Types of Uncertainty
There are two basic kinds of uncertainties, systematic and random uncertainties. Systematic un-
certainties are those due to faults in the measuring instrument or in the techniques used in the
experiment. Here are some examples of systematic uncertainty:
⢠If you measure the length of a table with a steel tape which has a kink in it, you will obtain
a value which will appear to be too large by an amount equal to the loss in length resulting
from the kink. On the other hand, a calibration error in the steel tape itselfâ"an incorrect
spacing of the markingsâ"will produce a bias in one direction.
⢠If you measure the period if a pendulum with a clock that runs too fast, the apparent period
will be systematically too long.
⢠The stiï¬ness of many springs depends on their temperature. If you measure the stiï¬ness of
a spring many times, by compressing and decompressing it, the internal friction inside the
spring may cause it to warm. You may see this by a systematic trend in your data set; for
example, each data point in a data set will be smaller than the previous one.
Random uncertainties are associated with unpredictable variations in the experimental conditions
under which the experiment is being performed, or are due to a deï¬ciency in deï¬ning the quantity
being measured. Here are some examples of random uncertainty:
Changes in room temperature, electrical noise from nearby machinery, or imperfect connec-
tions to the voltmeter probes may cause random ï¬uctuations in the magnitude of a quantity
measured by a voltmeter
The length of a table may depend on which two points along the edge of the table the
measurement is made. The "lengthâ is imprecisely deï¬ned in such a case....
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...ken.
The standard deviation s deï¬ned by Eq. (2) provides the random uncertainty estimate for any one
of the measurements used to compute s. Intuitively we expect the mean value of the measurements
to have less random uncertainty than any one of the individual measurements. It can be shown
that the standard deviation of the mean value of a set of measurements Ïm, ("sigma-emâ) when all
measurements have equal statistical weight, is given by
Ïm =
sPN
i=1(xi â' x)2
N(N â' 1)
= s
â
N
.Note that Ïm is necessarily smaller than s. When we speak of the uncertainty Ï of a set of measure-
ments made under identical conditions, we mean that number Ïm and not s. It is most important
that the student distinguish properly between standard deviation associated with individual data
points, s, and standard deviation of the mean of a set of data points, Ïm.
The 2SD Rule, to use this rule, you start by estimating what the mean or average value is and what the standard deviation is. The 2SD Rule then gives you a way to translate those statistics into numbers people will relate to.
There are many errors that can occur when surveying a piece of land. When calculating measurements, it is very unlikely that any two measurements will ever be the same. There will most likely always be a degree of variance no matter how many different methods and types of equipment are used. In order to reduce the variance, the discrepancies need to be reduced in order to be as accurate
The data which was collected in Procedure A was able to produce a relatively straight line. Even though this did have few straying points, there was a positive correlation. This lab was able to support Newton’s Law of Heating and Cooling.
As well as prove the point that the standard deviation shows that the data was all close together.
The degrees of freedom (df) of an estimate is the number or function of sample size of information on which the estimate is based and are free to vary relating to the sample size (Jackson, 2012; Trochim & Donnelly, 2008).
A parameter is used in inferential statistics and is used to describe the scores of a population—letters of the Greek alphabet symbolizes a parameter. An estimate in statistics is a value, which was produced by the sample, and inferred to be the value of the
Briefly Describe One Important Tool that Can Be Used to Measure its Occurrence in a Population
This would become the calculated number of what our arm’s length in centimeters would be. Before I used the meter stick to actually figure out my arm’s correct length in centimeters, I assumed that the observed number would be very close, if not exact, to the expected. However, it was soon observed that this was not the case. My calculated number was smaller than my measured number by six digits. Fortunately, I was the biggest margin between the expected and observed numbers.
Another example of a systematic error that might have taken place during this experiment could have been that the room temperature water could have been in flux due to the fact that the temperature of the room may not have been constant and therefore the temperature of the room temperature water could have changed. This error could have been prevented by making sure that there were no occasional blasts of cold or warm air coming into the room that the experiment would be taking place
People are familiar with measuring things in the macroscopic world around them. Someone pulls out a tape measure and determines the length of a table. A state trooper aims his radar gun at a car and knows what direction the car is traveling, as well as how fast. They get the information they want and don't worry whether the measurement itself has changed what they were measuring. After all, what would be the sense in determining that a table is 80 cm long if the very act of measuring it changed its length!
The wire represents all 5 wires on a board. · Then draw up a table with 8 columns, as follows: WIRE diameter (mm) length (cm)
resolve problems. With the scientific method you have four steps to follow which include defining the
by the user. This setup usually consists of one or two instrumented gloves that measure
...inty between 1.0% (0.1/10.00*100) and 2.13% in the measured volume and 0.1/4.70*100). We also used a digital thermometer that allowed us to read the temperature readings from five degrees celcius to eighty degrees celcius. Since the digital thermometer have an absolute accuracy of plus or minus one degree celcius, it gives a percent uncertainty between 0.125 % (0.1 / 5.00 * 100) and 0.2 % (0.1/ 80.0 * 100). One of the difficulties we faced during the lab is reading the inverted graduated cylinder. To account for the inverse meniscus, we subtracted 0.2 mL from all the volumetric measurements to account for that. Volumetric uncertainty is the most important in determining the accuracy of this experiment since we are constantly checking for the volume throughout the lab. It also is the factor that gives the highest percent uncertainty out of all the instruments used.
whereβ the intercept 0 and β the slope 1 are unknown constants and ε is a random error component .