error analysis COMSATS, Summaries of Applied Mathematics

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COMSATS University, Islamabad

LAB REPORT

Lab Partners: - Affan, Irshad and Daniyal

Department: Computer Engineering FA21-BCE

Topic: Error Analysis

Introduction

All measurements have some degree of uncertainty that may come from a variety of sources. The process of evaluating this uncertainty associated with a measurement result is often called uncertainty analysis or error analysis. Error analysis may seem tedious; however, without proper error analysis, no valid scientific conclusions can be drawn. In fact, terrible things can happen if error analysis is ignored. The failure to specify the error for a given measurement can have dire consequences in science and in real life. Since there is no way to avoid error analysis, it is best to learn how to do it right. Error in a scientific measurement usually does not mean a mistake or blunder. Instead, the terms "error" and "uncertainty" both refer to unavoidable imprecision in measurements. The uncertainty of a single measurement is limited by the precision and accuracy of the measuring instrument, along with any other factors that might affect the ability of the experimenter to make the measurement. To determine the accuracy of a particular measurement, we must know the true value. Sometimes we have a "textbook" measured value that is known precisely, and we assume that this is our "ideal" value and use it to estimate the accuracy of our result. Other times we know a theoretical value that is calculated from basic principles, and this also may be taken as an "ideal" value. The main purpose of error analysis is to check whether the result of the experiment agrees with a theoretical fiction or results from other experiments or not. A measured result agrees with a theoretical prediction if the prediction lies within the range of experimental uncertainty.

Lab Procedure:

Take a set of a ruler or any length measuring instrument and measure the length,

width, and height of the table available at your workstation. Make sure that the

measurements are taken from various positions or angles if possible. Use these

measurements and work out the upper surface area of the table. Formulate a table

and conduct an error analysis to determine how far off the answer could be from its

actual value due to systematic, environmental, or human error. Work out Average

deviation, Standard Deviation and Standard error (Standard deviation of Mean)

Standard Deviation

Standard deviation of length Count, N= 15 Sum, Σx=2286.8, Mean, x̄=152. Variance= s^2 = 0.099809 s = 0. Standard deviation of width Standard deviation of height

Standard deviation of Area

Standard Error

Standard error of length = 0. standard error of width = 0. Standard error of height= 0. Standard error of area = 14.