In this lab, the density of 20 glass beads were determined using two different methods and the results were compared to see how close the values were to each other. In first method the volume of each individual bead was measured using the diameter of each bead, along with the mass. In the second method the beads we treated as a whole unit. The total mass was measured and volume was measured based on the amount of water that was displaced in a graduated cylinder. Then, the beads were swapped with 20 different glass beads of the same type. The procedure was repeated and the results were compared to the data of the first bead set to look for any systematic errors that may have occurred. During the experiment, the data was used to see whether the diameter, mass, and density were constant between the individual beads. However, the main goal of the experiment was to answer the question of whether or not individual density average agreed with the bulk density.

Analysis
Through error analysis, the data found was used to determine if the calculated densities were the same when comparing twenty individual beads versus the entire set of twenty beads treated as one unit. For the first data set, the average diameter is 1.42 cm. The average mass is 3.90 g. The average density is 2.62 g/cm3. The average variation of the diameter is 0.04 cm. This amount shows how much the beads varied in diameter. The average variation of the mass is 0.28 g, which shows how much the mass of the beads varied from one another. The average variation between the densities of the individual beads is 0.06 g/cm3. The average percent variation of the diameter is 2.8%. The average percent variation of the mass is 7.2%. The average percent variation of the density is 2.4%. The uncertainty for the diameter in the first data set is 0.005cm and the percent uncertainty is 0.37%. The uncertainty of the mass is 0.005g and the percent uncertainty is 0.15%. Since the percent of...

...Basic Concepts of ErrorAnalysis
1. Significant Figures:
The laboratory usually involves measurements of several physical quantities
such as length, mass, time, voltage and current. The values of these quantities
should be presented in terms of Significant Figures as follows.
For example, the location of the arrow is to be determined in Fig. 1. It is
obvious that the location is between 1 cm and 2 cm. The correct way to express
this location is to make one more estimate based on your intuition. That is, in
this case, a reading of 1.3 cm is estimated. This measurement is said to contain
two significant figures. Note that there should only be one estimated place in
any measurement. So, in the example shown in Fig. 1 do not try to locate the
position of the arrow as 1.35 cm.
If data are to contain, say, three significant figures, two must be known, and the
third estimated.
1
2
3
4
5
cm
Figure 1.
The following rules dictate the handling of significant figures:
(a) Specify the measured value to the same accuracy as the error in the
measurement. For example, we report that a physical quantity is x =
3. 45 ± 0. 05 , not 3. 4 ± 0. 05 and not 3. 452 ± 0. 05 ; in other words, the least
significant figures in both numbers (the main value and the error) are on the
same decimal position;
(b) When adding or subtracting numbers, the answer is only good to the
least accurate number...

...ErrorAnalysisLab
By: Lab Team 5
Introduction and Background: In the process of learning about the importance of measurement and data processing, lab teams were given prompts to design experiments as well as address the precision, accuracy, and erroranalysis within the experiment. Lab teams collaborated their data to find similarities and differences within their measurements. Through this process, students learned the importance of the amount of uncertainty as well as the different types of experimental errors that might have caused a margin of difference within the lab teams results.
Measurement and data processing is a topic discussed in IB Chemistry SL; it is important within the scientific community as it discusses the reliability of the data presented. Uncertainty is used to determine a range of a value in a measurement or instrument. Uncertainty of an analogue instrument is plus or minus half of the smallest division present; while uncertainty of a digital scale is plus or minus the smallest division present. To identify the amount of uncertainty, significant figures (the digits in measurement up to and including the first uncertain digit) are used. Certain rules are used to discover the number of significant figures in a value:
* 1-9 are always significant
* included zeroes (1009= 4 significant...

...these deviations should probably be called uncertainty analysis, but for historical reasons is referred to as erroranalysis. This document contains brief discussions about how errors are reported, the kinds of errors that can occur, how to estimate random errors, and how to carry error estimates into calculated results. We are not, and will not be, concerned with the “percenterror” exercises common in high school, where the student is content with calculating the deviation from some allegedly authoritative number.
Significant figures
Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m. To record this measurement as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many significant figures as are consistent with the estimated error. The quantity 0.428 m is said to have three significant figures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement in centimeters would be 42.8 cm and still be a three significant figure number. The accepted convention is that...

...Experimental Errors and Uncertainty
No physical quantity can be measured with perfect certainty; there are always errors in any measurement. This means that if we measure some quantity and, then, repeat the measurement, we will almost certainly measure a different value the second time. How, then, can we know the “true” value of a physical quantity? The short answer is that we can’t. However, as we take greater care in our measurements and apply ever more refined experimental methods, we can reduce the errors and, thereby, gain greater confidence that our measurements approximate ever more closely the true value. “Erroranalysis” is the study of uncertainties in physical measurements, and a complete description of erroranalysis would require much more time and space than we have in this course. However, by taking the time to learn some basic principles of erroranalysis, we can: 1) Understand how to measure experimental error, 2) Understand the types and sources of experimental errors, 3) Clearly and correctly report measurements and the uncertainties in those measurements, and 4) Design experimental methods and techniques and improve our measurement skills to reduce experimental errors. Two excellent references on erroranalysis are: • • John R. Taylor, An Introduction to...

...5.3. Data Analysis
The errors committed by both groups of participants are classified in this study as follows:
1. Categories:
a. Omission errors, which is omitting some required elements.
b. Addition errors, which is adding unnecessary elements.
c. Selection errors, which is selecting incorrect elements.
2. Subcategories:
a. Morphological errors.
b. Syntacticalerrors.
The total number of errors, found in the writings of both groups L2 and L5, in all categories was: 74 errors. The classification of those errors was according to their categories and subcategories.
Regarding omission errors, there were 33 errors in both morphological and syntactical omissions. As for morphological omission errors, there were 14 errors. Syntactical omission errors, on the other hand, were about 19 errors.
With respect to addition errors, 19 errors were committed by the participants in this category, 7 of them were morphological and 12 were syntactical.
Concerning the third category which is selection errors, there were 24 errors. 6 errors were morphological and the other 18 were syntactical. Figure 1 shows the number of...

...ERRORS IN MEASUREMENT
Errors in Measurement
Structure
2.1
Introduction
Objectives
2.2
Classification of Errors
2.2.1
Gross Errors
2.2.2
Systematic Errors
2.2.3
Random Errors
2.3
Accuracy and Precision
2.4
Calibration of the Instrument
2.5
Analysis of the Errors
2.5.1
ErrorAnalysis on Common Sense Basis
2.5.2
Statistical Analysis of Experimental Data
2.6
Summary
2.7
Key Words
2.8
Answers to SAQs
2.1 INTRODUCTION
The measurement of a quantity is based on some International fundamental standards.
These fundamental standards are perfectly accurate, while others are derived from these.
These derived standards are not perfectly accurate in spite of all precautions. In general,
measurement of any quantity is done by comparing with derived standards which
themselves are not perfectly accurate. So, the error in the measurement is not only due to
error in methods but also due to standards (derived) not being perfectly accurate. Thus,
the measurement with 100% accuracy is not possible with any method.
Error in the measurement of a physical quantity is its deviation from actual value. If an
experimenter knew the error, he or she would correct it and it would no longer be an...

...LabAnalysis Questions
1. What are the important ions for most neurons when considering changes in membrane potential? (3 points)
2. What is the resting membrane potential? (3 points)
3. What does it mean that the voltage just inside the membrane is negative? (4 points)
Neurophysiology of Nerve Impulses Activity 2: Receptor Potential (20 points total)
Notes:
• After reading the Overview and Introduction, Click on Experiment.
• Follow the directions on the left side of the menu to complete the lab. Use the data chart to answer the following questions. You do not have to submit your lab to be recorded.
4. LabAnalysis Questions (5 points each)
1. Pacinian corpuscles only respond to changes in:
2. Which sensory receptor responds to more than one stimulus? What were the different stimuli?
3. Which intensity of which modality created the greatest amplitude of response? Why?
Connections to Human Physiology
1. Considering what you learned about sensory receptors, what do you think would be most damaging to an individual: being born without olfactory receptors, pacinian corpuscles or free nerve endings in the hands or feet? Explain your answer.
Neurophysiology of Nerve Impulses Activity 8: Chemical Synaptic Transmission and Neurotransmitter Release (20 points total)
Notes:
• After reading the Overview and Introduction, Click on...

...and volume of the air bubble, along with the pressure in the air bubble which is equal to the pressure in the room of the can be used with the ideal gas law to find .
ErrorAnalysis
The standard deviation of the slope of the best fit line was 116.83 of the -4747.76 slope value. The standard deviation of the y-intercept was 0.3458 of the 12.716 y-intercept value. The standard deviation the ΔHvap(water) was 0.9714 of the 39.475 ΔHvap(water) value. The percent deviation of the ΔHvap(water) from the reported literature value of 40.66kJ/mol was 4.0826%.
The 10ml graduated cylinder used had an uncertainty of +/-0.1ml. In the original measurement of water in the graduated cylinder of 8.75ml there would be a 1.14% uncertainty. The yellow digital thermometer had an uncertainty of +/-0.1 degrees Celsius. The thermometer is taking temperatures from 79.5 degrees Celsius to 3.1 degrees Celsius so the percent uncertainty would be anywhere from 0.126% to 3.23%.
In this experiment there were minimal experimental errors and uncertainties. Small errors and uncertainties like the 10 ml graduated cylinder not being flat on the bottom of the 1000ml beaker, leads to a slight misread of the volume but this is such a minimal error that the results would not be too skewed because of it.
The largest sources of error come from the standard deviation for the slope, y-intercept, and ΔHvap(water). Also...