# Part I of Fundamental Measurements: Uncertainties in addition to Error Propagation Simple Content 1. Systematic & R in addition to om Errors

## Part I of Fundamental Measurements: Uncertainties in addition to Error Propagation Simple Content 1. Systematic & R in addition to om Errors

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Simple Content 1. Systematic in addition to r in addition to om errors. 2. Determining r in addition to om errors. 3. What is the range of possible values 4. Relative in addition to Absolute Errors 5. Propagation of Errors, Basic Rules 1. Systematic & R in addition to om Errors No measurement made is ever exact. The accuracy (correctness) in addition to precision (number of significant figures) of a measurement are always limited: by the degree of refinement of the apparatus used, by the skill of the observer, in addition to by the basic physics in the experiment. In doing experiments we are trying to establish the best values as long as certain quantities, or to validate a theory. We must also give a range of possible true values based on our limited number of measurements. Why should repeated measurements of a single quantity give different values Mistakes on the part of the experimenter are possible, but we do not include these in our discussion. A careful researcher should not make mistakes! (Or at least she or he should recognize them in addition to correct the mistakes.)

Accuracy (correctness) & Precision (number of significant figures) Uncertainty, error, or deviation – the synonymous terms to represent the variation in measured data. Two types of errors are possible: 1. Systematic error: 2. R in addition to om errors Systematic Errors The result of A mis-calibrated device, or A measuring technique which always makes the measured value larger (or smaller) than the “true” value. Example: Using a steel ruler at liquid nitrogen temperature to measure the length of a rod. The ruler will contract at low temperatures in addition to there as long as e overestimate the true length. Careful design of an experiment will allow us to eliminate or to correct as long as systematic errors. R in addition to om Errors These remaining deviations will be classed as r in addition to om errors, in addition to can be dealt with in a statistical manner. This document does not teach statistics in any as long as mal sense. But it should help you to develop a working methodology as long as treating errors.

Average Example 1 Problem Find the average, in addition to average deviation as long as the 5 following data on the length of a pen, L. To get the average : sum the values in addition to divide by the number of measurements. To get the average deviation L, Find the absolute values of the deviations, L – Lave Sum the absolute deviations, Get the average absolute deviation by dividing by the number of measurements To get the st in addition to ard deviation Find the deviations in addition to square of them Sum the squares Divide by (N-1), (here it is 4) Take the square root. The pen has a length of (12.22 + 0.14) cm or (12.2 + 0.1) cm [use average deviations] Or (12.22 + 0.22) cm or (12.2 + 0.2) cm [use st in addition to ard deviations]. Average Example 2 Problem: Find the average in addition to the average deviation of the following measurements of a mass. This time there are N = 6 measurements, so as long as the st in addition to ard deviation we divide by (N-1) = 5. The mass is (4.342 + 0.022) g or (4.34 + 0.02) g [using average deviations] or (4.342 + 0.023) g or (4.34 + 0.02) g [using st in addition to ard deviations].

Built-in Functions in Excel use a spreadsheet such as Excel there are built-in functions that help you to find these quantities. To round the uncertainty to one or two significant figures (more on rounding in Section 7), in addition to To round the average to the same number of digits relative to the decimal point. Thus the average length with average deviation is either (15.47 ± 0.13) m or (15.5 ± 0.1) m. If we use st in addition to ard deviation we report the average length as (15.47±0.18) m or (15.5±0.2) m. Follow your instructor’s instructions on whether to use average or st in addition to ard deviation in your reports.