Measurement and Uncertainty

No Measurement is exact,

measurement is a best estimate which has some degree of uncertainty.

We can only be certain of an amount when we count.

 

Here are some of the methods to determine the degree of uncertainty:

Absolute Uncertainty

Expressed in the units of measurement, not as a ratio.

Method 1: Make at least 3 measurements and calculate average.

                  The absolute uncertainty is the largest different between the average and lowest or

                  highest reasonable measurement. Discard the unreasonable data.

e.g. 5.9, 5.8, 5.9, 6.0, 6.5 <- the 6.5 here would be an unreasonable data that we don't need

now find the average: 5.9+5.8+5.9+6.0 = 23.6 -> 23.6 / 4 = 5.9

final answer: 5.9 ± 0.1 <- absolute uncertainty

Method 2: Determine uncertainty of instrument

                   Always measure to the best precision,

                   estimate to a fraction 0.1 of the smallest segment of the instrument scale

e.g. Smallest division: 1 cm, measure to 0.1 cm

Relative Uncertainty = Absolute Uncertainty ÷ Estimated Measurement x 100

a ± b  ->  b ÷ a x 100 = ___% relative uncertainty

Or use sig figs,

 number of sig figs indicates relative uncertainty

Here is a video to help understand this lesson better: