Experiment 1: Errors, Uncertainties, and Measurements Measurements Laboratory Report Daud Abraham jr, Dela Cruz Mariel, Dioso Clarenz Clare, Dionisio Karl Anthony
Department of Biology College of Sciences, Sciences , University of Santo Tomas Tomas España Street, Manila Philippines that remains constant or depends in a Abstract All measurements of quantities quantities that can assume a continuous range of values consist of two parts: the reported value itself and the uncertainty of the measurement. Measurements are subject to error which leads to the uncertainty of the result. Error does not only mean just outright mistakes. Gross errors sometimes happen and usually yield results that are sufficiently unepected. Accuracy is the goal we aim for in scientific measurements. 1. Introduction The purpose of measurement is to provide information aout a !uantity" !uantity" #o measurement is e$act" %hen a !uantity is measured, the result depends on the measuring system, the measurement procedure, the s&ill of the person, and the environment" Measurement uncertainty is a non'negat 'ne gative ive parame par ameter ter characteri(ing the dispersion of the values attriuted to a measured !uantity )%ester*" The uncertainty sho+s the incomplete &no+ledge of the !uantity" ll ll measurements are su-ected to uncertainty, uncertaint y, and a measured value is only complete if it is associated y a statement of the uncertainty given" The measuring system may provide measured values that are not far from the true value" There are t+o types of measurement error, systematic and random" systematic error is a component of error
specific manner on some other !uantity" .eadings +ill consistently e either too high or too lo+, thus, repeated trials +ill not reduce systematic error" /n the other hand, a random error is associated +ith the fact that +hen a measurement is repeated, it +ill provide a different value" 0t is random since the ne$t measured value cannot e predicted from the previous values" The effect of random error can e reduced through repeated e$perimental trials, since there is an e!ual proaility of them eing high or lo+ each time a reading is ta&en" Accuracy refers to ho+ closely the measured value of a !uantity corresponds tits true value" Precision e$presses the degree of reproduciility, or arrangement et+een repeated measurements" 0n this e$periment, the group should e ale to achieve the follo+ing o-ectives1 )2* to study errors and ho+ they propagatein simple e$periment, )3* to determine the average deviation of a set of e$perimentalvalues, )4* to determine the mean of a set of e$perimental values as +ell as set of average deviation of the mean, )5* to familiari(e the students +ith the vernier caliper, micrometer caliper, and foot rule, )6* to compare the accuracy of these measuring devices, )7* and to determine the density of an o-ect given its mass and dimensions"
2.Theory Where a.d. is the average deviation which is the sum of the deviations (d), and divided by number of observations(n) Where A.D. is the average deviation of the mean diameter which is a.d. divided by the square root of (n) Where Percent error is equivalent to average deviation divided by mean diameter 3.Methodology 0n the e$periment, the materials used +ere a metal all +ith a mass of 28"86g and a density of 9"87g, foot rule, vernier caliper, micrometer caliper and electronic gram alance" :irstly, the measuring devices +ere chec&ed from errors" ;east counts of every device +ere otained" 6 independent measurements of the diameter of the metal all for each measuring device +ere ta&en" fter +hich, the mean diameter for each measuring device and the deviation of each measurement from the mean +ere otained" #e$t, the average deviation, a"d", +as otained" %ith the recently computed average deviation, the average deviation, "D", of the mean diameter +as computed" Then, the percentage error +as otained" The volume of the metal all +as computed using the otained diameter and +ith the volume and the mass of the metal all, the density +as computed" The computed density +as compared +ith the given accepted density and the percentage error +as calculated" Measurements of the +idth of the thum of each memer +ere otained y measuring +ith a foot rule 4. Data and Analysis of Data it is noticed from the data that the micrometer caliper has the least
percentage error" This is ecause the least count of the micrometer caliper is less than the other t+o ma&ing the micrometer caliper
Aroup memer %idth of thum
Diameter of Sphere)cm* :oot =ernier Micrometer rule caliper caliper 2"6>c 2"79>cm 2"774cm m 2"7>c 2"776cm 2"774cm m 2"6>c 2"776cm 2"774cm m 2"7>c 2"776cm 2"774cm m 2"7>c 2"776cm 2"774cm m 2"7>c 2"777cm 2"774cm m >">5c >">3cm >">>>cm m >">3c >" >>>?c m >">>>c m m 3"2 3"532 3"5>8 28"86g 28"86g 28"86gm 8"?8g 9"987g 9"838g
9"87g
9"87g
9"87g
25"35 @
"?5@
"52@
2 2"4
3 2"4
4 2"2
5 2"3
5.Conclusion n error is the difference et+een a computed or measured value and a true or theoretically correct value" .andom error is al+ays present in measurement and it refers to the statistical
fluctuations in the measured data due to the precision limitations of the measurement device +hile systematic errors are caused y the imperfect caliration of measurement, 0nstruments or imperfect methods of oservation, or interference of the environment +ith the measurement process, and al+ays affect the results of an e$periment in a predictale direction" 6. Alications 2" mong the three measuring devices, the vernier caliper gave the least percent error" es, the accuracy of a measurement is affected y the least count and the least count also indicates the degree of accuracy of measurement that can e achieved y the measuring instrument" 3" n error is a deviation from accuracy or correctness" Errors are classified into t+o categories" :irst is the systematic error, +hich results due to faulty measurement practices" Second is the random error, +hich are caused y un&no+n and unpredictale changes in the e$periment" %e encountered systematic error due to personal iases" 4" There are different parts of the ody that can e used for measuring, such as the hands, feet, reast, +aist and almost all parts of it" Many of the systems of measurement, +hich had een in use, +ere to some e$tent ased on the dimensions of the human ody according to the proportions and as an effect units of measure could vary not only from location to location, ut from person to person .
!. "eferences 2 !ealing with error and uncertainty in measured values ".etrieved on #ovemer 36, 3>2> from http1+++"chem2"comacad+ete$t premm3"html 3 Melissinos and #apolitano" 3>>4" Eperiments in modern physics. cademic Press, US1 Elsevier Science" 4 Tso&os" "hysics for the Camridge1 University Press"
