True value : The value of a parameter with absolute certainty is termed as its true value.
Standard deviation : It is a measure of the spread or dispersion of a probability distribution. It reflects the degree of variation in measurement. With reference to Figure 7.1, standard deviation is given by
Normal or Gaussian Distribution : It is a type of distribution most frequently used in the statistical analysis of surveying measurements (Figure 5.1).
The statistical analysis of survey measurements has indicated that the survey measurements follow normal distribution or Gaussian distribution. The normal distribution is expressed by
Where
y = frequency of occurrence of residual
u = residual
s = standard deviation
e = base of the natural logarithm (e = 2.718)
Standard Error : Standard deviation is also known as standard error.
Probable Error : The range for the 50 percent uncertainty, the range of error between -0.6745 s and +0.6745 s is called probable error.
Fundamental Measurements : Measurements obtained through actual observation in the field are called fundamental measurements.
Error of Closure (linear or angular) : The amount (of distance / elevation / angle) by which a set of observed measurements fail to comply their geometric / actual / correct value is termed as error of closure.