tables and graphsJason Edington
 
diagrammatic and graphical representation of data
 diagrammatic and graphical representation of data diagrammatic and graphical representation of data
diagrammatic and graphical representation of dataVarun Prem Varu
 

Similar to Math in science (20)

Graphing Notes
Graphing NotesGraphing Notes
Graphing Notes
 
Statistics for ess
Statistics for essStatistics for ess
Statistics for ess
 
Graphicalrepresntationofdatausingstatisticaltools2019_210902_105156.pdf
Graphicalrepresntationofdatausingstatisticaltools2019_210902_105156.pdfGraphicalrepresntationofdatausingstatisticaltools2019_210902_105156.pdf
Graphicalrepresntationofdatausingstatisticaltools2019_210902_105156.pdf
 
Analysing charts and graphics
Analysing charts and graphicsAnalysing charts and graphics
Analysing charts and graphics
 
Geographical Skills
Geographical SkillsGeographical Skills
Geographical Skills
 
Standard deviationnormal distributionshow
Standard deviationnormal distributionshowStandard deviationnormal distributionshow
Standard deviationnormal distributionshow
 
Lecture 2-PPT.pdf
Lecture 2-PPT.pdfLecture 2-PPT.pdf
Lecture 2-PPT.pdf
 
Lecture 2-PPT statistics.pdf
Lecture 2-PPT statistics.pdfLecture 2-PPT statistics.pdf
Lecture 2-PPT statistics.pdf
 
seminar.pptx
seminar.pptxseminar.pptx
seminar.pptx
 
Data handling
Data handlingData handling
Data handling
 
Data handling Presentation with solved examples
Data handling Presentation with solved examplesData handling Presentation with solved examples
Data handling Presentation with solved examples
 
4-types-of-graphs.pptx
4-types-of-graphs.pptx4-types-of-graphs.pptx
4-types-of-graphs.pptx
 
1-7 Presenting Data
1-7 Presenting Data1-7 Presenting Data
1-7 Presenting Data
 
Data Handling
Data Handling Data Handling
Data Handling
 
Top 7 types of Statistics Graphs for Data Representation
Top 7 types of Statistics Graphs for Data RepresentationTop 7 types of Statistics Graphs for Data Representation
Top 7 types of Statistics Graphs for Data Representation
 
Chapter 4 Problem 31. For problem three in chapter four, a teac.docx
Chapter 4 Problem 31. For problem three in chapter four,   a teac.docxChapter 4 Problem 31. For problem three in chapter four,   a teac.docx
Chapter 4 Problem 31. For problem three in chapter four, a teac.docx
 
merge ppt.pptx
merge ppt.pptxmerge ppt.pptx
merge ppt.pptx
 
Lecture 3 making data sets into tables and graphs
Lecture 3   making data sets into tables and graphsLecture 3   making data sets into tables and graphs
Lecture 3 making data sets into tables and graphs
 
diagrammatic and graphical representation of data
 diagrammatic and graphical representation of data diagrammatic and graphical representation of data
diagrammatic and graphical representation of data
 
Statistics and probability
Statistics and probabilityStatistics and probability
Statistics and probability
 

More from MrsKendall

Forces in fluids
Forces in fluidsForces in fluids
Forces in fluidsMrsKendall
 
Notes galaxies
Notes galaxiesNotes galaxies
Notes galaxiesMrsKendall
 
Notes nebula starlife
Notes nebula starlifeNotes nebula starlife
Notes nebula starlifeMrsKendall
 
Star Classification
Star ClassificationStar Classification
Star ClassificationMrsKendall
 
Asteroids, comets, meteors
Asteroids, comets, meteorsAsteroids, comets, meteors
Asteroids, comets, meteorsMrsKendall
 
Notes on our solar system
Notes on our solar systemNotes on our solar system
Notes on our solar systemMrsKendall
 
Sun, Earth, Moon System
Sun, Earth, Moon SystemSun, Earth, Moon System
Sun, Earth, Moon SystemMrsKendall
 
Notes revolution rotation
Notes revolution rotationNotes revolution rotation
Notes revolution rotationMrsKendall
 
CHONPS (basic o-chem intro)
CHONPS (basic o-chem intro)CHONPS (basic o-chem intro)
CHONPS (basic o-chem intro)MrsKendall
 
Balancing equations
Balancing equationsBalancing equations
Balancing equationsMrsKendall
 
Chemicall change
Chemicall changeChemicall change
Chemicall changeMrsKendall
 
Chemical reactions
Chemical reactionsChemical reactions
Chemical reactionsMrsKendall
 
Periodic table
Periodic tablePeriodic table
Periodic tableMrsKendall
 
Metallic bonds
Metallic bondsMetallic bonds
Metallic bondsMrsKendall
 

More from MrsKendall (20)

Forces in fluids
Forces in fluidsForces in fluids
Forces in fluids
 
Newtons laws
Newtons lawsNewtons laws
Newtons laws
 
Energy
EnergyEnergy
Energy
 
Motion etc
Motion etcMotion etc
Motion etc
 
Notes galaxies
Notes galaxiesNotes galaxies
Notes galaxies
 
Notes nebula starlife
Notes nebula starlifeNotes nebula starlife
Notes nebula starlife
 
Star Classification
Star ClassificationStar Classification
Star Classification
 
Asteroids, comets, meteors
Asteroids, comets, meteorsAsteroids, comets, meteors
Asteroids, comets, meteors
 
Keplers laws
Keplers lawsKeplers laws
Keplers laws
 
Keplers laws
Keplers lawsKeplers laws
Keplers laws
 
Notes on our solar system
Notes on our solar systemNotes on our solar system
Notes on our solar system
 
Sun, Earth, Moon System
Sun, Earth, Moon SystemSun, Earth, Moon System
Sun, Earth, Moon System
 
Notes revolution rotation
Notes revolution rotationNotes revolution rotation
Notes revolution rotation
 
CHONPS (basic o-chem intro)
CHONPS (basic o-chem intro)CHONPS (basic o-chem intro)
CHONPS (basic o-chem intro)
 
Acids bases
Acids basesAcids bases
Acids bases
 
Balancing equations
Balancing equationsBalancing equations
Balancing equations
 
Chemicall change
Chemicall changeChemicall change
Chemicall change
 
Chemical reactions
Chemical reactionsChemical reactions
Chemical reactions
 
Periodic table
Periodic tablePeriodic table
Periodic table
 
Metallic bonds
Metallic bondsMetallic bonds
Metallic bonds
 

Recently uploaded

CARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptxCARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptxGaneshChakor2
 
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher EducationIntroduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Educationpboyjonauth
 
Arihant handbook biology for class 11 .pdf
Arihant handbook biology for class 11 .pdfArihant handbook biology for class 11 .pdf
Arihant handbook biology for class 11 .pdfchloefrazer622
 
Paris 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activityParis 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activityGeoBlogs
 
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...Marc Dusseiller Dusjagr
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationnomboosow
 
Mastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory InspectionMastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory InspectionSafetyChain Software
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxheathfieldcps1
 
BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf
BASLIQ CURRENT LOOKBOOK  LOOKBOOK(1) (1).pdfBASLIQ CURRENT LOOKBOOK  LOOKBOOK(1) (1).pdf
BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdfSoniaTolstoy
 
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi  6.pdf1029-Danh muc Sach Giao Khoa khoi  6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdfQucHHunhnh
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfciinovamais
 
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Sapana Sha
 
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...RKavithamani
 
Employee wellbeing at the workplace.pptx
Employee wellbeing at the workplace.pptxEmployee wellbeing at the workplace.pptx
Employee wellbeing at the workplace.pptxNirmalaLoungPoorunde1
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)eniolaolutunde
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdfQucHHunhnh
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactPECB
 

Recently uploaded (20)

CARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptxCARE OF CHILD IN INCUBATOR..........pptx
CARE OF CHILD IN INCUBATOR..........pptx
 
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher EducationIntroduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Education
 
Mattingly "AI & Prompt Design: The Basics of Prompt Design"
Mattingly "AI & Prompt Design: The Basics of Prompt Design"Mattingly "AI & Prompt Design: The Basics of Prompt Design"
Mattingly "AI & Prompt Design: The Basics of Prompt Design"
 
Código Creativo y Arte de Software | Unidad 1
Código Creativo y Arte de Software | Unidad 1Código Creativo y Arte de Software | Unidad 1
Código Creativo y Arte de Software | Unidad 1
 
Arihant handbook biology for class 11 .pdf
Arihant handbook biology for class 11 .pdfArihant handbook biology for class 11 .pdf
Arihant handbook biology for class 11 .pdf
 
Paris 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activityParis 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activity
 
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communication
 
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
 
Mastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory InspectionMastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory Inspection
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptx
 
BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf
BASLIQ CURRENT LOOKBOOK  LOOKBOOK(1) (1).pdfBASLIQ CURRENT LOOKBOOK  LOOKBOOK(1) (1).pdf
BASLIQ CURRENT LOOKBOOK LOOKBOOK(1) (1).pdf
 
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi  6.pdf1029-Danh muc Sach Giao Khoa khoi  6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
 
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
 
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
Privatization and Disinvestment - Meaning, Objectives, Advantages and Disadva...
 
Employee wellbeing at the workplace.pptx
Employee wellbeing at the workplace.pptxEmployee wellbeing at the workplace.pptx
Employee wellbeing at the workplace.pptx
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
 

Math in science

  • 1. Yes, that’s right. I know we’re in science. You still need to do math. MATH AND GRAPHS IN SCIENCE
  • 2. Estimation  An approximation of a number based on reasonable assumptions.  Everyone take a guess!  Winner gets 2 tickets!!!! Estimation! (Theartof guessing!) How many marbles???
  • 3. Accuracy  How close a measurement is to the true or actual value. Accuracy All aimed for bulls eye: all in
  • 4. Reproducible  How close a group of measurements are to each other. Reproducibility This is also reproducible. What if the darts were in a corner?
  • 5. What is this??  Neither!!! Accurate? Reproducible?
  • 6. Sig-Figs:  This measurement includes all digits that have been measured exactly plus one digit whose value has been estimated.  How many sig-figs ??? Significant Figures! My phone is 4.75 inches long! 3!!!!!
  • 7. Precision  This tells you how exact your measurement is. 4.7563 inches long Precision, precision, precision. Which is more precise?  My phone is 4.75 inches long  OR  My phone is 4.7563 inches long
  • 8. Yep, more math… almost done!! (it’s worth it, trust me)
  • 9. Graphs:  A visual representation of your data (easiest way to know what your data is “saying”)
  • 10. Origin  Where the two axes meet (where the graph starts)  Origin
  • 11. Horizontal Axis (x-axis)  Think “Horizon” as in- what you see when you watch the sunset!  This axis should be labeled with the manipulated variable. Vertical Axis (y-axis)  Think “the other one”  This axis should be labeled with the responding variable.
  • 12. Coordinates  A pair of numbers used to determine the position of a point on a graph  This is used in locations on a map as well (maps are just like graphs!!) Data Points  The point where the coordinates intersect (points of data that are plotted on a graph)
  • 13. What is it??  A smooth line that reflects the general pattern of a graph Why is it useful??  This allows you to see the general trend of the data.
  • 14. Linear Graph:  The linear graph is a result of the data points falling in a straight line naturally on the graph.  This data is very predictable Non-Linear Graph:  Any graph who’s data points don’t naturally land on a straight line.  This is most typical of graphs
  • 15. Slope:  The steepness of the graph line  The slope of the line tells you how much “y” changes for every change in “x”  To calculate the slope, use the following equation: Slope = Rise/Run
  • 16. SawTooth= BAD!!!!!  In science, we never have a broken graph (saw tooth).  This is how people make graphs look misleading!  Most people will use a saw tooth because it makes their graph look more interesting. This is why you should NOT do that! If it’s a boring graph, it’s boring for a reason and should reflect your boring data!!  DON’T BE MISLEADING!!!
  • 17. Let’sAnalyze Some Graphs! •What Do you notice about these graphs? •What’s good about them? •What’s bad about them? •What are they telling you?