Misplaced Pages

#551448

75-489: An International Terrestrial Reference Frame ( ITRF ) is a realization of the ITRS. Its origin is at the center of mass of the whole earth including the oceans and atmosphere. New ITRF solutions are produced every few years, using the latest mathematical and surveying techniques to attempt to realize the ITRS as precisely as possible. Due to experimental error , any given ITRF will differ very slightly from any other realization of

150-755: A linear measurement model with X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} independent, a change in x i {\displaystyle x_{i}} equal to u ( x i ) {\displaystyle u(x_{i})} would give a change c i u ( x i ) {\displaystyle c_{i}u(x_{i})} in y . {\displaystyle y.} This statement would generally be approximate for measurement models Y = f ( X 1 , … , X N ) {\displaystyle Y=f(X_{1},\ldots ,X_{N})} . The relative magnitudes of

225-424: A mean . Drift is evident if a measurement of a constant quantity is repeated several times and the measurements drift one way during the experiment. If the next measurement is higher than the previous measurement as may occur if an instrument becomes warmer during the experiment then the measured quantity is variable and it is possible to detect a drift by checking the zero reading during the experiment as well as at

300-401: A measured value of a quantity and its unknown true value . Such errors are inherent in the measurement process; for example lengths measured with a ruler calibrated in whole centimeters will have a measurement error of several millimeters. The error or uncertainty of a measurement can be estimated, and is specified with the measurement as, for example, 32.3 ± 0.5 cm. (A mistake or blunder in

375-706: A spectrometer fitted with a diffraction grating may be checked by using it to measure the wavelength of the D-lines of the sodium electromagnetic spectrum which are at 600 nm and 589.6 nm. The measurements may be used to determine the number of lines per millimetre of the diffraction grating, which can then be used to measure the wavelength of any other spectral line. Constant systematic errors are very difficult to deal with as their effects are only observable if they can be removed. Such errors cannot be removed by repeating measurements or averaging large numbers of results. A common method to remove systematic error

450-438: A (different) rectangular, or uniform , probability distribution. Y {\displaystyle Y} has a symmetric trapezoidal probability distribution in this case. Once the input quantities X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} have been characterized by appropriate probability distributions, and the measurement model has been developed,

525-439: A ,  b ] is different from a rectangular or uniform probability distribution over the same range in that the latter suggests that the true value lies inside the right half of the range [( a  +  b )/2,  b ] with probability one half, and within any subinterval of [ a ,  b ] with probability equal to the width of the subinterval divided by b  −  a . The interval makes no such claims, except simply that

600-537: A mathematical interval might be a better model of uncertainty than a probability distribution. This may include situations involving periodic measurements, binned data values, censoring , detection limits , or plus-minus ranges of measurements where no particular probability distribution seems justified or where one cannot assume that the errors among individual measurements are completely independent. A more robust representation of measurement uncertainty in such cases can be fashioned from intervals. An interval [

675-537: A measurement model to define a measurand are known as input quantities in a measurement model. The model is often referred to as a functional relationship. The output quantity in a measurement model is the measurand. Formally, the output quantity, denoted by Y {\displaystyle Y} , about which information is required, is often related to input quantities, denoted by X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} , about which information

750-451: A measurement result and a product specification, to provide a simplified approach (relative to the GUM) to the evaluation of dimensional measurement uncertainty, to resolve disagreements over the magnitude of the measurement uncertainty statement, and to provide guidance on the risks involved in any product acceptance/rejection decision. The above discussion concerns the direct measurement of

825-425: A percentage) to the actual value of the measured quantity, or even to the value of a different quantity (the reading of a ruler can be affected by environmental temperature). When it is constant, it is simply due to incorrect zeroing of the instrument. When it is not constant, it can change its sign. For instance, if a thermometer is affected by a proportional systematic error equal to 2% of the actual temperature, and

SECTION 10

#1732772766552

900-514: A predictable direction. Incorrect zeroing of an instrument is an example of systematic error in instrumentation. The Performance Test Standard PTC 19.1-2005 "Test Uncertainty", published by the American Society of Mechanical Engineers (ASME), discusses systematic and random errors in considerable detail. In fact, it conceptualizes its basic uncertainty categories in these terms. Random error can be caused by unpredictable fluctuations in

975-407: A probability distribution to characterize each quantity of interest applies to the X i {\displaystyle X_{i}} and also to Y {\displaystyle Y} . In the latter case, the characterizing probability distribution for Y {\displaystyle Y} is determined by the measurement model together with the probability distributions for

1050-516: A quantity, which incidentally occurs rarely. For example, the bathroom scale may convert a measured extension of a spring into an estimate of the measurand, the mass of the person on the scale. The particular relationship between extension and mass is determined by the calibration of the scale. A measurement model converts a quantity value into the corresponding value of the measurand. There are many types of measurement in practice and therefore many models. A simple measurement model (for example for

1125-441: A scale, where the mass is proportional to the extension of the spring) might be sufficient for everyday domestic use. Alternatively, a more sophisticated model of a weighing, involving additional effects such as air buoyancy , is capable of delivering better results for industrial or scientific purposes. In general there are often several different quantities, for example temperature , humidity and displacement , that contribute to

1200-473: A smaller standard uncertainty associated with the estimate of Y {\displaystyle Y} . Knowledge about an input quantity X i {\displaystyle X_{i}} is inferred from repeated measured values ("Type A evaluation of uncertainty"), or scientific judgement or other information concerning the possible values of the quantity ("Type B evaluation of uncertainty"). In Type A evaluations of measurement uncertainty,

1275-575: A specified interval [ a , b {\displaystyle a,b} ]. In such a case, knowledge of the quantity can be characterized by a rectangular probability distribution with limits a {\displaystyle a} and b {\displaystyle b} . If different information were available, a probability distribution consistent with that information would be used. Sensitivity coefficients c 1 , … , c N {\displaystyle c_{1},\ldots ,c_{N}} describe how

1350-430: A specified probability is required. Such an interval, a coverage interval, can be deduced from the probability distribution for Y {\displaystyle Y} . The specified probability is known as the coverage probability. For a given coverage probability, there is more than one coverage interval. The probabilistically symmetric coverage interval is an interval for which the probabilities (summing to one minus

1425-419: Is the measurement uncertainty relative to the magnitude of a particular single choice for the value for the measured quantity, when this choice is nonzero. This particular single choice is usually called the measured value, which may be optimal in some well-defined sense (e.g., a mean , median , or mode ). Thus, the relative measurement uncertainty is the measurement uncertainty divided by the absolute value of

1500-425: Is a systematic reaction of the respondents to the method used to formulate the survey question. Thus, the exact formulation of a survey question is crucial, since it affects the level of measurement error. Different tools are available for the researchers to help them decide about this exact formulation of their questions, for instance estimating the quality of a question using MTMM experiments . This information about

1575-415: Is always present in a measurement. It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading. Random errors show up as different results for ostensibly the same repeated measurement. They can be estimated by comparing multiple measurements and reduced by averaging multiple measurements. Systematic error

SECTION 20

#1732772766552

1650-410: Is an example of systematic error in instrumentation. Systematic errors may also be present in the result of an estimate based upon a mathematical model or physical law . For instance, the estimated oscillation frequency of a pendulum will be systematically in error if slight movement of the support is not accounted for. Systematic errors can be either constant, or related (e.g. proportional or

1725-610: Is at most 0.001° and the ambient temperature at the time of measurement differs from that stipulated by at most 2 °C. As well as raw data representing measured values, there is another form of data that is frequently needed in a measurement model. Some such data relate to quantities representing physical constants , each of which is known imperfectly. Examples are material constants such as modulus of elasticity and specific heat . There are often other relevant data given in reference books, calibration certificates, etc., regarded as estimates of further quantities. The items required by

1800-427: Is attributed to such errors, they are "errors" in the sense in which that term is used in statistics ; see errors and residuals in statistics . Every time a measurement is repeated, slightly different results are obtained. The common statistical model used is that the error has two additive parts: Systematic error is sometimes called statistical bias . It may often be reduced with standardized procedures. Part of

1875-463: Is available, by a measurement model in the form of where f {\displaystyle f} is known as the measurement function. A general expression for a measurement model is It is taken that a procedure exists for calculating Y {\displaystyle Y} given X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} , and that Y {\displaystyle Y}

1950-563: Is changing in time (see dynamic models ), or is fundamentally probabilistic (as is the case in quantum mechanics — see Measurement in quantum mechanics ). Random error often occurs when instruments are pushed to the extremes of their operating limits. For example, it is common for digital balances to exhibit random error in their least significant digit. Three measurements of a single object might read something like 0.9111g, 0.9110g, and 0.9112g. Measurement errors can be divided into two components: random error and systematic error. Random error

2025-423: Is exact. When a quantity is measured, the outcome depends on the measuring system, the measurement procedure, the skill of the operator, the environment, and other effects. Even if the quantity were to be measured several times, in the same way and in the same circumstances, a different measured value would in general be obtained each time, assuming the measuring system has sufficient resolution to distinguish between

2100-406: Is known as attenuation bias . Measurement uncertainty In metrology , measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale . All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as

2175-410: Is known as the law of propagation of uncertainty. When the input quantities X i {\displaystyle X_{i}} contain dependencies, the above formula is augmented by terms containing covariances , which may increase or decrease u ( y ) {\displaystyle u(y)} . The main stages of uncertainty evaluation constitute formulation and calculation,

2250-423: Is known as the propagation of distributions, various approaches for which are available, including For any particular uncertainty evaluation problem, approach 1), 2) or 3) (or some other approach) is used, 1) being generally approximate, 2) exact, and 3) providing a solution with a numerical accuracy that can be controlled. When the measurement model is multivariate, that is, it has any number of output quantities,

2325-405: Is now aligned with ITRF2020, including PSD (post-seismic deformation), also called G2296. On the other hand GLONASS is using PZ-90.11, which is close to ITRF2008 at epoch 2011.0 and is using 2010.0 epoch (that means when you use reference transformation to PZ-90.11 you will get January 2010 date). Experimental error Observational error (or measurement error ) is the difference between

International Terrestrial Reference System and Frame - Misplaced Pages Continue

2400-402: Is predictable and typically constant or proportional to the true value. If the cause of the systematic error can be identified, then it usually can be eliminated. Systematic errors are caused by imperfect calibration of measurement instruments or imperfect methods of observation , or interference of the environment with the measurement process, and always affect the results of an experiment in

2475-441: Is represented in the solution for each station as a velocity vector. Previous ITRFs only continued the initial positions, using a motion model to fill in the velocity. 7910 8998 This version introduces extra parameters to describe the year-periodic motion of the stations: A (amplitude) and φ (phase) per-axis. This sort of seasonal variation has an amplitude of around 1 cm and is attributed to non-tidal loading effects (e.g.

2550-440: Is through calibration of the measurement instrument. The random or stochastic error in a measurement is the error that is random from one measurement to the next. Stochastic errors tend to be normally distributed when the stochastic error is the sum of many independent random errors because of the central limit theorem . Stochastic errors added to a regression equation account for the variation in Y that cannot be explained by

2625-528: Is uniquely defined by this equation. The true values of the input quantities X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} are unknown. In the GUM approach, X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} are characterized by probability distributions and treated mathematically as random variables . These distributions describe

2700-564: The X i {\displaystyle X_{i}} . The determination of the probability distribution for Y {\displaystyle Y} from this information is known as the propagation of distributions . The figure below depicts a measurement model Y = X 1 + X 2 {\displaystyle Y=X_{1}+X_{2}} in the case where X 1 {\displaystyle X_{1}} and X 2 {\displaystyle X_{2}} are each characterized by

2775-530: The i {\displaystyle i} th input quantity, consider a so-called standard uncertainty , given the symbol u ( x i ) {\displaystyle u(x_{i})} , defined as the standard deviation of the input quantity X i {\displaystyle X_{i}} . This standard uncertainty is said to be associated with the (corresponding) estimate x i {\displaystyle x_{i}} . The use of available knowledge to establish

2850-619: The Galileo Terrestrial Reference Frame ( GTRF ) is used for the Galileo navigation system; currently defined as ITRF2005 by the European Space Agency . The ITRF realizations developed from the ITRS since 1991 include the following versions: epoch 7903 8991 7904 8992 7905 8993 7906 8994 7907 8995 7908 8996 7909 8997 From this version onwards, the motion of the tectonic plate

2925-405: The environment which interfere with the measurement process and sometimes imperfect methods of observation can be either zero error or percentage error. If you consider an experimenter taking a reading of the time period of a pendulum swinging past a fiducial marker : If their stop-watch or timer starts with 1 second on the clock then all of their results will be off by 1 second (zero error). If

3000-403: The standard deviation . By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value. It is a non-negative parameter. The measurement uncertainty is often taken as the standard deviation of a state-of-knowledge probability distribution over the possible values that could be attributed to a measured quantity. Relative uncertainty

3075-568: The system . Systematic error may also refer to an error with a non-zero mean , the effect of which is not reduced when observations are averaged . For example, length measurements with a ruler accurately calibrated in whole centimeters will be subject to random error; a ruler incorrectly calibrated will also produce systematic error. Measurement errors can be summarized in terms of accuracy and precision . Measurement error should not be confused with measurement uncertainty . When either randomness or uncertainty modeled by probability theory

International Terrestrial Reference System and Frame - Misplaced Pages Continue

3150-626: The ITRF. The difference between the latest as of 2006 WGS 84 (frame realisation G1150) and the latest ITRF2000 is only a few centimeters and RMS difference of one centimeter per component. The ITRS and ITRF solutions are maintained by the International Earth Rotation and Reference Systems Service ( IERS ). Practical navigation systems are in general referenced to a specific ITRF solution, or to their own coordinate systems which are then referenced to an ITRF solution. For example,

3225-566: The above concepts can be extended. The output quantities are now described by a joint probability distribution, the coverage interval becomes a coverage region, the law of propagation of uncertainty has a natural generalization, and a calculation procedure that implements a multivariate Monte Carlo method is available. The most common view of measurement uncertainty uses random variables as mathematical models for uncertain quantities and simple probability distributions as sufficient for representing measurement uncertainties. In some situations, however,

3300-477: The accuracy of the measurement. If no pattern in a series of repeated measurements is evident, the presence of fixed systematic errors can only be found if the measurements are checked, either by measuring a known quantity or by comparing the readings with readings made using a different apparatus, known to be more accurate. For example, if you think of the timing of a pendulum using an accurate stopwatch several times you are given readings randomly distributed about

3375-462: The actual temperature is 200°, 0°, or −100°, the measured temperature will be 204° (systematic error = +4°), 0° (null systematic error) or −102° (systematic error = −2°), respectively. Thus the temperature will be overestimated when it will be above zero and underestimated when it will be below zero. Systematic errors which change during an experiment ( drift ) are easier to detect. Measurements indicate trends with time rather than varying randomly about

3450-537: The analysis of measurement data, and so on. The probability distributions characterizing X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} are chosen such that the estimates x 1 , … , x N {\displaystyle x_{1},\ldots ,x_{N}} , respectively, are the expectations of X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} . Moreover, for

3525-400: The assumption is often made that the distribution best describing an input quantity X {\displaystyle X} given repeated measured values of it (obtained independently) is a Gaussian distribution . X {\displaystyle X} then has expectation equal to the average measured value and standard deviation equal to the standard deviation of the average. When

3600-473: The competence of testing and calibration laboratories , which is required for international laboratory accreditation , and is employed in most modern national and international documentary standards on measurement methods and technology. See Joint Committee for Guides in Metrology . Measurement uncertainty has important economic consequences for calibration and measurement activities. In calibration reports,

3675-410: The coverage probability) of a value to the left and the right of the interval are equal. The shortest coverage interval is an interval for which the length is least over all coverage intervals having the same coverage probability. Prior knowledge about the true value of the output quantity Y {\displaystyle Y} can also be considered. For the domestic bathroom scale, the fact that

3750-405: The definition of the measurand, and that need to be measured. Correction terms should be included in the measurement model when the conditions of measurement are not exactly as stipulated. These terms correspond to systematic errors . Given an estimate of a correction term, the relevant quantity should be corrected by this estimate. There will be an uncertainty associated with the estimate, even if

3825-519: The effect of this offset would be inherently present in the average of the values. The "Guide to the Expression of Uncertainty in Measurement" (commonly known as the GUM) is the definitive document on this subject. The GUM has been adopted by all major National Measurement Institutes (NMIs) and by international laboratory accreditation standards such as ISO/IEC 17025 General requirements for

SECTION 50

#1732772766552

3900-426: The estimate y {\displaystyle y} of Y {\displaystyle Y} would be influenced by small changes in the estimates x 1 , … , x N {\displaystyle x_{1},\ldots ,x_{N}} of the input quantities X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} . For

3975-558: The estimate y {\displaystyle y} of the output quantity Y {\displaystyle Y} is not given by the sum of the | c i | u ( x i ) {\displaystyle |c_{i}|u(x_{i})} , but these terms combined in quadrature, namely by an expression that is generally approximate for measurement models Y = f ( X 1 , … , X N ) {\displaystyle Y=f(X_{1},\ldots ,X_{N})} : which

4050-419: The estimate is zero, as is often the case. Instances of systematic errors arise in height measurement, when the alignment of the measuring instrument is not perfectly vertical, and the ambient temperature is different from that prescribed. Neither the alignment of the instrument nor the ambient temperature is specified exactly, but information concerning these effects is available, for example the lack of alignment

4125-408: The experimenter repeats this experiment twenty times (starting at 1 second each time), then there will be a percentage error in the calculated average of their results; the final result will be slightly larger than the true period. Distance measured by radar will be systematically overestimated if the slight slowing down of the waves in air is not accounted for. Incorrect zeroing of an instrument

4200-685: The included X s. The term "observational error" is also sometimes used to refer to response errors and some other types of non-sampling error . In survey-type situations, these errors can be mistakes in the collection of data, including both the incorrect recording of a response and the correct recording of a respondent's inaccurate response. These sources of non-sampling error are discussed in Salant and Dillman (1994) and Bland and Altman (1996). These errors can be random or systematic. Random errors are caused by unintended mistakes by respondents, interviewers and/or coders. Systematic error can occur if there

4275-480: The latter consisting of propagation and summarizing. The formulation stage constitutes The calculation stage consists of propagating the probability distributions for the input quantities through the measurement model to obtain the probability distribution for the output quantity Y {\displaystyle Y} , and summarizing by using this distribution to obtain The propagation stage of uncertainty evaluation

4350-477: The learning process in the various sciences is learning how to use standard instruments and protocols so as to minimize systematic error. Random error (or random variation ) is due to factors that cannot or will not be controlled. One possible reason to forgo controlling for these random errors is that it may be too expensive to control them each time the experiment is conducted or the measurements are made. Other reasons may be that whatever we are trying to measure

4425-452: The magnitude of the uncertainty is often taken as an indication of the quality of the laboratory, and smaller uncertainty values generally are of higher value and of higher cost. The American Society of Mechanical Engineers (ASME) has produced a suite of standards addressing various aspects of measurement uncertainty. For example, ASME standards are used to address the role of measurement uncertainty when accepting or rejecting products based on

4500-496: The mean. Hopings systematic error is present if the stopwatch is checked against the ' speaking clock ' of the telephone system and found to be running slow or fast. Clearly, the pendulum timings need to be corrected according to how fast or slow the stopwatch was found to be running. Measuring instruments such as ammeters and voltmeters need to be checked periodically against known standards. Systematic errors can also be detected by measuring already known quantities. For example,

4575-411: The measured value, when the measured value is not zero. The purpose of measurement is to provide information about a quantity of interest – a measurand . Measurands on ratio or interval scales include the size of a cylindrical feature, the volume of a vessel, the potential difference between the terminals of a battery, or the mass concentration of lead in a flask of water. No measurement

SECTION 60

#1732772766552

4650-644: The measurement model Y = f ( X 1 , … , X N ) {\displaystyle Y=f(X_{1},\ldots ,X_{N})} , the sensitivity coefficient c i {\displaystyle c_{i}} equals the partial derivative of first order of f {\displaystyle f} with respect to X i {\displaystyle X_{i}} evaluated at X 1 = x 1 {\displaystyle X_{1}=x_{1}} , X 2 = x 2 {\displaystyle X_{2}=x_{2}} , etc. For

4725-489: The measurement process will give an incorrect value, rather than one subject to known measurement error.) Measurement errors can be divided into two components: random and systematic . Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to

4800-447: The person's mass is positive, and that it is the mass of a person, rather than that of a motor car, that is being measured, both constitute prior knowledge about the possible values of the measurand in this example. Such additional information can be used to provide a probability distribution for Y {\displaystyle Y} that can give a smaller standard deviation for Y {\displaystyle Y} and hence

4875-512: The probability distribution for the measurand Y {\displaystyle Y} is fully specified in terms of this information. In particular, the expectation of Y {\displaystyle Y} is used as the estimate of Y {\displaystyle Y} , and the standard deviation of Y {\displaystyle Y} as the standard uncertainty associated with this estimate. Often an interval containing Y {\displaystyle Y} with

4950-451: The quality can also be used in order to correct for measurement error . If the dependent variable in a regression is measured with error, regression analysis and associated hypothesis testing are unaffected, except that the R will be lower than it would be with perfect measurement. However, if one or more independent variables is measured with error, then the regression coefficients and standard hypothesis tests are invalid. This

5025-543: The readings of a measurement apparatus, or in the experimenter's interpretation of the instrumental reading; these fluctuations may be in part due to interference of the environment with the measurement process. The concept of random error is closely related to the concept of precision . The higher the precision of a measurement instrument, the smaller the variability ( standard deviation ) of the fluctuations in its readings. Sources of systematic error may be imperfect calibration of measurement instruments (zero error), changes in

5100-465: The relevant distributions, which are known as joint , apply to these quantities taken together. Consider estimates x 1 , … , x N {\displaystyle x_{1},\ldots ,x_{N}} , respectively, of the input quantities X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} , obtained from certificates and reports, manufacturers' specifications,

5175-422: The respective probabilities of their true values lying in different intervals, and are assigned based on available knowledge concerning X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} . Sometimes, some or all of X 1 , … , X N {\displaystyle X_{1},\ldots ,X_{N}} are interrelated and

5250-553: The shifting weight of water). 7911 8999 7912 9000 9989 9990 GNSS systems: National systems: The GPS reference epoch was moved from 2000.0 to 2001.0 in G1150 due to an Alaskan earthquake in November 2002. Still in 2022 ITRF2020 was released, yet GPS was only using G2139 in its antennas, which was aligned to ITRF2014 (IGb14) (though at epoch 2016.0, not reference epoch 2010.0). On 7 January 2024 move to IGS20 happened, so WGS 84

5325-431: The start of the experiment (indeed, the zero reading is a measurement of a constant quantity). If the zero reading is consistently above or below zero, a systematic error is present. If this cannot be eliminated, potentially by resetting the instrument immediately before the experiment then it needs to be allowed by subtracting its (possibly time-varying) value from the readings, and by taking it into account while assessing

5400-472: The terms | c i | u ( x i ) {\displaystyle |c_{i}|u(x_{i})} are useful in assessing the respective contributions from the input quantities to the standard uncertainty u ( y ) {\displaystyle u(y)} associated with y {\displaystyle y} . The standard uncertainty u ( y ) {\displaystyle u(y)} associated with

5475-418: The true value. However, this information would not generally be adequate. The measuring system may provide measured values that are not dispersed about the true value, but about some value offset from it. Take a domestic bathroom scale. Suppose it is not set to show zero when there is nobody on the scale, but to show some value offset from zero. Then, no matter how many times the person's mass were re-measured,

5550-442: The uncertainty is evaluated from a small number of measured values (regarded as instances of a quantity characterized by a Gaussian distribution), the corresponding distribution can be taken as a t -distribution . Other considerations apply when the measured values are not obtained independently. For a Type B evaluation of uncertainty, often the only available information is that X {\displaystyle X} lies in

5625-423: The values. The dispersion of the measured values would relate to how well the measurement is performed. If measured on a ratio or interval scale , their average would provide an estimate of the true value of the quantity that generally would be more reliable than an individual measured value. The dispersion and the number of measured values would provide information relating to the average value as an estimate of

#551448