For more information, please see full course syllabus of General Chemistry

For more information, please see full course syllabus of General Chemistry

### Tools in Quantitative Chemistry

- Dimensional analysis is the use of conversion factors to convert between different units, including the standard SI units of measurement.
- Percent error is related to accuracy, while standard deviation is related to precision.
- Significant figures are related to precision, and must be considered when performing calculations.
- Significant figures are a relate to a measurement’s uncertainty.

### Tools in Quantitative Chemistry

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Lesson Overview
- Units of Measurement
- Percent Error
- Standard Deviation
- Standard Deviation cont'd
- Precisions vs. Accuracy
- Significant Figures and Uncertainty
- Identifying Significant Figures
- The Rules of Sig Figs Overview
- The Rules for Sig Figs: All Nonzero Digits Are Significant
- The Rules for Sig Figs: A Zero is Significant When It is In-Between Nonzero Digits
- The Rules for Sig Figs: A Zero is Significant When at the End of a Decimal Number
- The Rules for Sig Figs: A Zero is not significant When Starting a Decimal Number
- Using Sig Figs in Calculations
- Using Sig Figs for Multiplication and Division
- Using Sig Figs for Addition and Subtraction
- Using Sig Figs for Mixed Operations
- Dimensional Analysis
- Dimensional Analysis Overview
- General Format for Dimensional Analysis
- Example: How Many Miles are in 17 Laps?
- Example: How Many Grams are in 1.22 Pounds?
- Dimensional Analysis cont'd
- Dimensional Analysis cont'd
- Dimensional Analysis cont'd
- Summary
- Sample Problem 1: Dimensional Analysis

- Intro 0:00
- Lesson Overview 0:07
- Units of Measurement 1:23
- The International System of Units (SI): Mass, Length, and Volume
- Percent Error 2:17
- Percent Error
- Example: Calculate the Percent Error
- Standard Deviation 3:48
- Standard Deviation Formula
- Standard Deviation cont'd 4:42
- Example: Calculate Your Standard Deviation
- Precisions vs. Accuracy 6:25
- Precision
- Accuracy
- Significant Figures and Uncertainty 7:50
- Consider the Following (2) Rulers
- Consider the Following Graduated Cylinder
- Identifying Significant Figures 12:43
- The Rules of Sig Figs Overview
- The Rules for Sig Figs: All Nonzero Digits Are Significant
- The Rules for Sig Figs: A Zero is Significant When It is In-Between Nonzero Digits
- The Rules for Sig Figs: A Zero is Significant When at the End of a Decimal Number
- The Rules for Sig Figs: A Zero is not significant When Starting a Decimal Number
- Using Sig Figs in Calculations 15:03
- Using Sig Figs for Multiplication and Division
- Using Sig Figs for Addition and Subtraction
- Using Sig Figs for Mixed Operations
- Dimensional Analysis 16:20
- Dimensional Analysis Overview
- General Format for Dimensional Analysis
- Example: How Many Miles are in 17 Laps?
- Example: How Many Grams are in 1.22 Pounds?
- Dimensional Analysis cont'd 19:43
- Example: How Much is Spent on Diapers in One Week?
- Dimensional Analysis cont'd 21:03
- SI Prefixes
- Dimensional Analysis cont'd 22:03
- 500 mg → ? kg
- 34.1 cm → ? um
- Summary 25:11
- Sample Problem 1: Dimensional Analysis 26:09

### General Chemistry Online Course

I. Basic Concepts & Measurement of Chemistry | ||
---|---|---|

Basic Concepts of Chemistry | 16:26 | |

Tools in Quantitative Chemistry | 29:22 | |

II. Atoms, Molecules, and Ions | ||

Atoms, Molecules, and Ions | 52:18 | |

III. Chemical Reactions | ||

Chemical Reactions | 43:24 | |

Chemical Reactions II | 55:40 | |

IV. Stoichiometry | ||

Stoichiometry I | 42:10 | |

Stoichiometry II | 42:38 | |

V. Thermochemistry | ||

Energy & Chemical Reactions | 55:28 | |

VI. Quantum Theory of Atoms | ||

Structure of Atoms | 42:33 | |

VII. Electron Configurations and Periodicity | ||

Periodic Trends | 38:50 | |

VIII. Molecular Geometry & Bonding Theory | ||

Bonding & Molecular Structure | 52:39 | |

Advanced Bonding Theories | 1:11:41 | |

IX. Gases, Solids, & Liquids | ||

Gases | 35:06 | |

Intermolecular Forces & Liquids | 33:47 | |

The Chemistry of Solids | 25:13 | |

X. Solutions, Rates of Reaction, & Equilibrium | ||

Solutions & Their Behavior | 38:06 | |

Chemical Kinetics | 37:45 | |

Principles of Chemical Equilibrium | 34:09 | |

XI. Acids & Bases Chemistry | ||

Acid-Base Chemistry | 43:44 | |

Applications of Aqueous Equilibria | 55:26 | |

XII. Thermodynamics & Electrochemistry | ||

Entropy & Free Energy | 36:13 | |

Electrochemistry | 41:16 | |

XIII. Transition Elements & Coordination Compounds | ||

The Chemistry of The Transition Metals | 39:03 | |

XIV. Nuclear Chemistry | ||

Nuclear Chemistry | 16:39 |

### Transcription: Tools in Quantitative Chemistry

*Hi, welcome back to Educator.com.*0000

*Today's lesson in general chemistry is on the tools of quantitative chemistry.*0002

*We are going to get introduced into how chemists go ahead and make measurements*0010

*and the basic concepts and methods of performing everyday calculations.*0015

*Our first point in the lesson is going to be the SI units of measurement.*0023

*Once we become familiar with the units of measurement,*0027

*we will then get into explaining how exactly good or bad your measurement was.*0030

*This is done by something we call percent error and also standard deviation.*0039

*We will then get into a discussion of what we mean by precision versus accuracy.*0044

*We will then get into something a little more quantifiable which is called significant figures and uncertainty.*0048

*Followed by the following: identifying sig figs; then using these significant figures in calculations.*0054

*We will then get into a very important concept which is fundamental to all of the physical sciences.*0063

*This is called dimensional analysis which is your use of what we call conversion factors for problem solving.*0069

*Finally we will wrap up the lesson with a brief summary followed by some sample problems.*0078

*The SI units of measurement are what we call the international system of units.*0085

*They are included as part of the measuring system.*0090

*It is used in all parts of the world except the United States.*0093

*The basic SI unit for mass of course is going to be the kilogram.*0098

*For length, it is going to be the meter.*0106

*For volume, it is going to be the liter.*0109

*Kg again stands for kilogram; lowercase m is going to be abbreviating meter.*0114

*Finally capital L is going to be symbolized for liter.*0122

*Again mass is going to be kilogram; length is going to be meter; volume is going to be liter.*0128

*When you make a measurement, how good or poor is it?*0139

*How close was a measurement to an actual or already known value?*0143

*This is what we call percentage error.*0148

*Percentage error is equal to the actual value minus the experimental value divided by the actual value.*0150

*Actual value is the known value.*0158

*The experimental value is what you actually measure in an experiment; what you measured.*0163

*Of course we always like to get as close as possible to the actual.*0172

*To illustrate this very simple equation to use, suppose you weighed an object and recorded a mass of 86.2 grams.*0177

*The known value is 97.9 grams; calculate the percentage error.*0185

*Known value is going to be actual.*0189

*What you recorded, this is our experimental value.*0194

*The percent error... let's just plug everything into the equation.*0202

*It is going to be equal to the actual value 97.9 grams minus the experimental value of 86.2 grams.*0206

*Divided by the actual value which was 97.9 grams.*0216

*All of this is going be multiplied by 100 to get you your percentage error.*0222

*The next statistic that we can also calculate is something called standard deviation.*0229

*Sometimes when you repeat an experiment several times, it is useful to know how successful you were in reproducing your results.*0235

*If you did for example ten trials of the same measurement,*0243

*how well were you able to get the same measurement in each of the ten trials?*0248

*For our purposes we want of course the standard deviation to be as low as possible.*0255

*Standard deviation has the following equations.*0261

*It is equal to the square root of all of these terms where x is equal to basically each individual score.*0263

*X-bar is simply the average of all the x's.*0271

*N is the number of values or the number of trials.*0274

*Summation of course means we are going to add up across all the values.*0278

*Let's go ahead and illustrate the use of this equation.*0283

*It looks like a lot but it is really not too bad.*0287

*You weighed an object three separate times with masses of 32.6, 31.8, 34.1 milligrams.*0291

*Calculate your standard deviation.*0297

*All I am going to do is set it up for us right now.*0300

*The standard deviation is going to be equal the square root of everything underneath it; summation x minus x-bar.*0302

*X is each score; 32 minus 6, minus the average, squared.*0311

*I am going to put all of this in brackets showing that we are going to add what is next.*0321

*Plus, 31.8 minus x-bar, squared; then plus 34.1 minus x-bar, squared; then closed brackets.*0326

*That is what is meant by summation x minus x-bar, squared.*0349

*Then divided by n minus 1 where n is going to be equal to 3 trials.*0353

*All of that divided by 3 minus 1.*0358

*All we need then to finish this problem is x-bar.*0362

*X-bar is just your average of the three values.*0368

*That is just going to be 32.6 plus 31.8 plus 34.1.*0371

*All of that divided by 3, giving you your average score; that is standard deviation.*0377

*The next item is what we call precision and accuracy.*0385

*Precision simply represents how well you were able to reproduce your results over several trials.*0388

*High levels of precision tend to support accountability and reliability.*0394

*Precision is going to be quantifiable by standard deviation; measured by standard deviation.*0399

*Again you want as low a deviation as possible; low standard deviation desirable.*0410

*The word accuracy however represents how well you were able to measure a value*0422

*in relation to an already known or published value from the literature.*0427

*Of course this is going to be measured by percent error.*0431

*Once again we want as low a percentage error as possible; low percent error is also desirable.*0443

*A lot of people use the terms precision and accuracy interchangeably.*0454

*But of course as you have just seen they are not the same.*0457

*One represents your ability to reproduce a certain measurement.*0461

*The second represents how well you were able to get to a known value.*0466

*The next item is very important whenever you make measurements.*0473

*This is called significant figures and uncertainty.*0476

*Consider the following two rulers; let me go ahead and draw one ruler.*0480

*I am going to go ahead and draw a second ruler on the bottom.*0486

*Now the difference is going to be their tick marks; one, two, three.*0489

*Then the next one is going to be the following; one and two.*0495

*Let's go ahead and measure a piece of wood.*0510

*That is this length right here measured by green.*0514

*I am going to do the same thing with the other ruler; just like that.*0517

*How would you measure the green stick with the above ruler?*0529

*One person could say maybe 1.4 cm; or another person could say 1.5 cm.*0533

*It turns out that neither person is incorrect.*0541

*Why?--because the 1 is what we know for sure.*0545

*We know that green object is longer than 1 for sure; 1 cm.*0549

*Really this last digit here, the .4 and the .5, is really uncertain.*0554

*It is the digit of uncertainty.*0560

*The digit of uncertainty is strictly up to you the user; up to person making the measurement.*0566

*Because the ruler is so poor, the tick marks are so large,*0578

*there is no way we can determine if it is .4 or .5.*0584

*It is not provided by the tick marks on the ruler at all.*0587

*However when we go ahead and look at this ruler down here,*0593

*we finally get the tick marks that is representative of the appropriate digit.*0596

*So you hear, one person could say 1.4.*0601

*Because it looks like the green mark is right on the .4, one person could even say 1.40 cm.*0606

*The other person could say 1.41 cm; one could say 1.42cm.*0613

*Someone could even say it is a little less; 1.39 cm.*0619

*It turns out that because of the tick marks, we can go one digit more.*0623

*We can provide a better measurement; better measurement due to what we call a higher level of precision.*0629

*Again it is a better measurement due to higher level of precision.*0651

*The rule of thumb is the following.*0656

*How far or how many digits do you know how to record a measurement?*0658

*You are always going to go one digit past whatever is given to you or whatever the limit is on the ruler.*0663

*Go one digit past what is given by the ruler or instrument.*0671

*For example when we go ahead and read a graduated cylinder, you always want to look at the bottom of the curve.*0690

*You see how this water level is slightly curved.*0698

*That is what you call the meniscus.*0701

*You always want to look at the bottom of it.*0705

*What is provided to us here on this graduated cylinder?*0707

*50 milliliters is right here; 55 milliliters is right there.*0712

*We know that the meniscus is approximately 53 milliliters.*0726

*The graduated cylinder can tell us if it is 51, 52, or 53.*0735

*What the rule is is we are going to go one digit past this.*0741

*We can say something like 53.0; we can say something like 53.1.*0745

*We could even go under and say 52.9 milliliters or even 52.8 milliliters.*0750

*Once again you are going to one digit past the last digit of certainty provided by the instrument.*0757

*When you make a measurement, it is important to always write it down with the correct number of these significant figures.*0765

*What are their significant figures?--what are the rules for identifying them?*0774

*The rules for sig figs are the following; all nonzero digits are significant.*0779

*A zero is significant when it is in between nonzero digits.*0786

*A zero is significant when at the end of a decimal number.*0791

*A zero is not significant when starting a decimal number.*0795

*Let's go take a look at a couple examples; all nonzero digits are significant.*0799

*For example 562, we have a grand total of three sig figs because none of them are zeros.*0804

*A zero is significant when it is in between nonzero digits.*0810

*Something like 501; this is three sig figs.*0814

*The zero counts because it is in between nonzero digits.*0818

*5001; both zeros count because they are in between nonzero digits.*0822

*How about 50010?--only the two zeros count here because they are in between nonzero digits.*0829

*This last zero here does not count; we only have four sig figs here.*0837

*A zero is significant when at the end of a decimal number; for example 500. and 500.0.*0843

*It turns out that in 500. all of these are significant.*0853

*The zeros come at the end of a decimal number.*0858

*Here, 500.0, these are all significant because they come at the end of a decimal number.*0860

*A zero is not significant when starting a decimal number.*0870

*For example 0.00321, the two zeros do not count here because they start a decimal.*0873

*We only have three significant figures here.*0882

*However 0.003210, these do not count at all.*0884

*However you see the zero here, that comes at the end of a decimal number.*0891

*This definitely does count; we have a grand total of four significant figures.*0895

*When we use significant figures in calculations, we have to learn how to incorporate the rules now.*0906

*For multiplication and division, the answer will have the same number of sig figs as the fewest number of sig figs present.*0913

*For addition and subtraction, the answer will have the same number of decimal places as the fewest number of decimal places present.*0921

*For example. 0.321 times 0.57, we are going to get an answer that is only two sig figs.*0929

*Why?--because here in 0.321, you have three sig figs.*0941

*Here in 0.57, you have two sig figs.*0946

*When we do the addition and subtraction with the same numbers, 0.321 minus 0.57,*0949

*you see now we go by digits after the decimal places.*0956

*Here there is three digits after the decimal; here there is two.*0960

*Our answer is going to have two digits after the decimal.*0963

*Finally when you have mixed operations, you never want to round until the end.*0971

*You want to carry all digits through.*0976

*Now that we have talked about significant figures, let's go ahead and discuss what we mean by dimensional analysis.*0982

*Dimensional analysis utilizes the following.*0989

*It utilizes ratios of different units that we call conversion factors to convert from one unit to another.*0991

*If you want to go for example from unit A to unit B, how do we go ahead and do that?*0999

*The general format is the following; we are going to take unit A.*1007

*We are going to multiply by this ratio, something over something.*1011

*That is going to go ahead and give me unit B.*1015

*Unit A goes downstairs to get cancelled.*1018

*Unit B goes upstairs to get carried through to the final answer.*1022

*This ratio right here of unit B to unit A, that is what we call your conversion factor.*1027

*Let's go ahead and look at a couple of examples.*1038

*There are 4 laps in 1 mile; how many miles are in 17 laps?*1040

*We are going to say 17 laps times something over something.*1045

*That is going to give us our answer in units of miles which is what the question is asking for.*1050

*I start with laps; but I want to cancel it.*1056

*It is going to go downstairs to get cancelled.*1059

*Miles goes upstairs to get carried through to the final answer.*1061

*The conversion factor is actually given to us in the problem because they state that 4 laps is equal to 1 mile.*1065

*This is then 1 mile on top and 4 laps on the bottom.*1071

*We are going to get 4.25 miles for your answer.*1075

*This is going to round to 4.3 miles.*1081

*Let me tell you why: 17 laps, you have two sig figs.*1085

*However for conversion factors, we are assuming that a conversion factor are what we call exact numbers.*1090

*That is they have infinite precision.*1097

*They have infinite significant figures; there is no uncertainty.*1100

*You are going to ignore conversion factors for sig fig purposes.*1104

*Once again you are going to ignore conversion factors for sig fig purposes.*1113

*Let's go ahead and look at one last example here on dimensional analysis.*1121

*One pound is 454 grams; how many grams are in 1.22 pounds?*1125

*1.22 pounds times something over something is going to give us our answer in grams.*1131

*I want to cancel the pounds; that goes downstairs.*1141

*I want to keep grams; that is going to go upstairs.*1144

*You are told that 1 pound is 454 grams; 1 pound on the bottom and 454 grams on top.*1147

*That is going to give us an answer of 553.88 grams.*1155

*Here we have three sig figs; our answer is going to round to 554 grams.*1162

*That again, that is what we call dimensional analysis.*1170

*It is important to really master this because we are going to be using this incredibly heavily throughout all our lessons in general chemistry.*1173

*One last example then; suppose a diaper cost us 35 cents.*1185

*You have a newborn who goes through about 14 diapers a day.*1189

*How much is spent on diapers in one week?*1192

*Suppose you have a diaper costing 25 cents; that is actually a statement already.*1196

*We are told that 25 cents costs us each diaper; 25 cents per diaper.*1203

*We are trying to multiply through and cancel units.*1211

*The other item we see here that has diapers is 14 diapers a day; that is another ratio.*1214

*14 diapers goes upstairs to get cancelled; then 1 day on the bottom.*1220

*Finally I want to get my answer into week or dollars per week.*1226

*This is going to now be 7 days on top to get cancelled, divided by 1 week on the bottom.*1233

*When all is said and done, you are going to get an answer of*1241

*24 dollars and 50 cents per week to be spent on diapers.*1243

*As you can see, the reason why we are doing these examples*1250

*that are not chemistry yet is to show you that dimensional analysis*1253

*which we use in chemistry and the physical sciences can actually be very easily applied to everyday life.*1256

*The next type of dimensional analysis deals with unit conversion.*1266

*You have heard of terms like centi and milli and kilo before.*1271

*But how do you convert between the three?*1276

*We are going to learn that dimensional analysis is all behind this; converting between units.*1278

*You should ask your chemistry instructor which units you actually have to know.*1284

*But let me go ahead and just point out a few.*1288

*Mega is 10 ^{6}; kilo is 10^{3}; deci is 10^{-1}; centi is 10^{-2}.*1291

*Milli means 10 ^{-3}; micro is 10^{-6}; nano is 10^{-9}.*1301

*Once again please ask your instructor if you have to memorize any of these*1309

*if at all or if they are going to be given to you.*1313

*Now that we have been introduced to these prefixes and what they mean,*1317

*let's go ahead and see how we can use them in calculations.*1322

*For example, 500 milligrams is equal to how many kilograms?*1326

*What I always like to say is that sometimes it helps to convert to the base unit first.*1330

*What I mean by the base unit is that it has no prefixes.*1335

*In other words, let's get to the unit with no prefixes first.*1341

*First step is to go from milligrams to regular grams then onto kilograms.*1347

*This is going to be a two step process.*1355

*500 mg, just going to set it up, times something over something.*1358

*The first step is to get g; g goes upstairs; mg goes downstairs to get cancelled.*1364

*Once I am in g, now I can go to kg; times something over something.*1369

*That is going to give us our answer in units of kg.*1375

*You see that g is upstairs here; it is going to go downstairs to get cancelled.*1378

*Kg goes upstairs to get carried through to the final answer.*1383

*What numbers do we put in and where?--the rule is the following.*1388

*For the prefix multipliers like kilo and milli, you put the multiplier with the base unit; put multiplier with the base unit.*1393

*Once again you should put the multiplier with the base unit.*1409

*For milli, milli stands for 10 ^{-3}.*1414

*That is going to go with the base unit here; 10 ^{-3} on top; 1 on the bottom.*1419

*Kilo stands for 10 ^{3}; that is going to go with the base unit.*1424

*1 goes to kg; 10 ^{3} is going to go the g.*1428

*Once again you always put the multiplier with the base unit.*1433

*Then you get your answer in kilograms.*1441

*Let's go ahead and do a last one; this is centimeters to micrometers.*1443

*The first step is to go from centimeters to regular meters; then from regular meters on to micrometers.*1447

*34.1 centimeters times something over something is going to give me my answer in meters.*1457

*Cm goes downstairs to get cancelled.*1465

*M goes on top to get carried through to the final answer.*1467

*Once I am in meters, I can then go on and get micrometers; times something over something.*1471

*That is going to give me my answer in micrometers.*1476

*You see that m is on top; it has to go downstairs to get cancelled.*1479

*Then micrometers goes upstairs to get carried through to the final answer.*1483

*When we look up the prefix for centi, centi stands for 10 ^{-2}.*1488

*That goes with the prefix-less unit; 10 ^{-2} on top; 1 on the bottom.*1492

*When we look up the multiplier for micro, it is 10 ^{-6}.*1497

*That goes downstairs with meters; 1 on top.*1503

*That is going to get you your answer in units of micrometers.*1507

*To summarize, when you perform measurements, you want to gauge how well you are doing.*1514

*We can do this by percentage error calculation which again is going to tell us a little about your accuracy.*1519

*We can also calculate what is called the standard deviation.*1527

*That is going to tell us of how precise you were.*1531

*We also learned the concept of significant figures; significant figures is related to precision.*1535

*Finally we learned a very fundamental concept in all of the physical sciences which is dimensional analysis*1545

*which follows the same basic pattern where we can go from unit A to unit B using a conversion factor.*1551

*There is our summary; now let's go ahead and tackle some sample problems.*1567

*An intramuscular medication is given at a dosage of 5.00 milligrams per kilogram of body weight.*1571

*If you give 0.425 grams of medication to a patient, what is the patient's weight in pounds?*1584

*0.425 grams of medication is here.*1592

*Somehow we want to go from grams of medication to whatever the question is asking for which is pounds of body weight.*1597

*In addition we see in the first sentence that we have a statement here*1611

*that 5 milligrams of medication are given per kilogram of body weight.*1615

*That represents a very nice ratio.*1619

*5.00 mg of medication for every kilogram kg of body weight; that is our conversion factor.*1622

*This unit is 5 milligrams of medication; we are given 2.45 grams of medication.*1637

*We have to get the 0.425 grams of medication into milligrams first.*1643

*0.425 grams of medication times something over something is going to give us our answer in units of milligrams of medication.*1648

*Milligrams goes upstairs; g goes downstairs.*1659

*When we look up the prefix for milli, it is 10 ^{-3}.*1662

*That goes with the prefix-less unit on the bottom; then 1 on top.*1666

*That is going to give us milligrams of medication which is going to be 425.*1670

*We can then take the 425 milligrams of medication, multiply it by something over something.*1677

*That is going to give us our answer in kilograms of body weight.*1684

*Mg is going to go on the bottom; kg is going to go on top.*1698

*We know that from the sentence, it is 1 kg for every 5.00 mg.*1701

*Finally we can then take our kilogram of body weight and we can go to pounds of body weight.*1708

*We do that from the conversion factor where 1 kilogram is equal to approximately 2.20 pounds.*1717

*We are going to take kilograms of weight, multiply it by something over something.*1726

*That is going to give us our answer in pounds.*1732

*Pounds goes upstairs; kg goes downstairs; just 2.20 divided by 1.*1736

*When all is said and done, we should get an answer of 187 pounds using the correct number of sig figs.*1743

*That is our lesson from general chemistry on quantitative tools.*1752

*I want to thank you for your attention.*1758

*I will see you next time on Educator.com.*1760

1 answer

Last reply by: Peter Ke

Mon Sep 7, 2015 2:17 PM

Post by Peter Ke on September 7, 2015

At 4:43, why X= 32.6 and not 31.8 and 34.1?

2 answers

Last reply by: Debora Oppong

Fri Jan 29, 2016 1:19 AM

Post by Davon Shackleford on December 20, 2014

Would 5.0008 be four sig figs because the three zeros demonstrate the zero sandwiched between non-zero digit numbers?

5 answers

Last reply by: Denny Yang

Thu Jun 4, 2015 4:41 PM

Post by brandon oneal on June 19, 2014

You said the rule of thumb is to put the prefix multipliers with the base unit. I thought kg was the base unit for mass?

0 answers

Post by James Pelezo on March 24, 2013

Suggestions: a polite FYI...

Accuracy is the variation of data about an 'accepted' value and is quantified by %Error as indicated in your lecture. However, some scientist use the %Error relationship = [(Experimental - Accepted)/Accepted]100%. For a set of results, the %Error may calculate to be a 'negative' number indicating that the average is 'below' the accepted value, or if 'positive' the variation of data is 'above' the accepted value.

Tying Accuracy into Precision:

Precision is the variation of data about the 'average' of a set of measurements all obtained in the same way and is, as indicated, quantified by Standard Deviation. However, I would add that the 'utility' of STDV can be more than just trying to obtain a 'small' range value.

If one is trying to 'reproduce' a set of data points defined in a research paper or published academic experiment, the credibility of ones experimental methods can be confirmed if a given 'Accepted Value' (assuming there is one) is found to be within the bounds of the calculated STDV. Such results indicate that the experimental procedures were 'correctly' followed as defined by the author of the experiment.

If the Accepted Value is 'outside' of the bounds of the STDV, then the experimental results of the one reproducing the experiment would be questionable, or the research paper is flawed. Most academic experiments are well developed and typically have reliable 'Accepted Values'. Having the Accepted Value within the bounds of the STDV is a credible method of verifying ones experimental methods. Great lecture on this topic. Keep up the good work. :-)