# Errors and Uncertainties in Measurement

Joe Mari Isabella Caringal, Rowena Chiang, Khrista Maria Evangelista, Berthrand Martin Fajardo

Department of Biological Sciences

College of Science, University of Santo Tomas

España, Manila, Philippines

Abstract

All measurements contain a certain degree of error. These errors may be categorized as either Random Error or Systematic Error. The source of random error is inherent and can only be minimized through conducting a series of same trials and using statistics. In contrast, systematic error has a known source and can be removed by following the exact procedure given in an experiment. In the experiment done, these errors were observed through the comparison the results of the measurement taken from a single metal sphere using three different measuring devices namely the foot rule, the Vernier caliper, and the micrometer caliper. The metal sphere was subjected to 10 trials for each measuring device. The diameter of the metal sphere was taken and the mean was obtained which are 1.84cm, 1.900cm, 1.8544cm, respectively. Also, the average deviation of the mean was obtained which are 0.016cm, 0.000cm and 0.0018cm, respectively. Given these values, the percentage of error of each device was computed and yielded 0.89%, 0%, 0.10%, respectively.

1. Introduction

All measurements of physical quantities are subjected to errors. Variability in the results of the repeated measurement arises because of the different factors that can affect the measurement result are impossible to hold constant [1]. Understanding these possible errors is an important issue in any experimental science. The conclusions drawn from the data, especially the strength of those conclusions will depend on how well the error is minimized and the uncertainty controlled. The first laboratory experiment deals exclusively with this important subject. The techniques studied here will be essential for the rest of the laboratory course. More specifically, this laboratory experiment aims to:

study errors and how they propagate in simple measurements

determine the average deviation of a set of experimental values

determine the mean if a set of experimental values as well as a set of average deviation of the mean

to familiarize the students with the Vernier caliper, micrometer caliper, and foot rule

to compare the accuracy of these measuring devices

to determine the density of an object given its mass and dimensions

2. Theory

Uncertainty is the notion of having doubts in the measurement you obtain from a given object using a measuring device. There are two degree of uncertainty, there are the accuracy which means the given variables are somewhat are near from the exact value while the precision have almost have the same measurement but far from the exact value. Also if there is uncertainty, error is evitable. Error is the deviation from standard or accepted value. There are two sources of error, One is systematic error which is very vital because we have different preferences and different accuracy in using a specific instrument we use for measurement. The other source which is a random error which is from as simple careless mistake of the one who is measuring the given object. In this experiment, we have to find the accurate weight of the object using measuring devices and instruments and a series of formulas and data we gathered from the set of experiments. Equations:

Mean Diameter :

M.D. = Σdiameter/n

Σdiameter= Summation of Deviation

n= Number of trial

Deviation:

d=|Reading-Mean Diameter|

Average Diameter:

a.d. = Σd/n

Σd= Summation Deviation

n= Number of trial

Average Deviation of the Mean:

A.D. = (a.d.)/√n

a.d. = Average Deviation

n= Number of trial

Volume:

V= 4/3 πr^3

Radius: r= (M.D.)/2

R3: Diameter

Density:

D = mass/volume

Percent Error:

(E-S)/S x 100

E= Experimental Value

S=...

References: Bauer RC, Birk JP & Marks PS. Introduction to chemistry (2nd ed.). McGraw Hill; 2007: 38. [1]

Cutnell JD & Johnson KW. Introduction to physics (9th ed.). John Wiley and Sons; 2013. [2]

Navaza DC & Valdes BJ. You and the natural world: Physics (3rd ed.). Phoenix Publishing House; 2004. [3]

http://www.columbia.edu/cu/physics/pdf-files/Lab_1-01.pdf

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