Hanin Athirah Harun

Please refer to the international standard on measurement uncertainty "Evaluation of Measurement Data - Guide to the Expression of Uncertainty in Measurement (GUM). It is available from https://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf

According to the GUM, any measurement result (an estimate of the measurand) should be presented with its uncertainty (in terms of standard uncertainty or expanded uncertainty).

+/- before each measurement is very unusual, full well knowing that all measurements are approximate to some degree. ± is common after.

Also common is to put the letters ca. (for the Latin circa ) if there is definite doubt about the value, e.g. "year is ca.1920".

A more compact notation to indicate some uncertainty is to use the tilde, e.g. the value of Pi is ~3.14.

In Statistics, Astronomy and Physics, we try to indicate our certainty or uncertainty by giving the low or high standard deviation sigma, e.g. 5.368 E10, sigma = 1.45.

Hanin Athirah Harun

Please refer to the international standard on measurement uncertainty "Evaluation of Measurement Data - Guide to the Expression of Uncertainty in Measurement (GUM). It is available from https://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf

According to the GUM, any measurement result (an estimate of the measurand) should be presented with its uncertainty (in terms of standard uncertainty or expanded uncertainty).

All data in this universe are relative and never exact (Heizenberg's uncertaintly principle). Average of repeated observations must be shown as variablity ( + & -) from the mean value. There are standard statistical methods to do it in scientific observations.

Following Hening Huang,

Yes, according to JCGM-100, the results should be represented by the expectation value (e.g. the average) and its uncertainty. However, it is recommended to use the +/- sign for the expanded uncertainty (the standard uncertainty multiplied by the appropriate coverage factor at certain confidence interval).

See also https://www.researchgate.net/post/Confidence_intervals_CIs_do_not_specify_measurement_uncertainty

In a good paper the errors of measured quantities have to be discussed. In principle and quantitatively. sometimes you need the average, some times you need a special function to describe your results. Without error bars you will never have a chance to Perform. +- is only one method to show uncertainties.

In any scientific report it is needed to show the dispersion of your measurand when a measurement is executed. +/- sign is used to show the range of variation and its concept is closer to the expanded uncertainty rather than the standard uncertainty. Study of GUM is highly recommended for this case, although some parts of it are a little vague.

So, It is a writer's choice -within GUM (JCGM 100:2008) context it is no needed-, but for all readers will be clearer if the sign +/- appears.

SIMPLE RULE: All models is an estimate. All estimates contained a range of error. Therefore, include upper bound (+) and lower bound (-).

Thanks for your valuable comments that I have received till now. I appreciate all the contributions.

Hello. I think there is a confussion since is needed to say what are referring to. I mean: the uncertainty u (or expanded uncertainty U) hasn't got two values ( +/- values), but only one. Thus, in this casi is needed to express the value WITHOUT +/-. i.e. U = 0,027 g (please read JCGM 100:2008 7.2.2 case 1)

The second case is when we are referring to the measurand and the dispersion of the quantity values being attributed to it (measurand). In this case there is no doubt that these dispersed values (that can be with a probability attributed to the measurand), are distributed to BOTH sides of the average value or result.

Thus, this case should be expressed as Mass = (25,013 +/- 0,027) g or Mass = 25,013 g +/- 0,027g. JCGM 100:2008 7.2.3 b) is clear: "state the result of the measurement as Y = y ± U and give the units of y and U;"

Greetings coleagues