Home11.1 Uncertainties and errors in measurements and results

11.1 Uncertainties and errors in measurements and results

Qualitative & Quantitative Analysis

Analysis of data can be classified into two types

Qualitative Analysis

Comes from observations and non-numerical methods

Quantitative Analysis

Comes from measurements and always associated with uncertainties determined by either the apparatus and human limitations such as reaction times and sight

Uncertainties

In science, numerical data is divided into two types

Data with exact numbers (no uncertainty)

Data with inexact numbers (Degree of uncertainty involved)

Precision vs Accuracy

Precision: Closeness of agreement between interdependent test results

Accuracy: Closeness of agreement between the result of measurement and the true value

Significant Figures

Number of digits reflecting precision of a given measurement

Sometimes it is useful to write in Scientific notation

Here are some examples:

Some rules for significant figures in calculation

For multiplication or division: Result should be expressed based on measurement with smallest number of significant figures.

For addition or subtraction: Result should be expressed based on measurement with smallest number of decimal places

(A simple rule on the side is that your final answer should be expressed in the number of significant figures of the measurement with the lowest number of significant figures)

Experimental Error

Every measurement has a degree of uncertainty with it called experimental error

There are two types of experimental error

Systematic error: A flaw in experimental design or methodology. This affects the accuracy of the results.

Random error: Occur because of uncontrolled variables. Cannot be eliminated. This affects the precision of the results.

Absolute and Relative Uncertainty

Absolute Uncertainty is the margin of uncertainty associated with the result from a measurement.

Its symbol is given by ΔA

Relative Uncertainty is the ratio comparing the size of the absolute uncertainty.

Relative uncertainty = ΔA / A

All experimental results should be reported in form: