Measurement and Uncertainty

Hello

We are going to cover measurement and different types of uncertainty.

There are some rules that you need to know regarding Measurement and Uncertainty

• no measurement is exact
• every measurement is a best estimate which has some degree of uncertainty
• only when we count a set of objects, we get an exact number

Absolute Uncertainty

This is expressed in units of measurement; not ratio

In order to express uncertainty:

• Make at least 3 measurements
• Calculate average
• Absolute uncertainty is the largest difference between the average and lowest or highest reasonable measurement
• Discard unreasonable data

Eg.1  47cm, 48cm, 45cm, 46cm
          
Calculate the average of these numbers ((47+48+45+46)/4)) = 46.5

Then calculate the difference 46.5- 45 = 1.5 or 48 - 46.5 = 1.5 (does not matter because the result is the same)

Therefore + 1.50cm is the absolute uncertainty.

Absolute uncertainty:

This is determined by uncertainty of each instrument

• Always measure to the best precision
• Estimate to 1/10 or 0.1 of the smallest segment of the instrument scale

Eg.
Take a ruler

The smallest scale is 0.1cm
0.1 of the scale is 0.01 cm
Therefore the absolute uncertainty is 0.01cm

This is how you express it: (the average value) + (absolute uncertainty)

 Eg. 15.6 + 0.03cm

Don't forget the units.

Relative Uncertainty

Relative Uncertainty is absolute uncertainty/estimated measurement
It is expressed in percent or significant figures(the number of significant figures indicates relative uncertainty; the last digit is uncertain)

Written by JK (Oct 31,2010)