The Ever-confusing Statistical Terms

The Ever-confusing Statistical Terms

To illustrate the different statistical terms we usually run into when we discuss data accuracy, let us consider the five error values (3-in., 2-in, 1-in., 5-in., and 4-in.) that were calculated on a population of data.

1. Mean (average) $=\frac{3+2+1+5+4}{5}=3.0$
2. Range = the distance between the largest error and the smallest error, i.e. Smallest = 1, Largest = 5 3)
3. Variance = measure of spread or dispersion around the mean. It is the mean square of all the errors $=\left({\left(3-3\right)}^2+{\left(2-3\right)}^2+{\left(1-3\right)}^2+{\left(5-3\right)}^2+{\left(4-3\right)}^2\right)\frac{1}{5-1}=\frac{0+1+4+4+1}{4}=\frac{10}{4}=2.5 inc{h}^2$
   Here, inch² is a meaningless unit and a better statistical term to use is the standard deviation.
4. Standard deviation, also called one-sigma, is the square root of the variance = $= \surd 2.5=1.581 inch \left(\text{is sample mean}\right)$
5. Root Mean Square Error (RMSE)
   • RMSE is not Standard deviation or sigma; they are different.
   • Root Mean Square Error (RMSE) is computed as follows:
     $RMSE=\surd \left(\Sigma {\left(Z–Z_i\right)}^2/n\right)$
     Where,
     Z = Measured Value from the data
     Z_i = Control Value (field surveyed)
     n = number of measurements