TYPES OF UNCERTAINTIES

Uncertainties can be broadly classified into two categories.

1)   Uncertainties due to known causee systematic uncertainty

2)       Uncertainty due to known causes- Random uncertainty

 

Systematic uncertainty

They may arise due to various reasons. For example,(i) Incorrect design or calibration of the instrument gives certain uncertainty in the measurement. Limitations of the methods used for measurements causes this type of uncertainty. Lack of accuracy of the formula being used in the measurement, can also lead to this uncertainty. Usually the systematic uncertainty leads the measurement to consistently higher or consistently lower than the true value. In other words, systematic uncertainty is of the same sign( either +ve or –ve) and usually of the same size. Repeated observation will have no effect on this uncertainty. This uncertainty can be removed,

i)                 by careful design of the instrument and calibration with greater accuracy;

ii)                  by using improved methods of measurement.

RANDOM UNCERTAINTY

These uncertainties have no specific cause. They may arise due various factors. For example, carelessness of the observer, flexibility in the setting of apparatus, interference on the instrument from external physical factors like temperature, vibration, wind, moisture etc. These uncertainties have no set pattern and take place in a random manner, hence the name ‘random uncertainty’ or ‘random error’. A better experimenter can minimize these uncertainties but still they exist in the measurement to some extent. They can be reduced by taking a large number of observation and finding the average (arithmetic mean).This mean value can be supposed to be close to the ‘true’ value.

SIGNIFICANT FIGURE

Very often the uncertainty in the value of a quantity is not stated explicitly, specially when we are calculating (and not measuring). In those cases the uncertainty is indicated by the number of significant figures (meaningful digits). For example, the mass of a small marble is stated as 8.90 g. By writing it this way we mean that the first two digits are correct while the third digit is uncertain(but not incorrect). The uncertainty is about 0.01g. The rightmost or the doubtful digit is called the least significant digit and the leftmost digit is called the most significant digit. If we write the same value as 8.9g, the number of significant figures is two and the uncertainty is 0.1 g. The uncertainty in distance d=137 km is 1 km while the same uncertainty in d=137.0 km is about 100m