Calculate The Average Value And The Average Random Error
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it. In doing this it is crucial to understand that all measurements of physical quantities are subject to uncertainties. It is never possible to measure anything exactly. It is good, of course, to make the error as small as how to calculate average value in excel 2010 possible but it is always there. And in order to draw valid conclusions the error
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must be indicated and dealt with properly. Take the measurement of a person's height as an example. Assuming that her height has been
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determined to be 5' 8", how accurate is our result? Well, the height of a person depends on how straight she stands, whether she just got up (most people are slightly taller when getting up from a long http://www.rit.edu/~w-uphysi/uncertainties/Uncertaintiespart1.html rest in horizontal position), whether she has her shoes on, and how long her hair is and how it is made up. These inaccuracies could all be called errors of definition. A quantity such as height is not exactly defined without specifying many other circumstances. Even if you could precisely specify the "circumstances," your result would still have an error associated with it. The scale you are using is of limited accuracy; when you read the scale, http://teacher.nsrl.rochester.edu/phy_labs/AppendixB/AppendixB.html you may have to estimate a fraction between the marks on the scale, etc. If the result of a measurement is to have meaning it cannot consist of the measured value alone. An indication of how accurate the result is must be included also. Indeed, typically more effort is required to determine the error or uncertainty in a measurement than to perform the measurement itself. Thus, the result of any physical measurement has two essential components: (1) A numerical value (in a specified system of units) giving the best estimate possible of the quantity measured, and (2) the degree of uncertainty associated with this estimated value. For example, a measurement of the width of a table would yield a result such as 95.3 +/- 0.1 cm. Significant Figures The significant figures of a (measured or calculated) quantity are the meaningful digits in it. There are conventions which you should learn and follow for how to express numbers so as to properly indicate their significant figures. Any digit that is not zero is significant. Thus 549 has three significant figures and 1.892 has four significant figures. Zeros between non zero digits are significant. Thus 4023 has four significant figures. Zeros to the left of the first non zero digit are not significant. Thus 0.000034 has only two significant figures. This is more easily seen if it is w
the empirical resources are exhausted need we pass on to the dreamy realm of speculation." -- Edwin Hubble, The Realm of the Nebulae http://www2.sjs.org/friedman/PhysAPC/Errors%20and%20Uncertainties.htm (1936) Uncertainty To physicists the terms "error" or "uncertainty" do not mean "mistake". Mistakes, such as incorrect calculations due to the improper use of a formula, can be and should be corrected. However, even mistake-free lab measurements have an inherent uncertainty or error. Consider the dartboards shown below, in which the 'grouping' of thrown darts is a proxy for our how to laboratory measurements. A 'precise' measurement means the darts are close together. An 'accurate' measurement means the darts hit close to the bullseye. Notice the combinations: Measurements are precise, just not very accurate Measurements are accurate, but not precise Measurements neither precise nor accurate Measurements both precise and accurate There are several different kinds and sources of error: Actual variations in the how to calculate quantity being measured, e.g. the diameter of a cylindrically shaped object may actually be different in different places. The remedy for this situation is to find the average diameter by taking a number of measurements at a number of different places. Then the scatter within your measurements gives an estimate of the reliability of the average diameter you report. Note that we usually assume that our measured values lie on both sides of the 'true' value, so that averaging our measurements gets us closer to the 'truth'. Another approach, especially suited to the measurement of small quantities, is sometimes called 'stacking.' Measure the mass of a feather by massing a lot of feathers and dividing the total mass by their number. Systematic errors in the measuring device used. Suppose your sensor reports values that are consistently shifted from the expected value; averaging a large number of readings is no help for this problem. To eliminate (or at least reduce) such errors, we calibrate the measuring instrument by comparing its measurement against the value of a known standard. It is some